>>16173665
Would be kinda of cool if they came up a shit load of irrefutable evidence and mathematical proofs to support this idea. Then we could all sit back and relax and say "Well fuck, that's it then."

>>16173665
No. Infinity is an affront to God. We of the ONE TRUE FINITE FAITH have suffered for years under the tyranny of those GOD CURSED INFINITY LOVING SODOMITES. Our time has come to rise up enmasse and put them to the sword.

>>16173665
>Is the universe infinite?
No one knows anon.

>>16173674
>kinda cool
or
>kind of cool
but not
>kinda of cool
:)

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>>16173679
Jesus wouldn't want that.
Love does not delight in evil, but it doesn't murder evil in cold blood either.

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>>16173674
>>16173995
Honestly it's very easy to prove that the universe isn't infinite. Finitism is true and nothing can be actually infinite. Quick, easy, and simple proof here: https://www.youtube.com/shorts/W4_OXMCswKU

"Infinity" is a self-contradictory concept and hence always brings logical contradictions with it

>>16173997
Holy fuck people like you are stupid.
The point of language is to communicate ideas. You've missed the point entirely and probably your entire life you've been doing this.
Learning nothing, minding inane details that don't fit your fancies.

You don't have a woman guaranteed.

>>16173665
The observable universe is finite. The observer being part of the finite observable universe has no business asking wether there is an infinite continuation beyond the limit of observability. It can not be observed and it has no influence on the observer. It's effectively not there. The universe is finite. Sometimes something can be seen slipping over the edge. For all intents and purpose the object is gone thereafter.

>>16173665
No, because that doesn't make any sense.

>>16173665
Funny to think, that if universe is infinite, at some level we are parts of some kind of thinking creature. And he is part of some even greater creature and it goes on forever.

>>16174087
Until somebody discovers FTL travel.

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>I'M GOONNAA FLY THROUGH SPACE AT THE SPEDE OF LYGHT IN MUH SPACE SHIP WITH FRIENDLY ROBOTS AND WE'LL TIME TRAVEL THROUGH BLACK HOLES AND TELEPORT TO THE MULTIVERSE JUST LIKE IN MUH STAR TREK MOOOOVIES
>WE'LL HAVE LASER SWORDS AN SHEEIIIIIITTT TOO OMG I'M GOING TO CUM JUST THINGING ABOUT IT I FUCKING LOVE SCIENCE SO MUCH!!!!

>>16174081
Finitism is a philosophical position within the philosophy of mathematics that rejects the existence of actual infinite mathematical objects or processes. Instead, finitists argue that mathematics should only deal with finite entities and operations that can be completed in a finite number of steps.

Whether finitism is "true" depends on one's philosophical stance and interpretation of mathematics. Finitism is one of several philosophical positions regarding the foundations of mathematics, and there is ongoing debate among mathematicians and philosophers about its validity.

While finitism provides a coherent framework for mathematics that avoids certain paradoxes associated with infinite sets, it also imposes limitations on mathematical reasoning and the scope of mathematical inquiry. Ultimately, whether one subscribes to finitism or not is a matter of philosophical perspective and mathematical intuition.

>>16174216
I've heard teleportation is the real deal.

>>16174231
>Whether finitism is "true" depends on one's philosophical stance and interpretation of mathematics.
As I used the term I wasn't making a subjective claim. It's a claim about the objective world: nothing is, ever has been, ever will be, or ever can be actually infinite. And that would be true even if there had never been anybody with a philosophical stance who was ever born.

>it also imposes limitations on mathematical reasoning and the scope of mathematical inquiry.
This is like saying "by objecting to eight-sided triangles you impose limitations on geometrical reasoning and the scope of inquiry in geometry".

>>16174259
Finitism, as you've defined it, asserts that nothing in the objective world is actually infinite, and it's not contingent on subjective interpretation. It's a claim about the nature of reality itself.

Regarding limitations on mathematical reasoning, your analogy with eight-sided triangles is apt. Just as rejecting the concept of eight-sided triangles doesn't limit geometrical reasoning because such objects don't conform to the rules of geometry, similarly, finitism imposes restrictions on what is considered mathematically valid due to its rejection of actual infinities.

While finitism provides a consistent framework for mathematics that avoids certain paradoxes, it does indeed restrict the types of mathematical objects and operations that can be considered valid. This limitation is inherent to the philosophical stance of finitism and may influence the scope of inquiry within mathematics.

>>16174259
There are several arguments that suggest the possibility of an infinite universe:

1. **Cosmological Observations:** Some interpretations of cosmological observations, such as the large-scale uniformity and isotropy of the universe, suggest that the universe could extend infinitely in all directions.

2. **Inflationary Cosmology:** Inflationary cosmology proposes that the universe underwent a rapid expansion phase shortly after the Big Bang. This theory suggests that the universe may be much larger than the observable universe, possibly infinite in extent.

3. **Quantum Physics:** Certain interpretations of quantum mechanics, such as the Many Worlds interpretation, propose the existence of a potentially infinite number of parallel universes, each with its own set of physical laws and constants.

4. **Philosophical Considerations:** From a philosophical perspective, some argue that the concept of infinity is a fundamental aspect of reality, and therefore, it's plausible that the universe itself could be infinite.

5. **Consistency with Theories:** The concept of an infinite universe is consistent with certain theoretical frameworks, such as some versions of string theory, which allow for extra dimensions and potentially infinite spatial extent.

These arguments do not conclusively prove that the universe is infinite, but they provide plausible reasons to consider the possibility. Ultimately, our understanding of the universe's size and structure is limited by the current state of scientific knowledge and technological capabilities.

>>16173665
That's the current best guess, yes. The universe can have one of three basic types of geometry: positively curved, negatively curved, or flat. If it's flat, then it's necessarily either infinite or bounded. It's hard to imagine the universe having a boundary. Cosmology experiments suggest that the universe is flat, therefore it's most likely to be infinite.

>>16174280 #
>it does indeed restrict the types of mathematical objects and operations that can be considered valid
That's because they aren't. Again this is like objecting to the geometrical position that all triangles have three sides by saying it somehow restricts intellectual inquiry into nine-sided triangles.

>>16174287 #
>There are several arguments that suggest the possibility of an infinite universe
And they're all disproven by the simple argument that the very short video I linked presents.

>>16174295
One of the rules of infinity is when you divide by infinity the result is zero. It's like that guy never went to highschool.

>>16174299
>>16174301

>>16174301
>One of the rules of infinity is when you divide by infinity the result is zero
No it isn't. You love ChatGPT so much: ask it and it will agree with me.

Something divided by infinity gets you an infinitesimal, not zero.

>>16174309
>Something divided by infinity
Infinity isn't a number and you can't divide by it. It's like saying "something divided by banana".

>>16174298
>Cosmology experiments suggest that the universe is flat
What happens if the Universe is curved or a globe?

>>16174314
>Infinity isn't a number
This is what Finitism holds. Numbers are amounts and to say infinity is not an amount is to agree that nothing has that amount.

>It's like saying "something divided by banana".
I very much agree with you, but this isn't as obvious to others as it might be to you or me. Picture if you found yourself in a world where people wholeheartedly believed that that was a legitimate and indeed even profound question. You'd need to work them through the illogical results so they could see the problem, right?

>>16174309
Dividing by infinity can lead to various results depending on the context in which it's used:

1. In mathematical analysis: When dealing with limits, dividing by infinity often leads to zero. For example, if you have a finite number divided by a very large number (approaching infinity), the result approaches zero. Mathematically, this is represented as \( \lim_{x \to \infty} \frac{a}{x} = 0 \), where \(a\) is a constant.

2. In calculus: When considering limits involving functions, dividing by infinity can help determine the behavior of the function as it approaches infinity. For example, if you have a rational function \( \frac{f(x)}{g(x)} \) where \(f(x)\) and \(g(x)\) are polynomials, dividing both numerator and denominator by the highest power of \(x\) helps simplify the expression and determine its limit as \(x\) approaches infinity.

3. In other contexts: Dividing by infinity can sometimes lead to undefined or indeterminate forms, especially when dealing with complex or indeterminate expressions. In such cases, further analysis or mathematical techniques may be required to determine the result.

Overall, dividing by infinity is a mathematical operation that depends on the specific context and can lead to various outcomes, including zero, undefined, or specific limits.

>One divided by infinity approximately equals two divided by infinity.

>>16173665
the universe is flat

>>16174325
>Overall, dividing by infinity is a mathematical operation that depends on the specific context and can lead to various outcomes, including zero, undefined, or specific limits.
See? Told ya. Even the chatbot you spam agrees: "One of the rules of infinity is when you divide by infinity the result is zero" is not a true statement.

>>16174337
Yeah I dropped out of highschool. I'm just now getting it finished.

>>16174081
Well said my Brother in the Finite. Yet despite these obvious proofs those GOD CURSED INFINITY LOVING FREAKS continue to spout their nonsense.
Burn them at the stake I say. In front of their children. Heresy must be stomped out .

>>16174337
It is a rule, it's just missing some details.

>>16174342
Random acts of violence may never have helped anyone.

>>16174081
>>16174314
Dividing by infinity is a concept used in mathematical analysis, particularly in the context of limits. When we say "dividing by infinity," we're often referring to taking the limit of a function as its argument approaches infinity.

In mathematical notation, this is represented as:

\[ \lim_{x \to \infty} f(x) \]

Here, \( f(x) \) is a function, and \( x \to \infty \) means that the variable \( x \) is approaching infinity.

For example, consider the function \( f(x) = \frac{1}{x} \). As \( x \) approaches infinity, the value of \( \frac{1}{x} \) approaches zero. So, in this case, "dividing by infinity" results in zero.

Similarly, if we have a rational function like \( g(x) = \frac{1}{x^2} \), as \( x \) approaches infinity, \( \frac{1}{x^2} \) approaches zero even faster than \( \frac{1}{x} \).

So, while you can't technically divide by infinity in the same way you divide by a finite number, taking the limit as a variable approaches infinity is a way of understanding how functions behave as their arguments grow without bound.

>>16174315
Less to colonize. What if it's a torus?

>>16174343
>It is a rule, it's just missing some details
"Missing some details"? What you said was a radical misrepresentation. Depending on the exact details something divided by infinity can equal essentially anything! That's the "rule". One of those results is zero but it is not somehow the exclusive result.

>>16174360
In this post you are directly endorsing Finitism. This is its entire point: infinities are only potentials you can "approach" in the sense of getting larger and larger. As your chatbot explained: "grow without bound".
There are no completed, actual infinities.

>>16174368
When you divide a single number by infinite the result is zero.

>>16174397
>When you divide a single number by infinite the result is zero.
Don't break form, ask your chatbot. What's it say?

>>16174397
Please. Just stop posting on /sci/.
>>>/x/ or whatever is closest to a religion board.

>>16174399
It's /his/. Not to be rude but I'm going to keep on posting on /sci/ whenever I work up the nerve to talk to smart people.

>>16174405
>Not to be rude
AI spam is rude

>>16174408
It's just a tool I use to help articulate my thoughts, and to help expand my vocabulary.

>>16174408
Just because you say that doesn't make it true. I'm here to learn.

Its over for all boards, all social media. The rise of the chatbots. They are taking over. Only the tards and the bots will be left to make posts. Guess that means we will have to go back to facing real life instead of endlessly shitposting.

>>16174595
Just shitpost in discords and group chats like the normies.

But yes we won't be able to have *the same thread* every single day anymore.

>>16173665
For us, it functionally is. Think about it. No matter where you go, Universe is expanding and its doing it faster than the speed of light. So, there will always be space in the direction you are going to.

>>16174731
If the universe can move faster than the speed of light why can't we?

>>16174748
Its not movement in the sense we move. Its more like the distance between stuff is growing.

>>16174748
Matter can't move at faster than the speed of light. Space can.

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>>16174753
>Space can
wrong, as evidenced by gravitational waves travelling at c, if space could expand faster than c then the current model of gravity wouldn't work, which is the inherent compression of the spacetime manifold/g-field due to some interaction with mass, this compression could not take place if space was expanding faster than light, as it would counteract the effect mass has on it, resulting in no gravitational potential, even black holes would not be observed, because they work on the principle that the spacetime curvature is deformed to such a degree that nothing can leave it, which means it is getting deformed at the speed of light at the schwarzschild radius

>>16174081
If even nothing can be infinite, why can't everything else that comes after and depends on nothing?

Infinity is not self-contradictory, it is positively defined by a lacking property which can introduce logical contradictions, that video only says it doesn't make sense to use infinity as a number which it doesn't because infinity is not a number, it is a lack of upper limit just like nothing is the lack of a lower limit and also introduces logical contradictions when trying to treat the lack of value as a value which is why nothing can also be actually infinite and every other number is surrounded by infinite 0s.

>>16174087
Then exactly how many things do you observe at any given time if all your observations are necessarily finite?

>>16174259
So if counting can't continue indefinitely, then what is the last number?
How many atoms are in the observable universe and how can possibly be outside of it?

>>16174314
More like trying to divide by addition.

>>16174368
>There are no completed, actual infinities.
Completeness would imply a boundary which as you said infinity does not have, so the only way to know something is infinite is to prove it can not ever be completed or at least to have no proof that it can ever be completed.

>>16174414
If you have to use a tool to generate thoughts, they aren't your thoughts.

>>16174416
No you aren't, you spent weeks spamming a thread similar to this on other boards where you almost exclusive use GPT to responds and while people continuously told you things to update your model, you never once updated your spam to indicate that you learned a single thing.

>>16174748
You aren't dense and uniform enough to evenly collapse all the bits of nothing in and around yourself into something else.

>oh mah "expanding universe"~ hurr~

Okay fuckheads, listen up. The Universe is NOT expanding. That shit story is what they serve up to popsci twats like you, much in the same way children are first taught about the atomic mode,l with a little hard balls whizzing around REALLY FAST!
Fortunately for you barely sentient inferiors I am here to educate you with my superior intellect.

Okay get this. The Universe is everything. There is nothing for it to expand into. Pretty simple to grasp when you stop picking the wingnuts off you butt cheeks and actually listen. What is actually happening with all this perceived "expansion" of space is quite the opposite. The space stays the same but the matter/energy in the Universe is shrinking in on itself. Every minute we are getting smaller and so is every other bit of matter/energy in the Universe. Which is why we dont notice it. Everything gets smaller at the same rate.

Ask any anyone with a brain and they will agree. Go on, ask a competent mathematician, physicist, or a cosmologist. There is no actual difference between shrinking and expanding in this context, and since the Universe by definition is FUCKING EVERYTHING then its obviously the matter that is shrinking because that's the only available option.
There is no big empty void out there to expand into. There is only the Universe and there is only non-existence, and one cant expand into something that DOES NOT FUCKING EXIST.
Got it numbnuts?
Good.
Now you can go back to your dirty little pointless lives.
Didn't get it?
Well yeah, of course, subhumans aren't expected to understand anything that requires them to think. Yes, you should transition and end your genetic line.

>>16173665
What's right in front of you is everywhere in the universe, infinitely

>>16173665
i think it appears infinite like the surface of a globe is 'infinite' to travel across but again like a globe it is not actually infinite

>>16174301
i don't even know if he went to preschool

>>16174764
>wrong, as evidenced by gravitational waves travelling at c
are they?, to me they just seem like ants on rubber space
https://en.wikipedia.org/wiki/Ant_on_a_rubber_rope

>>16174081
>Quick, easy, and simple proof here:
*sigh*
https://en.wikipedia.org/wiki/Extended_real_number_line
https://en.wikipedia.org/wiki/Projectively_extended_real_line

>>16175680
I can see why you'd think that but gravity is not physically a manifold distortion

>>16174997
>If even nothing can be infinite
I think you've misunderstood: it isn't saying there is an entity called "nothing" and this entity is infinite, it is saying that there is not anything that is infinite. Nothing is infinite in that sense.

Much like if you say "nothing stopped him" you are not saying he was stopped and what stopped him is called "nothing", you are saying he was not stopped.

>number which it doesn't because infinity is not a number, it is a lack of upper limit
Yes, that's what Finitism holds - you're agreeing with me!

>>16175001
>then what is the last number?
This is like asking "Is the door open?". You haven't provided enough information to form an answer. The last number in what context?
The last whole number before ten? Nine.
The last number I saw written down? 2.

>How many atoms are in the observable universe
Idk

>and how can possibly be outside of it?
Could you rephrase this part of the question?

>>16175682
https://en.wikipedia.org/wiki/Red_herring

>>16176202
>finitard treating "what's the last number" as if it where a supertask
lmao
>*wiki link*
thank God for making you retarded, life's been abnormally tiring and i really needed a good joke

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>>16174081
kek, this guy

>>16174086
>You've missed the point entirely
No, I'm just pointing out a typo, drama queen.

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>>16173665
>Is the universe infinite?
Anon forget all this yapping about finitism and what not. The truth is no one can see beyond the visibility limit of the visible universe, and we can only ponder and throw math ideas back and forth, but no one knows.
Also, because of "dark energy", which is whatever is making spacetime expand further, and faster the further it is away from us, it means that eventually, beyond a certain distance from us, spacetime might be already expanding faster than the speed of light, and so we will never be able to observe what is beyond that "limit" since no information regarding the matter there, or radiation emitted from, will ever reach us
Therefore, we don't know if the universe is finite or infinite. That's the the answer.

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>>16174081
W-Wildberger bros?

>>16176241
We can likely deduce that infinities aren’t real in the natural universe since we have not confirmed one single infinity in nature. ”Infinity” really should be renamed ”unlimited sequence” because that is all it is. Any ”infinity” in nature (like 0.333…) is just a logic for a sequence you can follow however far you like, only the numbers of that sequence you can represent in reality are real in any sense.

>>16176221
>what's the last number" as if it where a supertask
I simply asked for clarification: "last number" in regards to what?

>*wiki link*
If you say nothing but wiki links then that's all you deserve P:

>>16176253
I think you're misusing the meme since he's a Finitist too if I remember right?

>>16176202
>it isn't saying there is an entity called "nothing" and this entity is infinite
Ok, but there is and it is.

>Much like if you say "nothing stopped him" you are not saying he was stopped and what stopped him is called "nothing", you are saying he was not stopped.
Or it just means the stoppage was taken relative to oneself since the difference between him and himself is nothing.

>Yes, that's what Finitism holds - you're agreeing with me!
No finitism holds that everything is finite and bound by some upper limit while the fact that you can't point to any last number in the set of numbers proves that not everything necessitates an upper limit and is necessarily finite.

>This is like asking "Is the door open?".
No, its like asking where the back door is.

>The last number in what context?
Numbers.

>The last whole number before ten? Nine.
That isn't asking about a last number at all, that is asking what number precedes 10.
>The last number I saw written down?
Obviously I am talking about numerical order not some arbitrary idiot's chronological order of encountering random numbers.

>Could you rephrase this part of the question?
*how many, If everything is finite, what is the finite upper limit of atoms in the observable universe and what is the finite upper limit of atoms outside the observable universe.

>>16176257
.333... isn't, infinite, it isn't even as large as 1, let alone all the possible 1s added together, you are just encountering precision errors when trying to measure thirds in terms of tens, but that can easily be resolved by using a number system that is not based in tens.

>>16176921
.333… supposedly has an infinite number of 3s in it, you get the point. 1+1+1… is also never infinite. They’re formulations of a logic you can follow however far you like, an unlimited sequence and nothing more.

>>16173665
We have this fantasy infinite universe /cyclic universe thread what, 3 times a week now?

Yes the finite universe dramatically increases the Bayesian probability of simulation theory/religious reality/Boltzmann brains. That doesn't excuse fantasy of the gaps and copeposting.

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>>16173665
haha look at that gobeligook. imagine actual believing that this has anything to do with reality. fart sniffers not even once

>>16173665
Hundreds of years ago every "smart" person was assured the Sol system was the center of the Universe. Hundreds of years before that they were sure the Earth was the center. Hundreds of years before that the smartest minds were convinced the Earth was flat and England was in the dead center of the circle.

There is a long history of humans being wrong by assuming they are the center of the world they observe. In reality the opposite is always right. Why do retards keep making the same mistake? You are not a special snow flake. You are a worthless leaf a drift on the ocean of time. Deal with it cunts.

>>16177051
one doesnt follow the other, bucko

>>16176916
Honest question, not being mean but to help with ensure my response adequately explains the concepts: are you ESL? If so, what's your primary language?

>>16174081
>easy to prove universe isn't infinite
>see this yt short for proof
are you serious my nigger?

>>16173665
From our perspective it might as well be infinte

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>>16177051
>There is a long history of humans being wrong by assuming they are the center of the world they observe. In reality the opposite is always right. Why do retards keep making the same mistake?
Technically, the center of the universe is wherever you happen to be... So in that sense, they were all right - save for the flat earth thing, but I don't think any scholarly circle was ever stupid enough to actually write that down, until today.

>>16177528
No? It’s just the center of your observable universe.

>>16177542
Anything outside your observable universe effectively doesn't exist to you. Thus it is still technically true, which is the best kind of true.

>>16177553
>It doesn’t exist if I won’t interact with it!
Not true

>>16175143
>expanding collapsing hurr durr
The only actual problem is the excessive amount of shitposting both on this board and on the internet as a whole.

>>16177471
Do you feel that its argument isn't correct?

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>>16177609
There is no argument, it's another midwit incapable of processing and visualizing information so they just dismiss it without ever exploring further to see if it could hold any truth, it's like giving a microwave oven to retarded cavemen, they would just smash it to pieces

>>16177051
What does that have to do with the universe being infinite?

What comes to mind when you try to picture something infinitely complex? It is a concept that is difficult to fathom because it is, well, complex! To understand infinite complexity, you must first get a grasp of limited complexity. Every system, object, situation, circumstance, and idea we observe in this universe has limited complexity. This is because all of these things are finite. An object occupies a finite space. A system can only have so many functions, purposes, and factors. A situation can only have so many facets and factors, and so on. However, just because almost all observable systems are finite does not inhibit the fact that many of the things I have listed can be incredibly complex. These things can have hundreds of thousands, if not millions or billions, of functions, factors, purposes, qualities, interactions, and relationships all within their respective fields. Now an infinitely complex system is one where these qualities, factors, relationships, and interactions have no limit in their scope. Each part of this type of system has infinite functions and relationships with other parts of the system. Imagine a network like neurons or computer networks that has a complexity on this scale. Your brain has around 100 billion neurons, give or take, and this system and circuitry has such a valume of functions and purposes that it is absolutely one of the most misunderstood systems in the world, primarily because the brain is what supports and projects consciousness and reality for every given individual.
Captcha SYNN

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Now imagine a network that is infinitely complex, or close to that level. The only way this system could exist is if Existence, the state of everything that could possibly exist, is infinite as well. If it is truly infinite, that means that by being infinite it also must have existed, and will continue to exist forever. If such a complex system that has infinite factors, functions, links within the network, and relationships, exists, this system undoubtedly would have a consciousness so powerful that it could do anything it wants, concieve of anything it wants, and be present in any part of reality, within any and every universe or realm, and has authority over all things. If the system is infinite there is an infinite amount of possibilities to make manifest. This system you have would be akin to a deity. If existence is infinite and eternal, a component of this infinitely complex system would be that there are finite realities and universes of limited complexity within the broader infinite extistence. The reason this is the case is because you can have finite within the infinite. For example, let's say space is infinite in every direction, but your body occupies a finite space within that broader infinite space. There is something even crazier to think about; you can have an infinity within a broader infinity. Like a set of infinity within a broader paradigm of infinity. The reason I bring this up is because I believe that there is beauty in complexity. There is beauty and joy in being something finite within something infinite. Why?

Because you get to explore this infinitely complex system, and you would never run out of things to explore. If this system is eternal, I would argue that a component of ourselves is eternal as well, and we get to continue this never-ending process of exploration and experience forever. Infinite Complexity brings beauty, joy, and finally, probably the most important thing, PURPOSE!
Captcha 8HH8

>>16173665
>infinite space means infinite matter
>it also means infinite lack of matter
>if matter is infinite how is there lack of matter?
>if lack of matter is infinite how is there matter?

infinity can't exist because everything would either be everything forever or nothing forever. The existence of distinct particles disproves infinity.

>>16177879
There is no such thing as lack of matter, never was

>>16177879
>infinite matter/energy in all directions
>inverse square law on force by gravity is still greater than zero
>infinitely pulled in all directions
>die
i am extremely confident about this post, in fact, what i have said is so obviously true that nobody will respond to it, and it will forever be known on sci that space is not infinite, and we will never see this thread again
>inb4 infinite matter condensed into zero space in a timeless vacuum lacking physical laws

>>16174086
Well, if you don't use the language properly then you run the risk of not communicating your idea properly/effectively, do you?
But you are not so stupid to have not realized that before posting, right?

>>16177879
The concept of infinite space and matter raises intriguing questions about the nature of the universe. Let's break down the implications of each statement:

1. **Infinite space means infinite matter:** If space is truly infinite, then there would indeed be an infinite amount of space for matter to exist within. In an infinite universe, matter could potentially extend infinitely in all directions, filling the vast expanse of space.

2. **Infinite space also means infinite lack of matter:** Conversely, if space is infinite, then there would also be infinite regions where matter is absent or sparse. Even within an infinite universe, matter might not be uniformly distributed, leading to vast expanses of space with little or no matter present.

So, in an infinite universe, both scenarios could coexist: regions with infinite matter and regions with infinite lack of matter. The key idea here is that infinity encompasses all possibilities, including the presence and absence of matter on different scales and in different regions of space.

The concept of infinity in cosmology and physics raises profound questions about the structure and composition of the universe, and our understanding of these concepts continues to evolve as scientific research progresses.

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>>16177888
An infinite series with positive, non-zero values can still converge to a finite number.

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>>16177888
Checked
Greentech time
One God
Satan
One God remains
Satan evolves
God and Satan coexist perpetually
The idea that our universe could be a particle within a larger universe is a speculative concept that arises in various theoretical frameworks, such as certain interpretations of cosmology and physics. One such theory is the multiverse hypothesis, which posits the existence of multiple universes, each with its own set of physical laws and properties.

Within this framework, it's conceivable that our universe could be just one among many particles or entities within a larger cosmic structure. Each particle or entity within our universe could, in turn, contain its own universe, leading to a hierarchy of nested universes within universes.

While intriguing, the idea remains speculative and currently lacks empirical evidence. However, it illustrates the depth of questions raised by cosmology and theoretical physics about the nature of reality and the structure of the cosmos.

Exploring such concepts pushes the boundaries of our understanding and invites us to contemplate the nature of existence and the possibility of realities beyond our own. As scientific research progresses, we may gain further insights into these fascinating and profound questions about the universe and its place within a larger cosmic framework.

>>16176971
>durr grug think infinity not infinite, is unlimited instead

>>16177926
let's say that each direction in space gets its own term in our summation on the forces experienced by our object. there are infinitely many terms, and each applies infinite force onto the object, so we could say these infinities are similar and all cancel eachother out. CMB implies that they would nearly cancel out in the early universe, so, zero.
yet, as a midwit, i must admit to the simplicity of sum from 1 to infinity of (G*mass of earth*infinity)/(radius of observable universe/2)^2 which gives us a nice ballpark number of infinite force

>>16177051
Which is why reality is infinite rather than just the bits you can personally see.

>>16177155
While we are asking questions as our answers to other questions, how many grade levels were you held back?

>>16177879
>infinity can't exist because every number would either be 1 or 0. The existence of infinite distinct numbers extending to infinity disproves infinity.

>>16177941
half plus half that plus half that plus half that... doesn't diverge to infinity, though, it converges upon 1, so why would something much smaller than half, like an inverse cube not converge?

>sum from 1 to infinity
Its not 1, though, its the sum of 1/x^3 for x from 1 to infinity wh3ere 1/x^ gets really small really quickly as x increases.

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>>16177941
>so we could say these infinities are similar
No, they're not, it depends entirely on the framework in which you are measuring, the infinite amount of numbers between 0 and 1 still equates to less than the infinite numbers between 0 and 100

>>16177979
>the infinite amount of numbers between 0 and 1 still equates to less than the infinite numbers between 0 and 100
No, they are both unbounded sets that have an aleph cardinality.

>>16177986
And the only one that is truly infinite is aleph zero, every other defines the limit of the set, yes they can be divided into infinite amount of ordinals, ℵ100 is still summatively larger than ℵ1, no matter how many infinite numbers you count between 0 and 1 you will never reach 100, being divisible into infinite fractions =/= infinite in length

>>16177992
>no matter how many infinite numbers you count between 0 and 1 you will never reach 100, being divisible into infinite fractions =/= infinite in length
100 isn't infinite in length either, you have just undermined your entire point since you were originally clearly talking about infinite fractions.
>>16177979
> infinite amount of numbers between...
Aleph_0 is the amount of numbers between both 0 and 1 and 0 and 100.

>>16177999
*Aleph_0 is the amount of fractional numbers...

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>>16177999
>100 isn't infinite in length either
I didn't say it was??
Your whole hypothesis of any given region of space having to contain an infinite amount of energy just because it's divisible into infinite parts is retarded, you can take two different regions of space with differing energy densities and divide them into equally infinite parts, but one region is still more energy dense than the other

>>16178007
>I didn't say it was??
You implied it with your retarded red herring about how 0 to 1 will never reach 100, so there must be more fractions between 0 and 100 than 0 and 1 when both ranges have an aleph number of fractions.

>Your whole hypothesis of any given region of space having to contain an infinite amount of energy
Nobody said that, the claim was that infinite series show that adding up infinite fractions doesn't necessary equal infinity since fractional infinite series converge to 1 rather than diverging infinitely.

>>16177963
>this irrelevant equation resolves differently therefore

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>>16178011
>Nobody said that
>>16177941
>let's say that each direction in space gets its own term in our summation on the forces experienced by our object. there are infinitely many terms, and each applies infinite force onto the object

>>16177979
yes, we could, as we are talking about actual mass, a small subset of which we can measure, and a larger subset of which we can detect, and a larger still subset from which additional information can be inferred. everything points to things being largely the same in all directions, with incredibly small imperfections, so the question should rather be might these famous "cold spots" have any impact, gravitationally, on the infinities

>>16178013
Its not an algebra equation, it is completely relevant because it a basic example of an infinite series that you will learn all about if you ever graduate your remedial high school classes and enter higher education.

>>16178014
as half of those anons, I have to ask you to re-read both of those posts. It is not ANY region of space that has infinite energy. It is any line, going in any direction, which will encounter infinite energy if the universe is to be infinite, as a proxy for determining if the universe is infinite, assuming we can finally put to rest the overused question on sci: if infinite universe, why not infinite force?
the only difference between this thread and all the others is nobody has yet to troll by pretending that the newtonian force of gravity equation is infallible

>>16178014
Infinitely many inverse cubed terms does not mean infinite force, the infinite series of inverse cube values doesn't not add to infinity, it converges to 1.

>>16178018
>this completely irrelvant equation is relevant because it fails to share the property i think it shares with another equation
>also i have cubed the denominator for no apparent reason

>>16178019
>It is any line, going in any direction, which will encounter infinite energy if the universe is to be infinite
Not if the underlying manifold is non-euclidean, you can have finite energy contained in an infinite non-euclidean manifold, assuming the path vector loops back on itself through this manifold and the field doesn't normalize it would encounter a finite amount of energy on it's path and if it were to follow this non-euclidean manifold until every infinitely possible path was taken it would encounter a finite amount of energy, equivalent to counting from 0 to 1

>>16178024
>fails
No they are both infinite series, one is a fraction that decreases linearly and the other is a fraction that decreases by cubed, but even if you used inverse square for gravity instead of em energy, its still an infinite series of fractions that proportionally decrease in value with distance, so would still converge rather than being infinite.

>no reason
Its the same with halving each next value in the series or decreasing by a square with distance in the case of gravity or a cube with distance in the case of em force.

>>16178027
Good point. We don't actually know if space is flat or not, we've only set bounds implying it is either flat or very close to it, so the answer could very well be non-infinite.

>>16178028
How can we be sure that the squared or cubed term in the denominator will overpower the mass term?

>>16178046
The mass term is always finite, so it will always be reduced by the denominator, so it will never be infinite and will always be reduced to practically nothing by a relatively small distance, so the infinite distance thing doesn't really come into play and if you are just a couple of meters from the sun or similarly massive object, you are going to get ripped apart and die without infinite energy coming into play since the energy it takes to rip a human body apart is significantly less than infinity.

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>>16178020

>>16178050
Can we prove that the numerator will be practically nothing in comparison to the denominator for all stars, gas clouds, black holes, and unknown-unknowns?

>>16178062
Confirmed, it definitely converges and isn't infinity.

>>16178068
Are you currently being ripped apart by the gravity from those distant objects or is their effect on you practically nothing?

>>16178045
It appears flat, but if reality really was non-euclidean I'd suggest that all the extremely distant galaxies we see are illusions caused by light looping back to us through some different path through spacetime

>>16178111
>extremely distant galaxies we see are illusions
true, more so than most realize
https://youtu.be/nSJtzn2H3Do

>>16177626
I find this a very strange claim. It quite expressly argued that, allowing for infinities, all quantities would become equal to all other quantities.

>>16177949
0

>>16178293
What do they call it where you come from?

>>16176916
Taking your post as if you are a native English speaker:

>Ok, but there is
Isn't this like saying nowhere is an actual place you can be or nobody is an actual man who you can meet?

>and it is.
Well it can't be - the non-thing that the word nothing refers to has no properties at all and hence there isn't anything concerning this non-thing that could be infinite.

>that everything is finite and bound by some upper limit while the fact that you can't point to any last number in the set of numbers
But think: "the set of numbers" isn't an actual thing that exists. It has no causal potency, which is what it means to exist. It's like the number 4: it doesn't exist, on its own, out there in the aether somewhere. It's an amount, and it exists only insofar as there is that amount of things.

>No, its like asking where the back door is.
I agree! It isn't specific enough to be answered with a specific answer. You can only answer it in general terms: the back door would be found at the back, and the last number would be f at the end. If there wouldn't be a back then there's no back door, and if there wouldn't be an end then there's no last number.

>Numbers
But like I said, numbers aren't things that exist on their own out there somewhere. In the sense you're asking this question, viewing them as independent entities that exist apart from other things, there aren't any numbers at all.

>>16176916
>If everything is finite, what is the finite upper limit of atoms in the observable universe
That's a neat question! Let's calculate it..

According to https://www.newscientist.com/lastword/mg24732961-500-how-much-stuff-is-there-in-the-universe/ the volume of the observable universe is about 4*10^80 cubic meters. The smallest atom, a hydrogen ion (i.e. a proton) has a radius of 0.833 femtometers https://www.scientificamerican.com/article/ultraprecise-measurement-pinpoints-the-protons-size/ which is 10^-15 meters.

So taking a hydrogen ion as a sphere and crunching the numbers, you get 9.55×10^124 as the upper limit of atoms that could potentially be in the observable universe, assuming they aren't compressed into a smaller size than they're usually found it.

However in a neutron star you can compress protons to about 1/6 of their size, so assuming we can compress them all to a sixth of their usual size we get about 5.73*10^125 as the upper limit.

>and what is the finite upper limit of atoms outside the observable universe.
That depends on its volume, which is currently unknown

>>16178300
A pronoun

>>16177940
You can't even read nigger. I wrote that infinity is not something you can find in nature. You can define some axioms that make infinity have certain properties, but that doesn't make it a real thing.

>>16178291
And the argument doesn't hold

I STARTED COMBING ITS HAIR, WAHT DOES THAT DO/

>>16178540
Where does it seem to go wrong to you?

>>16177904
Deferring all your thinking to a language model is terrible because they are ill equipped to deal with contradictions and end up just repeating the statements in a wordy way to pretend being correct in a blatantly wrong manner, like you just showed by copy pasting a bot response, it address none of the issues and just say 'see they can both exists because I repeated both statements'

>>16178627
infinitely divisible =/= infinite in size, dividing two numbers into equal parts does not make them the same number

>>16178667
>infinitely divisible =/= infinite in size
Believe it or not, it does!
In a world with infinite divisibility:
1= (1/∞ + 1/∞ + 1/∞...)
2= (1/∞ + 1/∞ + 1/∞...)
3= (1/∞ + 1/∞ + 1/∞...)
...
∞= (1/∞ + 1/∞ + 1/∞...)

All of these infinite additions of one-infinityeths must simultaneously be equal and not equal. This is a fatal issue with infinite divisibility.

>>16178678
Wrong, each infinitesimal fraction of 2 is always some finite amount larger than the infinite fractions of 1, otherwise each division of any number should yield the exact same number, infinite or not, infinitely divisible =/= infinite in size

>>16178708
>Wrong, each infinitesimal fraction of 2 is always some finite amount larger than the infinite fractions of 1
How much is that?

>>16178710
2/1 ratio for each fraction?
If you haven't checked then 2-1=1, not 0, no matter how many times you divide both numbers the sum of one will always be larger than the other by their difference, which means each division is larger than the other by that difference divided by the amount of divisions, regardless of many infinite parts you divide them into, you can't just throw away the difference and pretend it isn't there because your limited numerical system can't convey the information properly

>>16178729
>2/1 ratio for each fraction?
What's 1/∞ divided by two?

>>16178736
(1/inf)/2

>>16178752
Is that equal or unequal to 1/∞?

>>16178756
Completely irrelevant, you still need two of them to get 2/inf

>>16178767
This is like saying if you divide the whole numbers into evens and odds that each resulting group is smaller than the set of all whole numbers.

We can prove (1/∞)/2 is equal to 1/∞ very easily:

(1/∞)/2= (1/∞)*(1/2)
(1/∞)*(1/2)= (1*1)/(∞*2)
1*1=1 and ∞*2=∞
So (1*1)/(∞*2)=(1/∞)
Ergo (1/∞)/2=(1/∞)

>>16178787
>We can prove (1/∞)/2 is equal to 1/∞ very easily:
Yes, this is irrelevant, the difference between 1/inf and 2/inf is 1/inf, which means each fraction of 2/inf is larger by 1/inf

>>16178787
>>16178793
More specifically (2/inf)/(1/inf)
Remove the infinities -> 2/1

>>16178793
You seem to be thinking of it as
1= (1/∞ + 1/∞ + 1/∞...)
2= (2/∞ + 2/∞ + 2/∞...)

But we can easily prove (1/∞ + 1/∞ + 1/∞...) = (2/∞ + 2/∞ + 2/∞...)

(1/∞ + 1/∞) = (2/∞)

(1/∞ + 1/∞ + 1/∞...)=(1/∞ + 1/∞ + 1/∞ + 1/∞ + 1/∞+ 1/∞...)

(1/∞ + 1/∞ + 1/∞ + 1/∞ + 1/∞+ 1/∞...) = ((1/∞ + 1/∞) + (1/∞ +1/∞) + (1/∞ + 1/∞)...)

((1/∞ + 1/∞) + (1/∞ +1/∞) + (1/∞ + 1/∞)...) = (2/∞ + 2/∞ + 2/∞...)

So (1/∞ + 1/∞ + 1/∞...) = (2/∞ + 2/∞ + 2/∞...).

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It's easy to pretend there are lots of smart people in /sci/ until you see them trying to do basic mathematics.

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> child free

how about the adventure always win?

>>16178828
>(1/∞ + 1/∞) = (2/∞)
>
>(1/∞ + 1/∞ + 1/∞...)=(1/∞ + 1/∞ + 1/∞ + 1/∞ + 1/∞+ 1/∞...)
>only dividing one side of the equation

>>16178814
>Remove the infinities
how exactly?

>>16178870
>>only dividing one side of the equation
Allow me to clarify: that wasn't an operation, just a starting statement. I.E. I was saying "bear in mind (1/∞ + 1/∞) = (2/∞)" rather than "(1/∞ + 1/∞) = (2/∞) directly leads to (1/∞ + 1/∞ + 1/∞...)=(1/∞ + 1/∞ + 1/∞ + 1/∞ + 1/∞+ 1/∞...)"

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>>16178883
(1/inf+1/inf) = (2/inf)
(((1/2)/inf+(1/2)/inf)+((1/2)/inf+(1/2)/inf)) = ((1/inf)+(1/inf))
You can keep dividing forever until both are infinite, but one fraction will always be larger than the other by a factor of x/y, this is even empirically provable by taking two (real) lengths and dividing them into equally infinite parts, no matter how many divisions you make one fraction will always be physically larger than other, because otherwise it wouldn't add up to the sum, ×/inf > (x-1)/inf, if you had to walk an infinite amount of steps to 100 meters, and your friend had to walk an infinite amount of steps to 1000 meters, his steps would still be larger than yours by a factor of 10/1, this still applies even if you make infinite divisions, because even on an infinitely divided line you can still point out a real number anywhere on that line and unless your lines are equal in length, not equal in divisions, then the numbers on the equal fractional distances of your lines will always be different

>>16178922
>You can keep dividing forever until both are infinite, but one fraction will always be larger than the other by a factor of x/y
Is that an issue if we can prove they're always equal, though?

I think you're picking up on an important issue though: they simultaneously must be equal but can't be equal. We can prove each opposite. It's because once we introduce an infinity, we introduce a contradiction, and so we've got an inconsistent system. In an inconsistent system we can prove anything true or false.

>if you had to walk an infinite amount of steps to 100 meters, and your friend had to walk an infinite amount of steps to 1000 meters, his steps would still be larger than yours by a factor of 10/1

Nah if each of his steps were a tenth of your's he would still arrive since ∞/10=∞

>>16178941
>Is that an issue if we can prove they're always equal, though
But they're not, the only way this would apply is if both fractions were equal in size, which is demonstratably wrong, for each x/inf you advance the other number will advance by ((x/inf) + (y-x)/inf), unless x=y, or all the numbers in existence are zero, these numbers will always differ

>>16178988
>is if both fractions were equal in size, which is demonstratably wrong
Didn't >>16178828 demonstrate it?

>>16179005
No, because that already assumes all the fractions are equal size without proving it, unless your divisor is zero then any infinite amount you divide with will always return a nonzero value (unless you're dividing zero), and for two different integers this value will always be different, just making the numbers arbitrarily small and then ignoring the difference doesn't make them go away, you could spread all the atoms of the universe an infinite distance from eachother such that you will never reach them, but the atoms themselves never disappear

>>16178352
>nothing refers to has no properties at all and hence there isn't anything concerning this non-thing that could be infinite.
So in your mind, the number one property of nothing is that it doesn't have properties?

>It's like the number 4: it doesn't exist, on its own
Are you saying only 4 atoms can possibly exist or you just don't really understand what you have been reading or what numbers mean?

> if there wouldn't be an end
What is the word for something without end?

>numbers aren't things that exist on their own out there somewhere.
Yet atoms do, and for the same reasons you can't identity any last number, you can't determine any upper limit to the number of atoms in the entire (not just observable or anecdotal like this retard >>1617835 who doesn't even understand why its "unknown" to try to find the limits of an infinite open system) universe because spoiler, infinity.

>>16178499
You can find the lack of limits in nature, though, or the observable universe would be the universe and it would end abruptly, there wouldn't be a bunch of unknowns beyond the scope of light.

>>16178829
disappointing, isn't it?

>>16179048
>that already assumes all the fractions are equal size without proving it
Which step of the calculation, specifically, assumed that?

>>16179380
>the number one property of nothing is that it doesn't have properties?
That's awkward English. That's a non-property. Much as "colorless" is not itself a color.

>Are you saying only 4 atoms can possibly exist
I was talking about the number 4 on its own, as an isolated entity.

>What is the word for something without end?
Endless
And note that I said "wouldn't be". There's a big difference between something that will not end and something infinite. For instance, time won't ever genuinely end, there will always be future moments. But that doesn't mean we're in the year ∞. A finite amount of time will always have passed at every point of time that will exist.

>you can't determine any upper limit to the number of atoms in the entire (not just observable or anecdotal
Again that's because we don't know its volume. If we did then we could calculate it with ease just like we did the observable universe. It's a simple formula, the total number of possible atoms (A) is equal to the smallest possible volume of an atom (Va) multiplied by the total volume of the universe (Vu):
A=Va*Vu

>you can't identity any last number
There's no last number because counting is just an algorithm you follow in order to generate symbols. That algorithm contains no instructions for a stopping point.

>>16179642
>Much as "colorless" is not itself a color.
Black is generally considered colorless while white is all the colors combined, but if you want to argue that, then the next colorless color value is transparent.

>I was talking about the number 4 on its own,
I wasn't so I don't know why you try to change the subject when there is clearly no upper limit to the total number of atoms.

>Endless
And what is the mathematical word for and endless set?

>But that doesn't mean we're in the year ∞
Because ∞ is not a number, it is a value that indicates endless sets.

>A finite amount of time will always have passed at every point of time that will exist.
Only if you arbitrarily pick a random point in time to be year 1.

>Again that's because we don't know its volume.
Then what is the upper limit of its volume if its not infinite in nature?

> counting is just an algorithm you follow in order to generate symbols.
No, the symbols are all predefined by the radix of the base of the counting system and it has no stopping point because there is no upper limit to the possible combinations just like there is no finite number of potential word choices because they are infinite.

>>16179659
I think I'm seeing the root of the issue here. Can you tell me the difference between the terms:
-"Potential infinity"
-"Actual infinity"

And how mathematical finitism views each concept?

>>16173665
yeah

>>16174081
lmao retard you're using the same arguments the catholic church did before galileo

1/inf exists, it's called dx retard

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>>16173665
>AI will save humanity
You have no idea just how wrong you are and why this is part of the reason why we likely exist to begin with.
Entropy is a perpetual state of death. God is literally killing themselves and made you in the process. You are just a small subset of it. God's eternal state of universal skitzophrenia and self-destruction.

No wonder he likes grunge.

>>16178829
Depends, some are clearly linguistically smart.
The problem is, the better you get at that, the shitter you get at math.

t. started engineering, went in law
Math used to be fucking easy to me. You lose it so quick.
I mean it's improving now I'm tackling the issue, but it's far more painful now after dealing with fuzzy logic and esoteric frameworks for so long.

I hate the human brain. It is a primitive dumb thing.

>>16177626
Sure, only your hindu decimal based symbolic language is capable of truth.

There's a reason why boolean/binary became important.

>>16179637
The one I pointed out in my reply, 1/x on a length 1 has a different value than 1/x on length 2, 1/2 smaller, even if you divided both lines with 1/inf the division lines would point to different values

>>16180154
If you're using the same units no it doesn't, half an inch on a one-foot ruler is the same as half an inch on a yardstick

>>16179868
>you're using the same arguments the catholic church did before galileo
I'm intensely skeptical you can actually quote anyone from that time making this argument, though I would enjoy reading it if you did

>1/inf exists, it's called dx
I don't see how this is meant to refute the argument that the video presents

>>16173665
Reject theoretical models, return to Christ.

>>16173665 Probably not. That would explain multiple universes.

>>16180154
>>16180309
Like let me illustrate. I see where you're coming from and you're extremely right that all infinities being the same size is where a lot of contradictions come from.

The math I did with division and infinity is valid. You seem to be under the impression that, say, ∞/4 is different from ∞.

But suppose we had five squares, all of area ∞. How this came about is that originally someone had two identical squares of area ∞, and then one was divided into quarters. Is there any way for us to distinguish which of the five squares was part of the original pair and which was made from the quartering of one member of that pair?

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>>16180309
>half an inch on a one-foot ruler is the same as half an inch on a yardstick
We're not talking about units, though, we're talking about taking two different numbers and making the same amount of divisions, [2/2=1, 1/2=0.5], [2/4=0.5, 1/4=0.25], they fundamentally can't point to the same number no matter how many divisions you make, same thing with the ruler and yardstick, the units and their distances from 0 are the same, yes, but they are a different fraction away from the total length of your measurement device
>>16180585
>∞/4 is different from ∞.
It is, one is split into 4 parts and the other is not, if you had 5 lines with one being infinite in length and the others being inf/4 in length then the undivided line would always be 4x longer than the other ones, you can't extend one line without extending the others if the ratios have to stay the same.

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>>16178829
>>16179448
This board has always attracted its fair share retards to it.

>>16181133
>We're not talking about units, though, we're talking about taking two different numbers
With infinity the same units is the better comparison, since ∞ divided by anything remains ∞.

>It is
Then answer my question about the squares.

>>16174081
>>16178787
You're trying to do arithmetic with something that specifically isn't a number. You can treat it like taking a limit (then lim_(x∞) (x * 1/x) = 1, lim_(x∞) (x * 2/x) = 2 and so on) or use a system like the hyperreal numbers with infinitesimals wherein I think you could maybe evaluate stuff like 1/∞ + 1/∞ + ... but instead of ∞ you'd have to use one of the infinitely many infinitely large numbers.
So you can make up a system where these contradictions don't appear, but in the end it's just as much a philosophical question regarding whether it makes infinity an invalid concept if it can not be treated like a standard number (in my opinion it doesn't).

>>16181957
>You're trying to do arithmetic with something that specifically isn't a number. You can treat it like taking a limit
Yes that's what Finitism holds. Infinity isn't an actual amount that things can really be. It's like a limit: something that can be approached but isn't ever reached

>or use a system like the hyperreal numbers with infinitesimals
Isn't the definition of an infinitesimal that it's 1/∞? (I.E. the smallest nonzero positive number...ostensibly)

>So you can make up a system where these contradictions don't appear
Care to demonstrate?

>>16173665
>infinite space

>>16181890
>Then answer my question about the squares.
I did, same principle as with the lines, one square will always have an area 4 times larger, for every measurement you take one square will always be bigger than the others unless you intentionally leave one area unchanged, but then it would not be infinite in size and the law of contradiction wouldn't hold, no?

>>16182222
>Care to demonstrate?
I'd just listed 2 systems wherein arithmetic with infinities is somewhat possible without contradictions, those are your demonstrations.
>Isn't the definition of an infinitesimal that it's 1/∞? (I.E. the smallest nonzero positive number...ostensibly)
Within said number system there are infinite "infinitely large" numbers so you don't have one ∞ hence you don't have one 1/∞ either. The larger the infinite number H, the smaller the infinitesimal 1/H, all of them are smaller than any real number but I'm not sure if there's a notion of "smallest infinitesimal", I don't think so?

>Yes that's what Finitism holds. Infinity isn't an actual amount that things can really be. It's like a limit: something that can be approached but isn't ever reached
We can't feasibly put a limit on how large the collection of natural numbers can be, hence it is useful to think of it as infinite. Whether or not any such "infinite collection of all the natural numbers" actually exists in some platonic world of things and concepts may be more of a philosophical and metaphysical question than a mathematical one. Even still, having conceptualized said collection(s) as infinite, we can do so in ways that yield both sensible results about the finite instances of this "infinite concept" and no contradictions, and hence it's a useful way to do math.

The fact that you can also do so in a way that leads to contradiction I feel like is not enough of an argument against the concept itself.
The sentence "This sentence is false." is contradictory. Does this mean logical inference or reasoning or self-reference do not exist at all? Just because you can weave them in a way that leads to a contradiction?

>>16182526
>one square will always have an area 4 times larger, for every measurement you take one square will always be bigger than the others

That's clearly not so here. Whatever method you use to determine size they would all be identical. If you tried to fill them with fluid all five could hold the same quantity. If you put a marker at each mile around their perimeter they would have an equal quantity of mile markers.

There is no possible method of measurement you could devise whereby any of these five squares would get you a different result from the others.

>and the law of contradiction wouldn't hold, no?
Exactly - once you introduce infinites the law of noncontradiction stops holding. You always get contradictions with them.

>>16182805
>I'd just listed 2 systems wherein arithmetic with infinities is somewhat possible without contradictions, those are your demonstrations.
Name-dropping a system isn't a demonstrating that it's not an issue. If I reply with “Euclidean geometry” does that do anything to say how, specifically, I think that system is relevant? Of course not. You have to do an actual demonstration of what you’re saying within that system, as I did at >>16180585

The two systems you mentioned, like I discussed, don’t in any way help resolve this issue for an infinitist. The first was calculus, you said “can treat it like taking a limit”, which amounts to a confession that the Finitist approach is the only one that avoids a contradiction. Limits in calculus describe something a system approaches but never reaches; a limit to infinity essentially demonstrates the very essence of Fintiism: infinity is something you can approach, but like any other limit, will never reach.

>>16182805
>>16183657
Your other system was “a system like the hyperreal numbers with infinitesimals”. That system essentially works by tagging infinitesimals with something like “infinitesimal that adds up to [some specific number]”. Which, yes, if you define something as “infinitely small fraction that adds up to 2 if you add infinite of them” then by definition it adds up to 2.
It has to posit “all infinitesimals must be tagged with what an infinite number of them adds up to” precisely because if you don’t do this then you get things like the contradiction we’re discussing.

This is akin to tagging/defining something as “1/3 but when you add three of them you get 4”, or “∞ but when you add a negative number to it you get 0”. You can define whatever you like, and play around with the implications, but that doesn’t mean it somehow always applies.

A hyperreal “infinitesimal”, specifically tagged to add up to a specific number, isn’t what I was utilizing and so it isn’t relevant. If you say “let’s make a system called onesietwosie where we define X as 1 and Y as 2 so X=1 and Y=2”, that’s great but that doesn’t mean you then look at all other equations that use X and Y and say “no no the onesietwosie system tells us X here means 1 and Y here means 2”.

>>16182805
>>16183657
>>16183661
Your core contention is that something divided an infinite number of times would be differently sized depending on what you started with. We can tell that this isn’t correct since what you start with doesn’t change the result if you multiply things by infinity, and division is simply the inverse of multiplication.

You can always keep showing subsets of infinity that are the same size as the whole. For instance, there are as many even numbers as whole numbers. There are as many multiples of 4 as there are even numbers. There are as many multiples of 8 as there are multiples of 4. There are as many multiples of 16 as there are multiples of 8. There are as many...

Even though you’re dividing this by half in a sense, it remains the same size, and you can keep doing this endlessly and it will never change size.

This is essentially what defines infinity: this notion of changes like this not actually changing its size.

So we see from that that (∞*1)=(∞*2)
Which means (1*∞)=(2*∞)

x/y is equivalent to y*(1/x)
So 1/∞ = ∞*(1/1)
And 2/∞=∞*(1/2)

Just as the quantity of even numbers is equal to the quantity of positive whole numbers despite the fact that you could frame it as being half, ∞*(1/1) and ∞*(1/2) are equal quantities. If you had index cards labeled with all of the positive whole numbers and index cards labeled with all of the even numbers, you could simply erase and relabel the ones labeled with even numbers with the whole numbers and the two would be identical.

The issue is that part of your intuition is right: it must be bigger, and we can prove that. But it must also not be bigger, and we can prove that. That’s why it’s contradictory.

>>16181957
why are you so gay so as to use such non-standard notation for the standard that is non-standard analysis?, what compels you to use "∞" and "1/∞"?

>>16180378
Too bad a fully developed theory with repeatable experiments is a much higher standard than some silly mythological anecdotes involving magic medicine men.

>>16179659
>Black is generally considered colorless
Black appears to be universally considered a color, https://www.merriam-webster.com/dictionary/black for instance defines it as "having the very dark color of the night sky or the eye's pupil:of the color black".

>I wasn't so I don't know why you try to change the subject
You certainly seemed to be; you talked about "the set of numbers", hence my comment about numbers taken as entities in of themselves, using the specific number 4 as an example.

>And what is the mathematical word for and endless set?
I don't think there are such things. Sets are completed entities by definition, no?

>Because ∞ is not a number
Right, this is what Finitism holds: ∞ isn't an amount that things can really be. It just denotes algorithms with no specified endpoints, essentially

>Only if you arbitrarily pick a random point in time to be year 1.
I don't think that's so, our calendar system has negative numbers (basically, with the BC era) so having 1 AD doesn't seem to effect this point.

>>16179659
>>16184479
>Then what is the upper limit of its volume if its not infinite in nature?
We really don't know for sure, though it seems likely that spaces of any specified finite size should be possible.

Again I think you're having a real hangup with the difference between potential infinites and actual infinites, which are radically different things. Can you tell me what the difference is between these two concepts, and which one mathematical Finitism holds is possible.

>No, the symbols are all predefined by the radix of the base of the counting system and it has no stopping point because there is no upper limit to the possible combination
I find it odd that you prefixed this with "No" - why do you feel this contradicts what I said?

>is no finite number of potential word choices because they are infinite
The word "potential" there is the key. A "potential infinite" just means something that could theoretically keep going or growing. Finitism has no issue with this since it always remains finite.

An actual infinity is what Finitism objects to. An actual infinity is what you would have if, say, you DID have a book that contained all word choice combinations or a complete list of all numbers. That is what Finitism derides as logically impossible.

>>16184483
You obviously have no idea what you are talking about and can't describe the difference yourself because its nonsense, there is no actual infinity vs potential infinity, all infinity means lack of limits, to limit that to some actual realized number is just shear lack of understanding of what you are talking about and the babbling nonsense that results from such a state.

>Wow, this is very dynamic

>>16185616
>there is no actual infinity vs potential infinity
This is a very widely acknowledged and discussed distinction anon. Some examples:
-https://math.vanderbilt.edu/schectex/courses/thereals/potential.html

-https://en.wikipedia.org/wiki/Actual_infinity

-https://sites.middlebury.edu/fyse1229pisapati/mathematical-work/potential-infinite-v-actual-infinite/

And so on. There is a vast amount of discussion on this. It's somewhat rare to see an extended mathematical discussion about infinity where this difference ISN'T discussed!

>>16186022
There are plenty of retarded people making links talking about base-pi too but that is also obvious bullshit as no one will ever actually show how to count from 1 to 10 in pi steps.
Also your links aren't even about actual math, the first one starts out by saying he isn't even a researcher and if you follow his profile, he links to some site call leftymathprof and says he isn't even involved in math anymore while your second link is some retarded derivative "philosophy of math" bullshit that doesn't even try to come off as actual legitimate math.
Also you still can't even discuss it in your own words or say how your semantic wankery has anything to do with the conversation because you clearly have no idea what you are talking about.

>>16174216
This but unironically.

>>16177553
>Things I can't interact with do not exist
Non sequitur.

>>16174301
You can't divide by infinity. You can take the limit, as x approaches infinity, of a real number divided by x, and it'll yield an answer of 0.

>>16186034
>There are plenty of retarded people
My man this is extremely well established by whatever you could conceivably consider to be a good and well-informed source on mathematics.

I can give you Aristotle talking about this. In his Physics book 3 part 6 (http://classics.mit.edu/Aristotle/physics.3.iii.html) "Now, as we have seen, magnitude is not actually infinite. But by division it is infinite. (There is no difficulty in refuting the theory of indivisible lines.) The alternative then remains that the infinite has a potential existence...When we speak of the potential existence of a statue we mean that there will be an actual statue. It is not so with the infinite. There will not be an actual infinite."

The Stanford Encyclopedia of Philosophy says (https://plato.stanford.edu/entries/infinity/), "there are processes that can be iterated indefinitely, giving rise to...‘potential infinity’. ...Any arbitrary segment can be extended in length (subject to cosmological restrictions mentioned below) or halved without limit, but at each stage we remain within the finite. Time is also potentially infinite in both directions and can be divided without limit. This conception stands in opposition to that of ‘actual infinity’, which would result if some infinite processes could be completed".

Here's a formally published scientific article arguing for a third categorization of infinities besides actual infinities and potential infinities: https://www.worldscientific.com/doi/abs/10.1142/9789814324700_0027

This has been discussed in mathematics since before the Roman Empire existed and is discussed all the time in modern mathematical discourse.

>>16186373
No, its just distracting semantics that have nothing to do with the conversation other than allowing you to go... butt akshully infinity might not be infinity because some philosopher when you don't even understand that you are just talking about infinite divisibility instead of infinite incrementation and neither of them have anything to do with infinity being an actual number rather than it referring to the lack of limit in the number of times you can either add or divide something.

>>16187391
>No, its just distracting semantics
It's really, REALLY not. The reason this distinction came up so early and comes up so often is because it's an absolutely essential one.
Something as simple as writing a book is (generally) potential infinite; there's no set length, you can add as much as you like. Unlike a post here, where there's a strict character limit.

That doesn't mean writing a book is an instance of infinity, obviously; your book is always going to be finite.

An actual infinity would be a book that really listed all of the multiples of 8, or which had a page ∞, or really had a page about each of the whole numbers.

These are of course radically different things, both of which fall into the semantic range of the word "infinite", so it's often very important to be specific about which you're referring to.

>butt akshully infinity might not be infinity
Yes, absolutely, potential infinities are colloquially called "infinite" but it's in a radically different sense than actual infinities are. I've shown six sources now that make this clear. This isn't a rhetorical question: what specifically do you need to see to show you that this distinction is well-established?

>some philosopher when you don't even understand that you are just talking about infinite divisibility
The most basic introduction to infinity I can think of, the Wikipedia page https://en.wikipedia.org/wiki/Infinity even says that "Aristotle (350 BC) distinguished potential infinity from actual infinity, which he regarded as impossible due to the various paradoxes it seemed to produce", linking to https://en.wikipedia.org/wiki/Actual_infinity which says exactly what I am saying.

>infinity being an actual number rather than it referring to the lack of limit in the number of times you can
Finitism agrees: there can never be any completed infinities, only operations without predefined endpoints.

>>16187630
>your book is always going to be finite.
>An actual infinity would be a book that
You can't immediately contradict yourself and expect to be taken seriously.

>a page ∞
∞ is not a number, it is a limit, get that through your thick water filled skull and you will finally stop talking nonsense and immediately contradict your self every time you try to make a point.

>potential infinities are colloquially called "infinite" but it's in a radically different sense than actual infinities are
No, your source just said potential is the act of dividing endlessly instead of multiplying for an actual, its nonsensical semantics that have been replace by better terminology hundreds of years ago.

Infinity by definition is not complete and never will be, it is an endless limit whether dividing infinitely or adding infinity, your jargon is trash and I already pointed out your wiki link is discarded philosophy, not actual modern math jargon.

>>16187630
And no that is not what finitism is, finitism does not even accept infinity as a limit or sets as having an unlimited cardinality, it posits that all of these things are actually finite.

>>16187648
>immediately contradict yourself
I didn't - successive addition at a finite speed over finite times won't ever yield an infinity. You need an infinity to get infinity: either infinite speed or infinite time or something equivalent depending on the exact context

>∞ is not a number, it is a limit
Do you mean a limit in the sense that term is used in calculus? In that case you agree so I'm not sure what you're disputing; as Finitism says it's something that can be approached but never reached.

Also there things universally called numbers that are infinite, aleph numbers being a prime example.

>No, your source just said potential is the act of dividing endlessly instead of multiplying for an actual
Let's look at how https://en.wikipedia.org/wiki/Actual_infinity summarizes Aristotle's words:

"Aristotle handled the topic of infinity in Physics and in Metaphysics. He distinguished between actual and potential infinity. Actual infinity is completed and definite, and consists of infinitely many elements. Potential infinity is never complete: elements can be always added".

See? Just what I'm saying.

>that have been replace by better terminology hundreds of years ago
If the modern sources I've shown you don't establish that this is the current terminology I'm not sure what could. Do you have a source saying these terms aren't used anymore or something along those lines?

>Infinity by definition is not complete and never will be
I don't think that's so; for instance "the set of whole numbers" describes something that's both infinite and complete.

But if you believe there are no completed infinities...then we agree!

>I already pointed out your wiki link is discarded philosophy, not actual modern math jargon
You did not "point this out", you merely asserted it. The multitude of other sources I presented shows that's not the case. Your reply was just the crass and thin "your second link is some retarded derivative 'philosophy of math' bullshit".

>>16187659
>finitism does not even accept infinity as a limit
It does. This is just a potential infinite, and really it means "does this without a predefined stopping point". The Finitist would emphasize that it can't ever reach that limit which the lazy eight symbolizes.

>or sets as having an unlimited cardinality
It treats such things more along the lines of algorithms. I.E. it doesn't deny that it's coherent to talk about "even numbers" but says acting as if you could actually have a genuine group of them is illogical.

>>16187648
Just curious about infinity as a limit. How does a number converge to a non-number?

>>16188120
Things don't CONverge to infinity; they DIVERGE toward infinity. Like the function y = x2, as you let x get bigger and bigger y gets ridiculous, DIVERGING toward infinity as you keep going.

It sounds as if we're all arguing semantics, only mathematically.

Arguments for the existence of infinite energy often hinge on theoretical, scientific, and speculative concepts. Here are a few:

1. **Quantum Vacuum Energy**: According to quantum field theory, even empty space is not truly empty but filled with fluctuating energy. This "vacuum energy" could potentially be harnessed, offering an inexhaustible source of energy.

2. **Zero-Point Energy**: A related concept to vacuum energy, zero-point energy is the lowest possible energy that a quantum mechanical physical system may have. Since this energy exists even in a ground state, some theorize it could be tapped as a limitless energy source.

3. **The First Law of Thermodynamics**: This law states that energy cannot be created or destroyed, only transformed. If interpreted broadly, it suggests that the universe contains a constant, albeit finite, amount of energy that can be utilized indefinitely through transformation processes.

4. **Dark Energy**: The mysterious force driving the accelerated expansion of the universe could potentially be a source of vast amounts of energy. Understanding and harnessing dark energy might reveal new ways to access seemingly infinite energy supplies.

5. **Infinite Universe Theories**: Some cosmological models suggest the universe is infinite in extent. In such a universe, there might be infinite energy resources distributed across an infinite space.

6. **Multiverse Hypothesis**: If our universe is one of many in a multiverse, then the total energy across all universes could be infinite. This could lead to theoretical possibilities of inter-universal energy transfer.

While these ideas are speculative and not currently practical, they provide fascinating perspectives on the potential for limitless energy in the future.

>>16188094
>yield infinity
Infinity is not a number, your statement is nonsense. Successive addition for all x+1 without yielding to a final number is infinity because endless growth is what infinity means, not a final number.

>Finitism says it's something that can be approached but never reached.
No finitism posits that there is some final finite value that has not yet been reached and you can't +1 to every x, ultrafinitism even says that finite numbers that are arbitrarily large but can still be expressed with digits are nonsensically meaningless.

>aleph numbers
Incoherent and not used as actual numbers, aleph_0 + aleph_0 doesn't actually equal 2*aleph_0 like actual numbers because they don't follow the axioms of arithmetic, they are not actually part of a counting system.

>A source saying these terms
The fact that your own source calls it philosophy instead of mathematics should have been clue enough, but this source doesn't distinguish itself as philosophy instead of an actual branch of mathematics like probability and statistics.
https://en.wikipedia.org/wiki/Infinite_divisibility_(probability)

>See?
Yet you somehow still don't understand that what you just typed only means infinite additive vs infinite divisibility and it doesn't infer some actual number called infinity, it just means adding or dividing endlessly.

>"the set of whole numbers" ... both infinite and complete.
Whole numbers is not a complete representation of value, there are clear geometries like diagonals and curves with lengths that can not possibly be expressed as whole numbers and you can not ever completely write down the set of whole numbers, there is no way to complete it.

>completed infinities
Infinity is never complete its entire definition is about being a stand in for a process that is uncompleteable, but you just contradicted yourself by claiming that whole numbers are a completed infinite set.

>merely asserted it
No, it is definitely in the link that you clearly didn't read.

>>16188110
>It does.
No.
https://en.wikipedia.org/wiki/Finitism
>Finitism is a philosophy of mathematics that accepts the existence only of finite mathematical objects. It is best understood in comparison to the mainstream philosophy of mathematics where infinite mathematical objects (e.g., infinite sets) are accepted as legitimate.
Its literally the first paragraph of your source right where it talks about finitism being a philosophy rather than actually provable mathematics.

>The Finitist would emphasize that it can't ever reach that limit which the lazy eight symbolizes.
No finitists would say its nonsensical to think about endless processes because only finite sets actually exists.

>"even numbers" but says acting as if you could actually have a genuine group of them is illogical.
They would say it is nonsensical to try to talk about the set of even numbers since infinite sets are nonsense in their philosophy.

>>16173674
>mathematical proof of a matter of fact
read Hume bozo

>>16189052
>>16189056
>Successive addition for all x+1 without yielding to a final number is infinity because endless growth is what infinity means
Our discussion has revealed that this is the core issue. I've brought forward source after source talking about this difference between potential infinities and actual infinites.

Here's another which might explain it in terms that are more to your liking: https://www.emerald.com/insight/content/doi/10.1108/03684920810863381/full/html. As it says, "it is known that set theory emphasizes actual infinities. Because each infinite set A={x|P(x)} consists of all elements x that satisfy the proposition P, it means that a perfect tense must be employed here. That is, if a procedure of listing all elements x satisfying the proposition P is used to generate this infinite set A, it is only after this process of listing is exhausted, the set A can be generated".

Does that make sense for what an actual infinity is?

It next says:

"However, on the other hand, in order to avoid the Berkeley paradox, the theory of limits employs the ε−δ and ε−N methods to define infinities and infinitesimals of sequences. So, these methods are completely established on the concept of potential infinities by indefinitely giving bounds..."
And does that clear up what a potential infinity is?

It then discusses how these are different:
"Consequently, the employment of actual infinities and actual infinitesimals is successfully avoided. Therefore, when calculus and its theoretical foundation N∪C∪Z are seen as a mathematical system, at the very elementary stage, as we just described, it has already contained the concepts of both potential and actual infinities."

This really is the core and fundamental issue here: there are two main things people can mean when they say "infinity" which are radically different, with one being logically possible and one not. But I think this paper explained it well. Do you see what I'm getting, now?

>>16189268
No you are just too dumb to understand that what you call actual infinity isn't actually a number its just the act of having x+1 indefinitely while what you call potential infinity is just the act of having x/x+1 indefinitely.

>Does that make sense for what an actual infinity is?
No because x+1 will never get exhausted, a process that can never be exhausted is the definition of infinity, it isn't an actual number or end point, you just don't understand old outdated jargon.

>And does that clear up what a potential infinity is?
It is a retarded wording and like I keep trying to say potential infinity doesn't have anything to do with not actually reaching some final end point, it just means infinite divisibility as opposed to infinite incrementability.

>one being logically possible and one not.
Both are logically possible, you can both increment a count without a necessary end and divide it in half without a necessary final division.

>>16189052
>Infinity is not a number
Not always in its broadest semantic range (since potential "infinity" seems to be causing you a titanic amount of confusion on this point), but there absolutely are numbers that are infinite in size.

For a basic overview of that look at https://www.britannica.com/science/transfinite-number. As it says "Transfinite number, denotation of the size of aninfinitecollection of objects...The size of infinite sets is indicated by the cardinal numbers symbolized by the Hebrew letter aleph...with subscript".

Those are universally referred to as numbers. Do you have a source that says they aren't?

>No finitism posits that there is some final finite value that has not yet been reached and you can't +1 to every x
Bear in mind that those who say it generally emphasize it in a practical sense rather than the abstract mathematical sense some might take them in

>Incoherent
As a Finitist I agree! But these are things of infinite size which are called numbers.

>and not used as actual numbers
Do you have a source that actually says they aren't numbers?

>The fact that your own source calls it philosophy instead of mathematics
No it doesn't? Nothing I've referred to says "but this is just philosophy not actual math" or anything like that. Finitism vs. Infinitism is a disagreement about the philosophy of mathematics so of course this falls into the field of the philosophy of mathematics.

>this source doesn't distinguish itself as philosophy instead of an actual branch of mathematics like probability and statistics
Could you go deeper into this point and what you feel the relevance of that article is?

>what you just typed only means infinite additive vs infinite divisibility

...No it doesn't? Again, it says: "Actual infinity is completed and definite, and consists of infinitely many elements. Potential infinity is never complete: elements can be always added". Where is any mention of addition vs. divisibility?

>>16189052
>Whole numbers is not a complete representation of value
I didn't say it was. I was referring to it ostensibly being a collection of all of the whole numbers.

>and you can not ever completely write down the set of whole numbers, there is no way to complete it
I agree! However an Infinitist might be inclined to reply to this with something like "sure you can bro it's right here: (W)" or the symbol for some other set that includes them. Those really are seen as completed collections of those numbers in their view.

You seem to be a Finitist already, it's just this actual vs. potential infinity issue that's getting in the way of embracing it fully

>Infinity is never complete its entire definition is about being a stand in for a process that is uncompleteable
See? This is my entire point. Remember the discussion goes back to the size of the universe. My point is that it can't have a size that's a completed infinite: if we knew its total size it would be some finite value. Who knows, maybe that value would be increasing, but at any given point in time that would not be completed and so it would be finite.

>you just contradicted yourself by claiming that whole numbers are a completed infinite set

In the same sense that this is one million dollars: $1,000,000. But there's not really a million things there, is there? Of course not, it's just a symbol for an amount. You could make a symbol for a million dollars even in a world that had only two subatomic particles and so actually having that would be impossible.

>No, it is definitely in the link
What is? There I was pointing out that all you said was "your second link is some retarded derivative 'philosophy of math' bullshit". Where does anything actually say this "is discarded philosophy, not actual modern math jargon"?

>>16189056
>Finitism is a philosophy of mathematics that accepts the existence only of finite mathematical objects
M-hm. A potential infinity isn't an infinity that actually exists. Look at https://arxiv.org/pdf/2208.13732 - "The locution ‘potential infinite’ is a technical term, there is no infinity (as opposed to a finite) involved in this concept".

>>16189287
>since potential "infinity" seems to be causing
No the actual/potential semantics causes you serious confusion since it has lead you to falsely believe that there is some actual number called infinity when is not a number, it is an unlimited limit that describes something that doesn't have an end point.

>Do you have a source that says they aren't?
They are not universal referred to as numbers, they have number in their name, but like aleph numbers, they are "numbers" in name only since they can't be used for counting or arithmetic or anything that makes numbers useful in communicating value and are completely incoherent where you end up with the "logic" aleph = aleph * aleph * aleph *...

>Bear in mind
No, finitism is the assertion that infinite objects are not valid mathematical objects.

>are called numbers
You can call anything a number, but alephs, transfinite and the like can't actually be used as numbers and they are not compatible with numerical operations because they are not actually numbers, infinity is a limit, not a number.

>Do you have a source that actually says they aren't numbers?
Do you have a source that shows they are compatible with numbers and can be used to count or do arithmetic or geometry?

>Nothing I've referred to says "but this is just philosophy not actual math"
The page on actual infinity that you provides does say that as its opening sentence.

>deeper into this point?
It has actual mathematical utility and is actually applied to modern theories rather than being pure philosophy that doesn't have applications and can't be used to even count let alone do more advanced numerical operations.

>Where is any mention of addition vs. divisibility?
When they describe how the process of coming to that assumption.
>Actual infinity is completed and definite
Then what is something that is actually infinite and if it is complete, what is its last element and what is the element just before it?

>>16189303
>I didn't say it was. I was referring to it ostensibly being a collection of all of the whole numbers.
You did and you just doubled down
>>16189287
>Actual infinity is completed and definite

>However an Infinitist might be inclined to reply to this with something like "sure you can bro it's right here: (W)" or the symbol for some other set that includes them
No.

>You seem to be a Finitist already
No, they don't believe in infinity as a limit or any use of infinity, they think anything infinite is always incoherent, whereas I understand calculus and series and sets that diverge to infinity.

>it's just this actual vs. potential infinity
Yes because you are very confused about what that means and think it somehow means that infinity is an actual number where that is not at all what it means in this context which is why it doesn't get used any more because undergrads like you are easily confused and go on for days about how infinity is an actual number because thousands of years ago someone used the phrase actual infinity and potential infinity.

>completed infinite:
Infinity is never complete as it is not a number, it is a description of endlessness please get this through your dense waterlogged skull so you stop talking nonsense and I stop having to repeat the truth over and over.

>In the same sense that this is one million dollars: $1,000,000
No, because that can be used like a number and you can divide it in half to have 2 stacks of 500,000, but numerical operations don't apply to infinity because it is not a number.

>"is discarded philosophy, not actual modern math jargon"?
If they are calling it philosophy instead of actually talking about what branch of mathematics it applies to it is obviously just a though experiment that has never actually been fruitful and is not used in the development of modern theories, thus it has been discarded from actual use in the field and its just mental wankery.

>>16189308
>A potential infinity isn't an infinity that actually exists.
It is just as actual as an actual infinity because it is the infinity divisions that some arbitrary value could be divided into as opposed to the infinite additions you could make onto any arbitrary value.

>Atheists: Everything in science is provable! We don't need faith!
>Also atheists: Its time to talk about what's outside the observable universe...

>>16174299
>restricts inquiry into the study of 9 sided triangles
But that's true. It took people thousands of years after pythagoraes to start studying shapes in 4 dimensions or higher.

>>16189326
>They are not universal referred to as numbers
You didn't answer my question anon. Do you have a source that says they are not numbers?

>finitism is the assertion that infinite objects are not valid mathematical objects
Actually infinite objects aren't. Potential infinities are fine. Remember https://arxiv.org/pdf/2208.13732- "The locution ‘potential infinite’ is a technical term, there is no infinity (as opposed to a finite) involved in this concept".

>You can call anything a number
So why be pedantic?

>but alephs, transfinite and the like can't actually be used as numbers and they are not compatible with numerical operations
And yet they're called numbers
Really a number is an amount, and when people refer to (actual) infinity they're referring to an amount, hence seeing things like aleph nought referred to as a number in the literature.

>Do you have a source that shows they are compatible with numbers and can be used to count or do arithmetic or geometry?
For sure, check out a quick intro to doing so at https://mathworld.wolfram.com/Aleph-0.html

>The page on actual infinity that you provides does say that as its opening sentence.
...what? In no way does it say it's somehow an invalid concept or somehow limited to the realm of philosophy and not mathematics. I've shown you multiple mathematical papers that discuss it.

>When they describe how the process of coming to that assumption.
You seem confused. He talked about the difference between an infinity of division (something always getting smaller) and the infinity of addition (something always getting bigger) but called both of these potential infinites. He never says just one or the other is potential.

>Then what is something that is actually infinite and if it is complete, what is its last element and what is the element just before it?
The set of real numbers between 0 and 1, inclusive. Its last element is 1 and its second to last is 0.999...998

>>16189741
>0.999...998
lmfao I knew your line by line posting was tragic. Nice bait.

>>16189338
>You did and you just doubled down
When I say "Actual infinity is completed and definite" I don't mean to imply such a thing actually exists. I mean it in the same sense as I might say "Hamlet wants to kill his father-in-law" or "Bigfoot is hairy".

>No.
Isn't that what the paper I showed you said about sets as modern set theory generally views them?

>they don't believe in infinity as a limit
You're thinking of Strict Finitism/Ultrafinitism, maybe even what's called Extreme Ultrafinitism.
As you can read at the basic introduction at https://en.wikipedia.org/wiki/Finitism, "those who allow potentially infinite objects as classical finitists, and those who do not allow potentially infinite objects as strict finitists: for example, a classical finitist would allow statements such as "every natural number has a successor" and would accept the meaningfulness of infinite series in the sense of limits of finite partial sums, while a strict finitist would not. Historically, the written history of mathematics was thus classically finitist until Cantor".

I think that actually might be the point that solves our entire dilemma here! I'm a Classical Finitist, not an Ultrafinitist. So as a Classical Finitist I don't hold the positions you seem to be disputing. Are you a Classical Finitist too? That would be good news, would mean we would be all settled, I think (^_^)b

>>16189746
It doesn't matter where you stand on the 0.999...=1 debate, if you believe it does then the answer is 0.999...998 and if you don't then the answer is 0.999...999. For the purposes of the discussion it doesn't matter which you prefer

>>16189755
What does "0.999…999" even mean? An infinite series of nines that ends in a nine?

>>16189780
Right

>>16189741
>Do you have a source that says they are not numbers?
Do you have a source that says they can function as numbers and are useful for counting or any other numerical operation?

>Actually infinite objects aren't. Potential infinities are fine
Nope, nowhere on that finitism page does it make any distinction, that is your head canon.

>So why be pedantic?
I don't know, why do you think that just calling something a number makes it as useful as a number?

>And yet they're called numbers
I can call words idea numbers, it doesn't make them actually work like numbers and obey the rules and operation of arithmetic.

>when people refer to (actual) infinity they're referring to an amount
Retarded people like you who don't understand that infinity refers to the upper most upper limit rather than any specific number no matter how many times it is explained to you.

>https://mathworld.wolfram.com/Aleph-0.html
That source doesn't have a single operation or show how you can add, subtract, multiply, or divide using an aleph number because it is not actually useful as a number, you clearly don't even understand what your own link is saying.

> In no way does it say it's somehow an invalid concept or somehow limited to the realm of philosophy and not mathematics.
It definitely doesn't say it is actual math or tied into any specific theory.
>I've shown you multiple mathematical papers that discuss it.
No, you showed a bunch of popsci sources that say the same thing and never actually show it can be used with other numbers or in any numerical operation or equation.

>The set of real numbers between 0 and 1
Except earlier you called that a potential infinity while only the set of real numbers was actual, you don't even understand your own sources and now you think that 1-0 equals infinity because you are completely retarded.

Also ... means forever, you can't have more numbers after a ..., you literally don't understand the basic intro level infinity.

>>16189927
So then 0.999...998 means an unlimited series of nines that ends in an 8?

>>16189754
>When I say "Actual infinity is completed and definite" I don't mean to imply such a thing actually exists. I mean it in the same sense as I might say "Hamlet wants to kill his father-in-law" or "Bigfoot is hairy".
So you are saying you don't actually know what you are talking about?

>Isn't that what the paper I showed you said about sets as modern set theory generally views them?
No.

>You're thinking of Strict Finitism/Ultrafinitism, maybe even what's called Extreme Ultrafinitism.
No, as I already explained, that is when you believe that exceedingly large finite numbers aren also nonsensical and even though you can write 1e25000, doesn't mean it is an actual value that can mean anything in reality.

>Are you a Classical Finitist too?
No, I think it is a retarded term for pedantic people like you who clearly don't understand basic math.

>>16190680
>as I already explained, that is when you believe that exceedingly large finite numbers aren also nonsensical
That's not really something you explained, just something you said you believed Finitism entailed. Doesn't even that basic overview I linked to though explain that there are different types of Finitism, and you're thinking of a specific kind?

>is a retarded term for pedantic people
My man this is the common terminology.

The Stanford Encyclopedia of Philosophy says in its article on Finitism in Geometry at https://plato.stanford.edu/entries/geometry-finitism/ that "Most constructivists [i.e. Finitists] allow for the potentially infinite, i.e., if a procedure or algorithm will (provably) terminate at some moment in the future, then the outcome is accepted as constructable...Strict finitism wants to go one step further and argues that an indefinite outcome is not be accepted as an outcome".

Even the article critical of Finitism at https://vixra.org/pdf/2206.0117v1.pdf says "Classical finitists allow for the
Aristotelian 'Potential infinity'" as opposed to "Ultrafinitists
reject the notion of potential infinities. But more than
that, they only accept numbers that are physically
realizable".

Making this distinction isn't being pedantic, its highlighting the difference between these two distinct positions.

Like I said, I think you're one of us but just didn't know it! A Classical Finitist (like me), not an Ultrafinitist.

>>16173665
>good topic
>immediately derailed with garbage

this is 4chan, even on /sci/

>>16173665
things that people thought were infinite turned out to be finite.
mathematically things appear to be infinite but irl ain't. I dont think the universe is infinite, the same way there is no infinite source of energy in the universe that allows the universe be infinite
If there's no infinite source of energy, then what would be making the universe to be infinite?

>>16189927
I feel weird stating something so blisteringly obvious, but you can't have an infinite series that ends. That's a contradiction in terms. Infinite series, by definition, do not ever end.

>>16191628
>I feel weird stating something so blisteringly obvious, but you can't have an infinite series that ends
Sure you can, there's an infinite quantity of real numbers between 0 and 1 inclusive. It has an endpoint, 1.

>>16191340
This is a routine shitpost, not a "good topic".

Your philosophical commitments predetermine the answer you're allowed to give

>>16191646
how so?

>>16191613
Arguments for the concept of infinite energy often emerge from theoretical physics and speculative ideas about the universe. Here are some refined arguments that delve into these ideas:

### 1. **Cosmological Theories and Dark Energy**
Dark energy is a mysterious force driving the accelerated expansion of the universe. If harnessed, it could potentially offer an enormous and seemingly endless source of energy. However, our current understanding of dark energy is limited, and practical methods to harness it are purely speculative.

### 2. **Quantum Field Theory and Vacuum Energy**
Quantum field theory suggests that even "empty" space is filled with energy due to quantum fluctuations, known as vacuum energy. In theory, if we could find a way to tap into this vacuum energy, it could provide a vast amount of energy. However, on macroscopic scales, this energy tends to average out, and current technology does not allow us to harness it effectively.

### 3. **Black Hole Energy Extraction**
Theoretical models, such as the Penrose process, propose methods to extract energy from rotating black holes. By sending material into the black hole's ergosphere, it is theoretically possible to extract more energy than the mass-energy of the material sent in. While this is far from practical with our current technology, it provides a theoretical basis for potentially vast energy sources.

>>16191613
### 4. **Tidal Forces and Gravitational Energy**
The gravitational interactions between celestial bodies can generate significant energy. Tidal forces, such as those between the Earth and the Moon, result in tidal heating and energy generation. In a broader context, harnessing gravitational interactions in space could potentially yield substantial amounts of energy over long periods.

### 5. **The First Law of Thermodynamics and Energy Transformation**
While the First Law of Thermodynamics states that energy cannot be created or destroyed, it implies that energy can be transformed indefinitely from one form to another. This principle underlies the idea that as long as there is a mechanism to efficiently transform energy, we could maintain a continuous flow of usable energy, provided we manage entropy and energy losses effectively.

### 6. **Renewable Energy Sources**
On a practical level, renewable energy sources such as solar, wind, hydro, and geothermal energy provide a continuous influx of energy. While not infinite in the absolute sense, these sources are effectively inexhaustible on human timescales. The Sun, for instance, will continue to provide solar energy for billions of years.

### 7. **Theoretical Frameworks and Advanced Physics**
Advanced theoretical frameworks, such as those involving higher dimensions, string theory, or multiverse theories, suggest that our universe might be one of many. These frameworks often propose the existence of vast, untapped energy sources. While these ideas are highly speculative, they open the door to the possibility of discovering new forms of energy in the future.

### Conclusion
While the concept of truly infinite energy remains largely within the realm of theoretical and speculative physics, several arguments suggest potential pathways to vast, nearly limitless sources of energy.

>>16191613
These ideas, ranging from dark energy and vacuum energy to renewable energy sources and advanced theoretical models, inspire ongoing research and exploration into the nature of energy in our universe.

What a stupid thread. Infinite objects exist because they are useful in mathematics. The inquiry into foundations of mathematics have put to rest the idea of one perfect, universal mathematical universe.
By arguing metaphysics you gain no insight into either the physical or the synthetic. Even intuitionists peddled their ideas as a way to solve certain problems and when more useful systems were able to answer these problems in an interesting way, intuitionism fell into obscurity because solutions it offered amounted to ignoring these potentially interesting problems.
It's incredibly ironic that finitists and naturalists must frame their arguments ideologically and platonists are the ones who stick with stuff that just works and focus on the actual meat of the subject.

>>16174216
yes that would be so amazing

>>16173665
I'm partial to the idea that the universe expands onto itself.

>>16173674
If the universe isn't infinite, then what became before the universe and so forth? What exactly is "nothing"?

1

>>16194169
Seems it could be that both "infinite" and "nothing" are fictional concepts.

>>16173665
>universe is infinite
>Redditors still think we're the only sentient lifeforms

>>16174081
If there are an infinite number of whole numbers, and an infinite number of decimals in between any two whole numbers, and an infinite number of decimals in between any two decimals, does that mean that there are infinite infinities? And an infinite number of those infinities? And an infinite number of those infinities? And…(infinitely times. And that infinitely times. And that infinitely times. And that infinitely times. And…)…

>>16194798
>cheek muscle twitch
not even close to making me lose. gg wp rere?

>>16194798
Numbers aren't things that independently exist. Numbers are amounts and there are amounts _of_ certain things, but amounts don't exist apart from what they're amounts of

>>16195159
>don't exist
please rephrase.

>>16173665
"Infinity" is only allowed in invented abstractions. It's literally not real. Regardless of your religious beliefs (or lack of), if you subscribe to the universe beginning 13.7 billion years ago then by definition it can't be infinite. If you claim the universe has been around forever, you can claim it's infinite. But if you claim it started 13.7 billion years ago and are also saying it's infinite, you are making an even more grandiose claim than "god did it". Things like space-time bending in on itself and dimensional shenanigan's to give the illusion of infinity don't count, the same way a circumference of a circle isn't "infinite".

Realistically, the universe is finite as is limited by its properties. As soon as you say "everything in the universe + 1" you've automatically entered fictional territory.

>>16195213
>It's literally not real.
prove it

>>16195213
the big bang wasn't necessarily the beginning of the universe.

>>16195213
Arguments for infinite complexity often involve concepts from mathematics, computer science, physics, and philosophy. Here are some refined arguments that support the idea of infinite complexity:

### 1. **Mathematical Systems and Fractals**
Mathematical systems can generate infinite complexity through simple rules. Fractals, such as the Mandelbrot set, exhibit self-similarity at different scales, revealing intricate patterns that continue infinitely as you zoom in. The complexity in fractals is not just repetitive; it reveals new structures at every level of magnification.

### 2. **Algorithmic Information Theory**
Algorithmic information theory explores the complexity of strings (or sequences) based on the shortest possible description of the string (its algorithmic complexity). Some sequences, like the digits of π, are infinitely complex because no finite, simple algorithm can predict every digit. This suggests an intrinsic infinite complexity in certain mathematical constructs.

### 3. **Emergence and Self-Organization**
In complex systems, simple rules and interactions can lead to emergent behavior that is vastly more complex than the sum of its parts. Examples include the behavior of ant colonies, the formation of galaxies, or the dynamics of ecosystems. These systems show how infinite complexity can emerge from finite, simple components through non-linear interactions and feedback loops.

>>16195213
### 4. **Theoretical Physics and the Multiverse**
In theoretical physics, concepts like the multiverse suggest an infinite number of possible universes, each with its own physical laws and constants. If our universe is just one of many, the diversity and complexity of all possible universes combined can be considered infinite. This introduces a level of complexity that transcends our own universe.

### 5. **Biological Evolution**
The process of biological evolution, driven by natural selection, mutation, and genetic recombination, creates an ever-increasing complexity of life forms. The diversity of life on Earth is a testament to the potential for infinite complexity, as new species and ecosystems continually emerge and evolve in response to changing environments.

### 6. **Computational Systems and Artificial Intelligence**
Computational systems, especially those involving artificial intelligence and machine learning, can exhibit behaviors and solutions that are not explicitly programmed. The iterative learning processes of AI can lead to unexpected and highly complex results, suggesting a pathway to infinite complexity through continuous learning and adaptation.

### 7. **Cultural and Technological Evolution**
Human culture and technology evolve in ways that generate increasing complexity. The accumulation of knowledge, technological advancements, and cultural innovations build upon each other, leading to a trajectory of infinite complexity. Each new discovery or invention adds layers of complexity to our understanding and capabilities.

### 8. **Philosophical and Metaphysical Perspectives**
From a philosophical standpoint, the concept of infinite complexity can be considered in terms of knowledge and understanding. The idea that there will always be more to learn and discover, that no matter how much we understand, there will always be deeper layers and more intricate details, supports the notion of infinite complexity.

>>16195213
### Conclusion
Infinite complexity arises from various fields and concepts, demonstrating how simple elements and rules can generate endlessly intricate patterns and behaviors. Whether through mathematical systems, emergent phenomena, theoretical physics, biological evolution, computational systems, cultural evolution, or philosophical perspectives, the idea of infinite complexity captures the boundless nature of discovery and understanding in our universe

>>16195222
>>16195223
>>16195224
These are all human conceptions or have finite limitations, and don't speak to infinity being a fundamental property of nature or the universe. The fact I can sit here and say "infinity + 1" does not imply infinity is real, it just implies that we have an abstraction of an idea. π is technically not even infinite, because it's certainly less than 3.142. The concept of a perfect 2D circle and the ratio between its diameter and circumference is not a real thing in nature. It's a useful tool for practical real-world purposes, but it's ultimately all pure abstraction. There's no version of infinity that we've invented that has any real meaning. The concept is basically numerical philosophy.

>>16195190
Aren't casually potent