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https://en.wikipedia.org/wiki/Halting_problem
https://en.wikipedia.org/wiki/Computability_theory
https://en.wikipedia.org/wiki/Turing_completeness
Why THEY igore all this?
>>
If you think CS is bogus, you'll be mind blown by ZFC theory
https://www.youtube.com/watch?v=U75S_ZvnWNk
>>
>>68415469
>Why THEY igore all this?
What? Those are well known by everybody.

>>68415495
Reals don't exist in our reality, so nothing to worry about.
>>
>>68415469
And by ignore you mean teach it first year?
>>
>>68415530
How can we use something that doesn't exist?
>>
>>68415469
>field has unsolved questions
>field is a scam
What?
>>
>>68416017
actualy all questions is solved, and answer is negative
but THEY still try to do somesting
>>
>>68416159
we have:
1. exist problems about Turing Mashine unsolvable by Turing Mashine
2. "functional programing" and all mathrmathic theories is equall to Turing Mashine or lower in hierarhy (i can solve you, you cant solve me, you is lower)
3. THEY still trying make "scaince" about Turing Mashines, but Turing Mashines is scaince itself
-------------------
CS - same lake philosophy but deffently not scaince
>>
>>68416255
>(i can solve you, you cant solve me, you is lower)
even more:
if some formal theory can solve something it also can be solved by Turing Mashine (but faster)
Turing Mashine cannot solve about Turing Mashine -> not exist any formal theory for sloving about Turing Mashine
>>
>>68415469
Because Networking exists. What good is a computer in this day and age if it can't communicate with other computers.
>>
OP is a flat earther, types and posts exactly like one.
>>
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the only legit way to make math scaince now is to write theories in
https://en.wikipedia.org/wiki/Coq
>>
the only scaince nowadays: computer programm!
books is not scaince!
if (You) cannor into programming (You) in not scaintist! (maybee colledje level retard, i dont know)
deal with it!
>>
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>>68415685
>>
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>>68415495
all the scaince is Religious Belive System
but this Scainse Religion gives superpower to human who own it.

Practice is the truth criterion - V.I. Lenin
>>
>>68416255
>>68416441
>>68416550
>>68416605
>>68416366
>>68416159
I'd just like to point out that all of these posts were written by the same person, he's samefaging, and the post/IP count proves it.
>>
>>68416710
thanx, will read all this
>>
>>68417108
IP count didn't go up with this post. OP is a mentaly ill functional illiterate who's being a retard samefag in his own thread for attention.
>>
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>>68417142
>>
>>68417162
I don't know why it is you have fake conversations with yourself on the internet, but you need to stop, and if you can't, you need to get somone to help you do it. Perhaps you've kidded yourself into believing that it's okay because it's only "ironic", but that doesn't change a thing. In fact, it might make it worse. Stop making yourself look like an idiot, and stop pretending you're replying to me for any other reason than because you want me to reply back. Just cut the bullshit and ask next time you want to talk to somone, it'll make it go a whole lot easier. Oh, and there's nothing wrong with being mentally ill.
>>
>>68417228
also (You) suck
>>
Is this today's schizo thread?
>>
>>68417486
Yes
https://en.wikipedia.org/wiki/Schizoid_personality_disorder
>>
The best messaget in this tread:
>>68416255
>>68416441
>>68416550
>>68416605
>>68416366
>>68416159
>>
>>68415469
Yes, it is
>>
>>68415685
We can't, but the mythematician community has brainwashed generations of students to believe in the reals and other infinite sets.
>>
>>68418397
>hurr dur muh reals aren't real
So? Division has worse problems, but it's still useful enough to use.
>>
>>68418397
Practice is the truth criterion - V.I. Lenin
Yes, this is religion, but bestone
>>
>>68418853
Huh? Division can be defined for rational numbers with no problem. Division of real numbers is of course nonsense since reals are nonsense.
>>
>>68415469
>Why THEY igore all this?
That's something everyone in CS learns early on, fuck off.

> Inb4 all science sucks because no scientists can produce another big bang at will
>>
>>68419569
>That's something everyone in CS learns early on, fuck off.
So why THEY igore all this?
>>
>>68416710
His “unique” and some how cute spelling didn’t give it away?
>>
>>68419569
>another
>implying
>>
>>68419622
They don't. Why would they?

I'm sure you will find some individual who ignored it, but you also would find tens of thousands of humans that leisurely walked their face into something despite having almost lifelong daily practice at walking...
>>
>>68419569
>scientists
Go back to (You)r https://en.wikipedia.org/wiki/Coq
(You) not finished with coding books into computer
>>
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>>68419668
THEY stiil truing to solve https://en.wikipedia.org/wiki/NC_%28complexity%29
lol retards
>>
>>68419684
> Go back to (You)r https://en.wikipedia.org/wiki/Coq
Obviously not everyone uses this even if they stay in science rather than switch over to engineering.

> (You) not finished with coding books into computer
Of course not. And even if it was finished, training programmers at how not to suck at programming also will be a thing that keeps academic comp.sci busy for maybe another 200+ years at the rate this is going.
>>
also all
https://en.wikipedia.org/wiki/Computational_complexity_theory
is useless, THEY calculate compexity at limit of infinity
it soo far from reality
WHAT THE BEST SORTING ALGO FOR SORT 4 VALUES?
Computational_complexity_theory dont have any answer, only optimising compilers have
-------------------
THE TRUTH - only legit from of knolige now is a computer prorgamm
>>
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>>68419771
>training programmers
it imposible
some people can some cannot it genetical
>>
>>68419547
Reals can also be defined with no problems. That's not the issue.
It's when it doesn't work and why.
>>
>>68419903
Reals don't work ever because they aren't well-defined.
>>
>>68419968
Pi work well
>>
>>68420283
Please exhibit a logically sound construction of the real number pi.
>>
>>68419968
Reals are well defined.
Except for undef you get with divide by zero (and operations on the result). Which is just a friendly way of saying they're not going to attempt to make conclusions about how to handle that odd case. You get to chose. Otherwise it's no different from integer math. You just need to understand them.
>>
>>68420292
https://en.wikipedia.org/wiki/Pi
>>
>>68419968
>>68420326
https://youtu.be/k12BJGSc2Nc
This is a good explanation if you need it.
>>
>>68420292
Do you accept the axiom of choice?
>>
>>68420326
They aren't. Using any "construction" of real numbers (eg equivalence classes of Cauchy sequences or Dedekind cuts) it can be shown that all reals are the same. Also what the fuck are you blabbering about division? Stay on topic retard.

>>68420334
I see no by-definition construction. The definition section assumes reals exist.

>>68420341
Floating points are all representable by finite-precision rationals anyway. This is irrelevant.

>>68420359
I reject infinite (no such thing, see) sets. Talking about AC is kind of irrelevant when you don't have infinite sets (which nobody has, as they don't exist).
>>
>>68420326
What is the use of defining something if you define it as the result of a process that can't ever be carried out to completion?
>>
>>68417486
>>68417558
>everyone I don't like is mentally ill
>>
>>68420376
>I see no by-definition construction. The definition section assumes reals exist.
reals exist cose Pi exist
>>
>>68420376
>Cauchy sequences
No, there are different representations of the same real, that doesnt mean "they are all the same".

Go read a basic undergraduate textbook on analysis.
>>
>>68420376
>I reject infinite (no such thing, see) sets
AC lets you define infinite sets.
Maybe infinite sets don't need to exist for us to work with their representations in a consistent logical system.
Maybe pi doesn't needs to exist (for physicalist definitions of "exist") for us to prove properties about it and use it as hypotheses in other proofs.
Maybe we don't need to create a finitist theory of mathematics, but a meta-theory or way of understanding and interpreting ZFC that satisfies finitists.
I mean, if we are gonna get pedantic, the natural number "1" doesn't exist either. According to nominalism, it's just a bunch of pixels on my screen, separate from your own bunch of pixels on your screen. We chose to conceptually group them together, but they aren't the same thing.
>>
>>68420414
The quantity Pi exists as the circumference of the unit circle. But is it sufficient to consider it a number? Opinions vary. If a number can only be the result of a finite-time algorithm, then you can doubt of the "number-ness" of pi.
>>
>>68420536
Finitists haven't been able to come up with a consistent logical system for math without infinities.
>>
>>68415469
These are theorems that show the limits of the theory, they do not tell anything about the consistency of the theory nor have practical use.
Because the halting problem is undecidable doesn't mean you cannot decide halting in particular cases (and by particular, that is, most of practical cases).
>>
>>68420499
I said equivalence classes. But the point is you need infinite resources to distinguish two "different" reals from each other, because the sequences can begin to differ at arbitrarily high tails.
>>
>>68420536
>implying circles are physical
Pi and the reals make a great approximation for a macroscopical universe with a very very high capability to be subdivided. Pi itself has to be a number as a specific quantity describing the geometrical space of a circle. No other quantity can take on it's role.
>>
>>68420633
What are circles if not physical? I hope for your sake you're not a Platonist, as Platonism is a totally broken philosophy. All circles that exist are physical circles, and for all physical circles the arc length of their circumference is a rational number.
>>
>>68418397
What? Is this whole thread bait or is this a new kind of retardation?
>>
>>68420611
also the
https://en.wikipedia.org/wiki/Computational_complexity_theory
is useless, THEY calculate compexity at limit of infinity
it soo far from reality
WHAT THE BEST SORTING ALGO FOR SORT 4 VALUES?
Computational_complexity_theory dont have any answer, only optimising compilers have
-------------

even more:
if some formal theory can solve something it also can be solved by Turing Mashine (but faster)
Turing Mashine cannot solve about Turing Mashine -> not exist any formal theory for sloving about Turing Mashine
>>
>>68420633
You could chose to just leave distance and length of a curve undefined.
>>
>>68420674
yes
>>
>>68415495
baesd Wildberger poster
>>
>>68420611
THEY stiil truing to solve https://en.wikipedia.org/wiki/NC_%28complexity%29
lol retards
>>
>>68420558
That's the other way round actually: without "infinities" (there's only one sort of infinity despite what Cantor's invention with diagonal proof), you can only make consistent systems, but they're necessarily incomplete. Most formal systems trying to be complete are either already proven inconsistent (like naive set theory) or are not proven yet to be either consistent or not (like ZFC).
>>
>>68420611
Computability theory studies less powerful systems than Turing complete ones as well (for example, systems in which all functions are total) and decidability in those systems. On the other hand a lot engineer types just happily do everything in Turing complete systems and scoff at the notion that some Turing incomplete language could be useful. Probably because they have been brainwashed that domain specific languages are "evil" and make code "unreadable" and everything should be programmed in a "general purpose" language (of course there is no general purpose language as the only correct choice is to make the language match the problem domain).
>>
>>68420735
>On the other hand a lot engineer types just happily do everything in Turing complete systems
Cose they can into Turing complete systems, Turing incomplete langiages for brainlets
>>
>>68420783
Is HoTT Coq for brainlets?
>>
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The best messaget in this tread:
>>68416255
>>68416441
>>68416550
>>68416605
>>68416366
>>68416159
>>
>>68420735
That's a sensible reading of what the study of computability is about. Too many people talking about it try too hard drawing philosophical consequences from the foundational results of the field.
>>
>>68420798
>Coq
is turing complete
>>
>>68420801
>philosophical consequences from the foundational results of the field.
if result is negative only philosophical shit can be prodised
>>
>>68420807
Guaranteed termination--nope.
>>
>>68420734
Interesting. But that's why I said "for math", I meant one that is powerful enough to do useful math with.
>but they're necessarily incomplete
Isn't ZFC proven incomplete too?
>there's only one sort of infinity despite what Cantor's invention with diagonal proof
Why do you say that?
>>
>>68420829
>Guaranteed termination
nor Guaranteed, "the stratrgies" can work infinity
>>
>>68420855
Dude, why do you write like such a retard?
>>
>>68416441
>not Metamath
shiggy
>>
>>68420872
>Metamath, Written in ANSI C
looks legit
>>
>>68420919
The language the verifier is written in is pretty much irrelevant because the actual body of proofs based on ZFC and predicate logic is on a single plaintext file of about 30 megabytes
>>
>>68420919
this, if it's not CompCert certified C, I don't trust it
>>
>>68420956
>body of proofs based on ZFC and predicate logic is on a single plaintext file of about 30 megabytes
math need serious refactoring
>>
>>68420968
It's called Homotopy Type Theory
>>
>>68420993
>Homotopy Type Theory
complety useles for programming
>>
>>68421009
This was about refactoring math, not programming
>>
>>68421019
at least it something repeatable
just rewrite all the math books in it for start
>>
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>/g/ can't into philosophy of science
Mathematics exists, as does God.
>>
>>68421370
buy (You) can only into the bibble
>>
>>68421370
>>>/pol/
>>
>>68420854
>hat's why I said "for math", I meant one that is powerful enough to do useful math with.
There are formal systems which are both consistent and complete, like first-order logic, which, obviously, you can't make arithmetic with. Systems able of such a feat fall under Gödel's incompleteness theorems. And as such, ZFC can prove its consistency only within an higher-order system, and so on... And yeah, it is incomplete by the same theorems.
>>there's only one sort of infinity despite what Cantor's invention with diagonal proof
>Why do you say that?
The interpretation of uncountability of the reals from Cantor's diagonal argument derives from an infinite procedure, which cannot be taken as a proof for constructivists. Cantor's argument is fishy enough for some not to consider his whole theory of infinite cardinals seriously.
>>
>>68416605
Science predicts the future.
Religion changes the past.
>>
>>68421431
constructivists are usually ok with infinities
it's the law of excluded middle they don't like
surely the diagonal argument is constructive, right?
>>
>>68421781
You're right, the controversy with the diagonal argument has to do with finitivism instead of constructivism.
>>
>>68421009
Actually it's probably the most useful type theory for programming thus far because it has a built in notion of abstraction and reuse. It's useful for maths for the same reason.





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