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Reposting from the previous thread.

I have v1 initial velocity, v2 final velocity and d distance and want to find a(x) acceleration that will change the velocity over that distance. Finding constant acceleration is pretty easy using basic acceleration equation. However I would like to ease the movement a bit by applying most of the acceleration only on the end or beginning of the path. Initially I used some easing functions with constant "area under graph"(integral?) but the problem is that same final change in velocity does not imply same displacement.

What kind of functions could I use for a(x) so that v(t) remains at v2 and disp(t) at d? Are there any functions like that except for constant value?
Or, if I choose some curve/easing function, how do I scale it to use as a(x), and how do I choose t to make sure that the velocity change and displacement matches my inputs.

Why does my bald spot not feel bald when I touch it? (My hair is shaved (less than inch) but feels mostly the same density of fuzzy hair. I know I have a bald spot. That's what prompted me to shave it in the first place.)

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>>16180665
I'm pretty sure this can be done. Pic related, I managed to find t(x) that works for any case, but the c(used for scaling the easing function to get a(x)) is just fine tuned for these specific v1, v2 and ease(x)(but works for any d). And so, my problem becomes, how do I find c for any v1/v2/ease?

Where on my throat can I cut/stab to permanently lose my ability to speak (without cutting artery)?

>>16180594
sexo

>>16180665
>You start at the origin of a (x,t) axes graph and you want to draw a curve whose final point ends when it crosses the x = d vertical line, with the conditions that the slopes of the initial and final points are given. Do you really not see how vague this curve is?

If you divide a 2D-shape into N pieces so that all pieces are the same shape as the original shape and also all pieces are the same size, what are the possible values for N?

>>16180984
Unknown since it is dependant on the shape and it's axes of symmetry.

>>16181066
Well what about we ask about just three pieces. Does such a shape exist that you can divide it into three pieces of equal area so that the pieces are congruent with the original shape?

I need help coming up with the right terms for this situation:

Suppose a sequence of letters which may arrive out of order from when they were sent (postmarked). I call the letter that was sent most recently the "latest", but what should I call the larger group of letters that were formerly the "lastest" at any time? Ironically, the letters excluded from that group for arriving after a more recent letter might well be called "late".

In math this is strict monotonicity. An analogous concept is record progression. For example, a sequence of race times. Most performances don't set new records, but there are a subset that do, culminating with the current fastest.


Naming the three groups "latest", "latests", and "late" seems like it might be confusing and retarded. Can you come up with anything better? You're competing with /lit/ btw. I'm curious who will give me the better answer.

>>16180954
I'm not sure what are you trying to say here, anon. Did you replied to the right post or just misformatted the post? Also see >>16180785, it might make more clear what's the main problem here.

>>16180984
>>16181075
all values of [math]n[/math] are possible, take a [math]\sqrt{n} : 1 [/math] rectangle
more interesting shapes are possible for some values of [math]n[/math]
https://en.wikipedia.org/wiki/Rep-tile

I don't get what's going on here
>In an isosceles triangle, the base is 6 cm and the two equal sides are 5 cm. Does there exist a triangle which has the same circumference and area?
I used a system of equation

2*5+6=16
(5*6)/2=15

2x+y=16
xy/2=15

y=16-2x
8x-x^2=15

8x-x^2-15=0
x1,x2=5,3
y=10-2*3=10
ans: A triangle with the sides 3 and base 10.

But they're giving a fucked up answer:
The equal sides are (15-sqrt(13))/2, base 1+sqrt(13)

How did they get to this answer?

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Why is the lower limit of [math]\rho[/math] = [math]asec(\phi)[/math]? ;-;
Is there any way to get without drawing the diagram?

>>16181213
You calculate the minimal value of rho that is in D.

[eqn] \rho = \frac{z}{\cos(\theta)} \geq \frac{a}{\cos(\theta)} = a \sec(\theta)[/eqn]

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I did a bit of biology and I understand a bit of neuroanatomy from a psych background, but whats the best way to learn what all the terms in this screenshot mean? And like properly learning about them. I remember trying to research g protein coupled receptors a while ago and getting overwhelmed

yeah i know, midwit or whatever, i just want to learn about this stuff, but googling one term brings up many more and it becomes a bit tricky to stay on top of everything

I want to prove that if a<=b<=c<=d and d-a<e then c-b<e. Is this correct?

the upper inequalities are equivalent to
0<=b-a<=c-a<=d-a<e
now since c-b<=c-a then c-b<e

Let [math]X[/math] be a Frechet topological vector space. Let [math]F_1, F_2 \subseteq X[/math] be closed (but non-compact) and [math]U \subseteq X[/math] be open. Assume [math]\overline{F_1 + F_2} \subseteq U[/math].

Can one find open sets [math]V_1, V_2[/math] containing [math]F_1, F_2[/math] respectively such that [math]\overline{V_1 + V_2} \subseteq U[/math]?

>>16181279
I forgot to add: may assume [math]0 \in F_1 \cap F_2[/math].

When doing synthetic division how do I know what to divide with man, I'm wasting so much time it takes almost an hour to fucking complete one problem set

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Are there any examples where knowing of 0!=1 has the direct practical application, i.e. when it actually important for the potential calculation?

>>16181203
Oh yeah right, it's like the A4 paper. I should have known that. Is the rectangle the only shape for which the n=3 or n=5 work?

>>16181469
It's important if you want to evaluate a Taylor series.

[eqn]\sum _{n=0}^{\infty }{\frac {f^{(n)}(a)}{n!}}(x-a)^{n}[/eqn]

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I'm stuck on this exercise 1.70 of Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand, Polimeni and Zhang. Can anyone offer some hints before I give up and look at the answer?
My thoughts are that [math]1 \notin D[/math] and [math]3 \notin D[/math], since otherwise (1, 1) and (3, 3) would not be in [math]R[/math]. So if [math]D[/math] isn't empty it can contain only 2 or 4, but not both, since [math](4, 2) \in R[/math]. Letting [math]D = \emptyset[/math] or [math]D = \{ 4 \}[/math] doesn't seem to help at all, so I presume [math]D = \{ 2 \}[/math]. This "restores" (2, 2) to [math]R[/math] but that doesn't make it any more apparent how to split this larger set into [math]A \times B[/math] and [math]C \times D[/math]: It seems like roughly [math]A = \{ 1, 2 \}, B = \{ 1 \}, C = \{ 2, 3, 4 \}[/math] and [math]D = \{ 2, 3 \}[/math] but this is obviously incorrect.
I'm really stuck on this and feel like I must be overlooking something basic. Any hints?

>>16181645
I won't really comment on the exercise since you can probably do it just fine and it seems a little bit like busywork.
What I'll say is that you really shouldn't be stuck.
What I'd advise you is to, before you start with specifics, write down some general observations or proof strategies.
Personally I try to think of ~five things before I start proving, but here this is a bit much since the problem is relatively simple.
Then, when you start proving, you work each idea out until you notice it's too weak to prove your result or some other dead end, and you move to the next idea. Usually you get more ideas while working one of them out.
Don't look at solutions until you either worked out all your ideas or (think you) have a proof.

I think you're doing this somewhat already, without being aware of it.
For example, you noticed that the subtraction of [math]D\times D[/math] is very restrictive, which you can leverage into conditions on [math]D[/math].
Have you tried working all cases out yet? That is, until you reach a contradiction or a valid construction.
Another thing I'd notice is that you have the four elements [math](3,2),(4,2),(3,3),(4,3)[/math], which must have come from one of the two products (again, cases to check).

>>16181408
It's the same as normal division. Literally just look up youtube videos. You choose the highest term in the numerator and denominator (divisor and dividend) and focus on them

>>16181673
Thanks, I appreciate the advice. The exercise is undoubtedly basic but this whole process of encountering a not-immediately-obvious problem in math and working patiently and creatively towards a solution is something I am still really struggling with. Hence my attempt to work through this book.
I have tried working out some possible cases with this problem but definitely not in an exhaustive manner. I'll go back to that again.
And I'll reflect on your comment more generally as this is very much the sort of thing I need to be learning. Again, thanks.

>>16181645
yeah idk man, i feel like that (1,1) or the (3,3) shouldnt be there, and can't think of anything else.

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>>16181590
you can do n=3 or n=5 with a right triangle

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>>16181255
Here you go.

>>16181645
>>16181731
Looking at the exercise again I think it's not possible. I guess I'll extend my advice to not expecting too much from books aimed at as much people as possible, since they'll often cram in lots of exercises without checking if they're useful (or even correct).
Can you prove it's impossible to find such sets?
>>16181696
You're very welcome. At least for me, it happens too often that I try to prove a theorem or make an exercise, and upon reading the proof/solution I think "ah, I should have thought of that". Not because you understand it after reading but because you probably could have done it before reading the answer.
Explicitly writing out a list of proof strategies before I start helps against that, I find.
These can range from simple things (contradiction, contraposition) to 'that one cool characterization you saw years ago'.

>>16181731
>i feel like that (1,1) or the (3,3) shouldnt be there
>>16181751
>Looking at the exercise again I think it's not possible.
I actually had the same hunch.
>Can you prove it's impossible to find such sets?
This would be a good exercise as well. I'll see what I can do.

I want learn STEM stuff for fun but should i?

Can people with STEM education tell me if there are any bonuses?Does it make you smarter?

Or today STEM(science) is the meme

>>16180665
I managed to get the desired effect simply by using a costant acceleration applied at the start/end of movement + some edge cases, which get rig of all the integrals and stuff. https://www.desmos.com/calculator/1bokyk74fb

>>16180829
Answer me

>>16181795
The discoveries and inventions based from science
helped many people in general to be smarter, at least
in terms of practical principles for the layman to implement,
and for actual people researching in the STEM fields a way
to broach former and current concepts to advance
science further.

I do caution that knowing that stuff may come off as
trivia for some and you might look like a smartass
(perhaps, endearingly?). Also, you'll have to contend
with those that are, in the worse case, willingly
ignorant of scientific concepts, or manipulative
to attain some goal (usually monetary). That's why
we must practice logic, judgement and patience with that.

So, yeah, nothing wrong with learning for fun...

Do you know that 22 people brings your chance
of having matching birthdates with one of them to 50%?

How dumb is it for me to want to take the ACT/SAT as an adult in his 20s? I think it would help to transfer into the local school I really want to go into because my transcripts are very poor. I just don't know if it looks stupid or would even help me that much. I've taken a few college classes in a different institution.

Would this even help me? I could probably get a top% score, so that's not the issue. I just don't know if it would matter or make me look like a gay faggot in a college application anyway.

Would Sabine have sex with me if I asked her?
I'm 20, surely she wouldn't reject me since she's so old?
Thoughts?

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How do you prove this?

>>16181885
sum of a geometric series from 0 to inf is 1/1-q where l q l < 1 so here since the sum is from 1 to inf the sum is q/1-q (jjust multiply it by q )here q=1/a and (1/a) / (1- 1/a)= 1/a : (a-1/a)=1/a-1. you can find the proof of a the series from k=0 to inf of q^k where l q l<1 easily on the internet

>>16181906
I understand that the infinite sum (1/4)^n is equal to 1/3. That makes sense but more generally it's difficult to think about

>>16181251
oh yeah right I'm so dumb thanks

>>16181881
I think it would help your application a lot since it shows you are serious and have academic aptitude.
Another thing that would help would be a reference letter from your current or previous employer attesting that you're competent at your job, able to learn and hard working.
University administrators don't really care about your age, they just want to admit students who are unlikely to drop out because their funding depends on high graduation rates. If you can convince them you are more likely to graduate than the typical 18 year old zoomer who applies there, you're good.

Also, your question is somewhat vague. Can you elaborate more on what you want to major in and why, what your current job is, and how selective this school is? And what made you perform poorly at your last college?

>>16181934
Never mind I found this video and now I get it https://www.youtube.com/watch?v=o0AyHmRV8RA

So I did some test that consisted of beginner, medium, and advanced questions for 3 subjects and I got a total percent score for each subject across each level of questions. But they don't make any sense, it appears beginner ones might be weighted higher which is counter-intuitive. I put it as a linear equation and asked chatGPT to solve and it gave me negative numbers which is obviously wrong.

Can anyone help me figure out how to solve this?

93a + 86b + 71c = 86%
100a + 75b + 71c = 88%
86a + 73b + 70c = 77%

(A = beginner, b = medium, c = advanced)
The percents are most likely rounded. In the first test you can see I got 7 less beginner, but 11 more advanced and it ended up bein 2% less. It just seems weird and unsure how to approach

ChatGPT says to use python scripts but I am only on my phone.

Anyone know a good tutorial on how to make a simulation + graphing of a mass spring damper system in python?

>>16181881
I did poor in high school but then I took some community college classes and was able to transfer to a top engineering university in a year and half(I sat my ass down and got straight A's tho and I was able to test into a calc 1 class). You really don't have to do SAT/ACT. I highly recommend avoiding giving college board money

>>16181958
Finance, money. The school is moderately selective. I'm currently working a factory job. Reason I performed poorly last time was because it was hard to balance things in my life.

>>16182017
makes sense, I think a test score would definitely help in your case

If X is a subset of R which is compact and discrete, prove that X is finite.

>>16181211
>(5*6)/2=15

This is the mistake. You need to multiply the base by the perpendicular height of the triangle when calculating area. You can find the height by splitting the triangle in half along its line of symmetry and then using Pythagoras' theorem).

Factory I work in has a chemist who creates dye formulas for the wool sold. He knows how to get the colour he wants based on the wool type and colour but couldn't some machine just so this? Measure the frequency of the colour of the original wool and then the colour needed to look a certain way also based on the type of dye? Feel like this dude could be replaced by a 20 dollar machine of temu (he obviously does more than that for his job but I feel this would be easy to get a machine to do) . Or is it a lot more complex than that?

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>>16182013
https://scipy-cookbook.readthedocs.io/items/CoupledSpringMassSystem.html

PH is logarithmic right so it's not like if I add 1l of a ph1 solution with 1l of a ph4 solution I'll get 2l of a pH 2.5 solution and I'm guessing what really matters is how they are going to react together anyway like if it's pH 1 and pH 13 you wouldn't necessarily get pH 7 or would you since its what equal parts oh and h

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I know this is basic trig and I feel like an absolute brainlet.
Why is [math]r = -Vcos(\sigma)[/math]?
If we draw a line that intersects [math]\vec{V}[/math] at a 90 degree angle, then [math]r[/math] is the hypotenuse, not the adjacent - so why is cosine appropriate here?

>>16182105
V is the hypotenuse, r is the adjacent. the right angle is at V_T, not V.

>>16182108
ah fuck because the coordinate frame origin is at [math]\vec{V_T}[/math]
it's a miracle I don't forget to breathe
thanks

>>16182063
Already solved this. No need to help anymore.

>>16182149
post your solution

>>16182009
Thawts

>>16182104
>or would you since its what equal parts oh and h
correct
> if I add 1l of a ph1 solution with 1l of a ph4 solution
you'd get pH 1.3.
the ph4 is basically water (0.1 M vs 0.0001 M), so if you water pH 1 in half you get +0.3 or pH 1.3

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What is the right way to think about fractions?

>>16182275
That's just a set of 3 simultaneous equations with 3 unknowns and it does have a solution. For once GPT is correct, one of the values is negative. So that means at least one of your assumptions you used to create those equations is wrong. Probably that each subject uses different weighting values or they have been graded on a scale and hence adjusted the results.

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Got this question from a sibling, I'm a brainlet that barely passed high school like 15 years ago.

>>16182604
Since you have cropped out the question it's kind of hard to answer it.

>>16182612
That's the picture as i got it, i believe it's meant to be a percentage and i got 24.53%, no idea beyond that.

>>16182255
Not her, but since [math]X[/math] is discrete for any [math]x \in X[/math] there is some [math]\varepsilon_x>0[/math] such that [math]B_{\varepsilon_x}(x)\cap X=\{x\}[/math].
Take the open cover [math]\{B_{\varepsilon_x}(x):x \in X\}[/math] of [math]X[/math] and note it has a finite subcover iff [math]X[/math] is finite.

>>16182620
I got .893

Did we already figure out all possible elements in the universe from chemistry?
Even though said elements don't exist on earth or it requires ways to produce it that are currently unknown to us.

If even light speed require so many years to travel across universe, does that mean even if we manage to spread out across the galaxy, there's simply no reliable way to communicate with each others since there will be years of delay for 1 message to be send through? (And will also take years to receive the reply)

I found a pseud with a superforecaster certification on his profile. I started down the Good Judgement rabbit hole. They recruit super forecasters from those who make the most accurate predictions on their open forecasting questions.

https://goodjudgment.com/how-to-become-a-superforecaster/

What sort of discipline does forecasting fall under?
It seems that statistics are required to build a forecasting model, but criteria selection and parameterization seems to be something else all together. Take sports betting as a simplified example, where there are collections of all player stats and various contributing factors. It is up to the gambler to decide which of those are the best things to use for predictions. There will obviously be statistical correlations, but they aren't going to always be sufficient for getting ahead of the bet line. Take weather as a confounding factor.
And so data always has context asterisks appended.
>if this is true
>under these (perhaps undefined) conditions
>etc

>>16182785
> Did we already figure out all possible elements in the universe
There is a possible 'island of stability' where some isotopes of new heavy elements might exist but we have never been able to create them (yet) and if they do exist somewhere in the universe we have no observational evidence for that. And just because they might be stable that could mean their half-lives are measured in seconds rather than micro-seconds, they wouldn't be around for very long.

> there's simply no reliable way to communicate
Given everything we know currently about physics, that would be the case. There is no way to communicate faster than the speed of light.

how can we justify the assumption that physical constants are truly constants throughout the universe when we are limited to what we can causally observe from our location here on earth

>>16182893
likewise how can we justify the assumptions that the physical laws that hold true in our vicinity, hold true throughout the universe

>>16182893
>>16182895
You are right that it's an assumption and we justify it because we have no evidence that the assumption is false or have any theory that can calculate those constants from first principals - that's why they are called fundamental constants. That's not to say those constants can never change, they might have been different in the very, very early universe moments after the big bang, but we currently have no observations that prove that conjecture but people have certainly looked into those ideas. A variable speed of light is a good example.

> how can we justify the assumptions that the physical laws that hold true in our vicinity, hold true throughout the universe
Because everywhere we look in the universe - here, close by, far on astronomical scales - physics appears to work the same way. For example it wouldn't take much variations in certain constants for nuclear physics to work differently, differently enough for stars to not look or act the same, or to not form at all.

>>16181645
>>16181673
>>16181731
To follow up on this: The answer given in the solutions manual is [math]A = \{1, 2\}[/math], [math]B = \{1, 2, 3\}[/math], [math]C = \{1, 2, 3, 4\}[/math] and [math]D = \{2, 3\}[/math]. By my figuring that would mean [math]((A \times B) \cup (C \times D)) - (D \times D) = \{(1, 1), (1, 2), (1, 3), (2, 1), (4,2), (4, 3)\}[/math], which is significantly different from what's stated in the question.
I'm working from the fourth edition of the book so I assume the question got mangled in the process of revising it.
Before I looked at the solution though I took the time to write out my reasoning as to why the original problem is unsolvable, trying to look at it case-by-case as suggested in >>16181673; basically, there's no way to reconcile [math]2 \in A[/math], [math]3 \in B[/math], [math]1 \notin D[/math] and [math]3 \notin D[/math] simultaneously, so there is no way to construct A, B and D in a way that solves the original problem, so by extension the problem has no solution.
Again, thanks for taking the time to read my post and respond.

>>16182828
Forecasting skill replicates pretty well across retests.
There's statistics involved (usually very elementary stuff like base rates and Bayes' rule), domain knowledge and intuition. The ones that explain their reasoning usually use simple models and vibes, but have a very fine feel for the difference between 60% and 70% odds of something happening, which in the long run adds up to betting success.
The only way to tell if some is a good forecaster or not is if they have a track record of successful predictions. Also, being able to predict stuff 1 year in advance doesn't necessarily translate to predicting 20 years in advance or being able to reason about scientific ideas.

>>16181279
Answering my own question in case anyone's interested: the claim is false. Here's a counterexample for [math]X = \mathbb{R}^2[/math]. Choose [math]F_1 := F_2 := \{ ( \mathbb{R}, 0) \}[/math] and [math]U := \{ (x,y) : |y| < 1/(1 + |x|)\}[/math]. Suppose there were [math]V_i[/math] as in the claim. Then there is some [math]\delta > 0[/math] with [math](0, \delta) \in V_1[/math]. Pick any [math]x \ge 1/\delta[/math]. Then [math](x, \delta) \in V_1 + F_2 \subseteq V_1 + V_2[/math] but [math](x, \delta) \notin U[/math], a contradiction.

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I need a scale that can measure 5-20mg accurately but every .001 scale I see all have reviews that say they aren't reliable or accurate. Anyone got recommendations? Cheaper is of course better but I can go up to $150 for something reliable and accurate. Anyone got suggestions?

Hey guys is annas archive shit now or something?

What's a math topic I can study enough of in 3 weeks to do some fun project on? I blew 2 weeks of time on the cliché picks like knots and fractals but my brain is shot when it comes to visualizing so it ended in failure. What's a good topic that doesn't demand being able to manipulate complex shapes? I know calculus, linear algebra, and some stuff about differential equations.

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>>16184583
Googology is my favorite recreational mathematics. It's a study of numbers so large there is no need or way to visualize them. It revolves around discreet math and set theory. It's somewhat abstract but it's not that big in terms of things you need to study to get it.
As of projects, I dunno, but I always wanted to make a clicker/incremental game that climbs up the fast growing hierarchy instead of linear grow you generally encounter.

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How can write so much, bros?

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How do you explain this?

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what math would i need to simulate an optics experiment with lenses? the equation for a plane wave?
>>16184737
pic related

>>16184583
some kind of cool algorithms
you can literally just copy some cool visual one and get pretty pictures

>>16183786
What changed?

>>16184883
there was like a 600 second timer

>>16184583
complex analysis is pretty easy if you know calc and can draw pictures

>>16184782
you start at a small angle approximations, then start at a 1-boundary problem with 2 different indices of refraction with different boundary shapes and see how the rays of light come in and out of infinity, After understanding the different 1 boundary cases (concave,convex) then start doing mirrors instead of lenses. After this, go onto two boundary cases (a lens).

It's all basically a geometry problem with the rules set by some algebra and the index of refraction rules.

>>16184986
thanks fren <3

Fix a real vector [math]v[/math] and consider the optimization problem [eqn]\min_{\|x\| = 1} \langle v, x \rangle.[/eqn] One solution is clearly [math]x = -v/\|v\|[/math]. Is this the only solution, and if so how can I prove that?

>>16185346
Use the Bunyakovsky inequality.

how come we can come up with a funny kludge number to let us take square roots of negative numbers, but we can't come up with one to let us take logarithms of negative numbers

>>16185521
>but we can't come up with one to let us take logarithms of negative numbers
The funny kludge numbers let you do that, too
only difference is that sqrt is a two-valued function while log takes infinitely many values on a complex plane, but you can just as easily pick the principal branch

>>16185346
i think u mean max there. The minimum would be within an orthogonal plane

>>16180594
Black board is proof chatgpt is retarded

Why is youtube's shuffle feature for playlists so dumb? It's not even random because it starts looping after a few videos.

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is [math]n_k = 1/{n^3} [/math] and [math]1/2n[/math]?

>>16185866
It's the same problem as spotify shuffle. The data shows that people don't want truly random. They see pattern in the randomness and get frustrated because they don't understand that true random shuffle can just play an album in order, or play just one artist for consecutive songs.
Add to that that youtube has an agenda in what type of video it wants you to watch (based on what is most likely to make you keep watching and stay on the platform watching ads) and you end up with a broken shuffle feature designed by marketing and not engineers.

I know very little about physics and am retarded, go easy on me
I am assuming the casimir effect is a consequence of quantum electrodynamic vacuum energy here
why can't gravity be explained as a large-scale casimir effect?
i.e. taking two physical bodies in space which are at rest - could zero-point gravitational field fluctuations, and the difference between the fluctuations in the space between the two physical bodies and the space beyond them, explain gravitation, as an unequal force would be acting on the bodies and push them together?

>>16185994
> I am assuming the casimir effect is a consequence of quantum electrodynamic vacuum energy here
Not completely true, the casimir effect does not require or prove the existence of a vacuum energy. What is requires is the existence of quantum fields and placing boundary conditions on the system. In this case two metallic plates that confine the available space so that not all allowed vibrations in the fields are possible within that gap.

The simplest reasons it can't have anything to do with gravity is that is doesn't depend on mass: [math]F_{casimir} = \dfrac{A \hbar c \pi^2}{240 r^4}[/math]

So the force only depends on the area of the boundary (the plates) A and falls off like [math]1/r^4[/math] and not [math]1/r^2[/math] like gravity. The fact the force depends on r (the distance between the places) and it falls off so quickly is why the effect only really applies at extremely small distances (on the scale of a few atoms).

>>16186245
appreciate the patience of your response; I know it's not pleasant talking to retards
>The simplest reasons it can't have anything to do with gravity is that is doesn't depend on mass
that is the electromagnetic casimir effect, correct?
I apologise if I wasn't very clear, but I was asking if a hypothetical gravitational casimir-/like/ effect (gravitonic perhaphs, rather than photonic?) could explain gravitation, rather than asking if the casimir effect itself was responsible

this is far, far outside of my comfort zone, so googling around to better ask the question, I found this:
>https://arxiv.org/pdf/1502.07429
which seems to be /similar/ to what I'm describing, I was just wondering if this could happen at much larger (i.e. planetary scales)
physical bodies shield, or enshadow each other from gravitational forces, meaning the force is weaker in the cavity between them, causing them to attract one another

I apologise if this is like pulling teeth for you

>>16186409
> appreciate the patience of your response; I know it's not pleasant talking to retards
this is the kind of question /sqt/ is for.

> that is the electromagnetic casimir effect, correct?
Kind of. It is electrifying the plates that creates the boundary conditions (the EM field has to be zero on them / it blocks the EM field passing through them). In theory you could create other scenarios that form a boundary, they would all still be the Casimir effect. This just happens to be the easiest to think of and do experiments with.

> so googling around to better ask the question, I found this:
What the paper says is correct, it is not just about the EM field. Any quantum field would work, so in theory gravity (though no one has actually proven it's a quantum field yet).

However ...
>Therefore one may imagine plates which are opaque to the gravitational field.
Yeah, good luck finding such a material.

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Teorema de Stokes UwU <3

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is there a term for these kinds of knots in knot theory?

>>16186723
>the virgin category theorist

>>16180594
There used to be a /sci/ Discord. Is it still around?

Can poisons be absorbed from the asshole? I'm writing a short story about a guy trying to get revenge on people who did bad things to his family. One of my assassination methods I thought of was that he would put a poisonous substance in the water that's used for a bidet. The pill will dissolve and transfer the corrupted water into the person's ass hole (at high pressure) when they go to use the bidet. Is this a plausible scenario?

>>16187139
the colon is very absorbent, but the anus less so. theres no poison that would work on the anus that wouldnt also work anywhere else. dimethyl mercury, for instance.

How do I solve for the dimensions of a cylinder if I know its volume and diameter:height ratio?

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>>16187160
I chose a ratio of D=2H arbitrarily, results will vary a lot but the logic should be this

Why does this:
[math]\vec\nabla \times \vec{A}(\vec{r})=0 [/math]
imply that there exist a function [math]f(\vec{r})[/math] such that:
[math]\vec{A}(\vec{r})=\vec\nabla f(\vec{r}) [/math]
?
It's probably a trivial property but I don't know what it's called.

In beta decay one electron leaves, a neutron turns into both an electron and proton. Meaning from the parent nuclide we now have two more protons but only one more electron. So why isn't the daughter nuclide an ion?

>>16187921
Define [math]f(\vec{r})[/math] by choosing a point [math]\vec{r_0}[/math] and setting [math]f(\vec{r}) = \int _{\gamma} \nabla \vec{A} (\vec{r'}) dr'[/math], where [math]\gamma[/math] is a random path from [math]\vec{r_0}[/math] to [math]\vec{r}[/math], and Green's theorem plus the condition you have tells you [math]f[/math] is well defined.
I don't recall there being a name for it in this context. It spins out into closedness and de Rham theory etc etc later.

>>16187921
> It's probably a trivial property
Maybe because the curl of the gradient of any continuous scalar field is always zero?

>>16187935
> Meaning from the parent nuclide we now have two more protons
Incorrect, you have one more proton.

> So why isn't the daughter nuclide an ion?
It is.

>>16187936
>[math]f(\vec{r}) = \int _{\gamma} \nabla \vec{A} (\vec{r'}) dr'[/math]
My bad, I meant [math]f(\vec{r}) = \int _{\gamma} \vec{A} (\vec{r}') \cdot dr'[/math]

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Is it possible to show that limit exists using epsilon/delta definition of limits? If yes then how to show it for (a)?

>>16187935
The daughter nuclide is written as being without charge in my textbook

>>16187954
Because it rarely makes any difference. It will tend to pick up an electron from the environment fairly quickly and not remain an ion for long.

>>16187949
Polar coordinates are helpful for this type of functions.
In general limits of multivariable functions are tricky because the limit must be the same along all possible paths in order to exist.
In this case you can write
[math]L = \lim_{r\rightarrow 0} \frac{r^6\sin^3\theta(r)\cos^3\theta(r)}{r^2} = 0 [/math] because [math]0 \leq \theta(r) \leq 2\pi \quad\forall r \in \mathbb{R} [/math]
You can recast this argument in epsilon-delta form but you must take care to cover *all* possible paths [math]\theta(r)[/math] not just radial lines of fixed [math]\theta[/math].
Proving non-existence is easier because it's sufficient to find 2 paths that give a different limit.

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>>16187949
For this kind of problem you should just appreciate how much leeway you're being given with inequalities.
For [math]|x|, |y| < 1[/math]
[math]\left| \dfrac{x^3 y^3}{x^2 + y^2} \right| < \left| \dfrac{x^3}{x^2 + y^2} \right| < \left| \dfrac{x^3}{x^2} \right| = |x| [/math], which converges to 0.

>>16187969
instead of [math]r \rightarrow 0[/math] couldn't we show[math](r\cos(\theta),r\sin(\theta))\rightarrow(0,0)[/math]?
>>16187975
I did think of that but that only proves that the limit is 0 when [math]|y| < 1[/math] right? Wouldn't we have to show it for [math]y \geq1[/math] as well?

Also any recommended books, I can just refer for this? Thomas Calculus isn't really helping

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>>16187988
>I did think of that but that only proves that the limit is 0 when |y|<1 right? Wouldn't we have to show it for y≥1 as well?
Nah, we just set [math]\delta = \min(1, \epsilon)[/math], then [math]|x|, |y| < \delta[/math] automatically implies [math]\left| \dfrac{x^3 y^3}{x^2 + y^2} \right| < |x| < \delta \leq \epsilon[/math]. As simple as that.

ooo another avatarfag. or maybe remi just got into MiA, iunno he kinda types like him.

>>16188071
Satokofag you need help.

>>16188093
im gettin on vyv soon.

vyvanse

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>>16188106
Good.

>>16187936
>>16187940
Thank you

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>>16180594
I am confused, can anyone help me with particle physics? I have a question which asks me to read of R values above the thresholds at which vector mesons rho, omega, phi, J/Psi, Y are created. Then, I have to calculate the Q^2 value of quarks that take part up until that energy level.

The problem is, the resulting values are clearly way too big. Say for energies reaching the omega meson, I get Q^2 = (1/3)^2 + (1/3)^2 + (2/3)^2 = 6/9 (e is omitted, charges of s, d, u quarks).

Then what? Do I divide by values lying in R in [20, 1]? Obviously the result is odd, I need to get the number of color charges.

Pic related is from the particle data group.

>>16188316
Alright, I've figured it out, you anons can ignore it.

when will there be a cure for aging?

>>16188345
long after you are dead.

Why does my book say for g(y) = {1 if y =/= 0 and 0 if y = 0}, lim y->0 g(y) does not exist?

>>16188586
Because it's retarded.

Hello.

I am trying to calculate [math]\left\langle \frac{1}{1-k} \right\rangle[/math] for a geometric distribution, where [math]k=0,1,...[/math] and [math]p(k)=p(1-p)^k[/math]

Here is my attempt at a solution:

Let [math]q = p - 1[/math], then
[eqn]
\left\langle \frac{1}{1-k} \right\rangle = \sum^\infty_{k=0} \frac{p q^k}{k+1}
[/eqn]
now
[eqn]
\sum^\infty_{k=0} q^k = \frac{1}{1-q}
[/eqn]
integrating with respect to q yields
[eqn]
\sum^\infty_{k=0} \frac{q^{k+1}}{k+1} = A - \log (1 - q)
[/eqn]
for constant [math]A[/math], thus
[eqn]
\left\langle \frac{1}{1-k} \right\rangle = \frac{p}{q} \left(A-\log (1 - q) \right) = \frac{p}{1 - p} \left(A-\log p \right)
[/eqn]

But I can't seem to determine the value of the constant [math]A[/math].

By computing the sum numerically (pic related), I can see that we should have [math]A=0[/math], but if I try to fix [math]A[/math] algebraically, I get non-converging sums.

For instance, with [math]p=0[/math] we expect [math]\left\langle \frac{1}{1-k} \right\rangle[/math] to be 0, since k would tend to infinity, but plugging this in, we get the equation

[eqn]
0 = 0 \cdot (A - \log 0)
[/eqn]

For [math]p=1[/math] we expect [math]\left\langle \frac{1}{1-k} \right\rangle[/math] to be 1, since k should always be 0. Here we get
[eqn]
1 = \frac{1}{0} A
[/eqn]

Neither of these equations make sense, and contain invalid operations. This may be expected, since I implicitly assumed that [math]0<p<1[/math] in my derivation. Taking limits as p approaches 0 or 1 doesn't appear to help either.

Is there some other way I can argue A should be 0, or some other method that can be used to calculate this sum?

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>>16188609
Forgot pic related

>>16188606
You're the retard. Asking what is g(0) is not the same thing as asking what is [math]\lim_{y \to 0} g(y)[/math]

>>16188586
The function needs to be continuous at all points. g is discontinuous at y =0

>>16188609
>But I can't seem to determine the value of the constant A.
[math]\sum^\infty_{k=0} \frac{q^{k+1}}{k+1} = A - \log (1 - q)[/math] with q = 0 immediately tells you A = 0 and seems to be a valid point for evaluating A.

>>16188621
>The function needs to be continuous at all points. g is discontinuous at y =0
buddy, you're not one to be calling anyone retarded

>>16188629
Ah, yes you're right!

>>16188609
set q to 0

>>16188633
I was trying to do this, but I was only considering the equation after I had already divided by q and therefore obviously running into problems. I was being dumb as usual.
>>16188629
>>16188633
Thanks anons!

>>16187975
That's pretty neat

Yeah, I know, no homework.
But if anyone knows some algebraic geometry and stuff about the classical topologies on sites like Nisnevich, flat, étale and ofc Zarisiki:
Any ideas, especially for the Exercise 2 (***)? Apparently it is not super hard (stars imply difficulty level outside the "normal" range of the course)?
https://www.mathematik.uni-muenchen.de/~morel/Teaching/ExSheetAG3/ExSheet4.pdf

>>16189385
Oh and I forgot: apparently Ex 2 (***) the answer is: no, the quotient is not necessarily a scheme (contrary to stacks I guess)

>>16188630
Explain it to the rest of us then anon.

>>16189460
already done by >>16188606
but if you really need convincing that continuity doesn't matter, remind yourself that arguably the main usage of limits is to discuss the behaviour of a function arbitrarily close to a point where it is not defined
and if it is not defined at that point, then it obviously isn't fucking continuous there, so continuity obviously doesn't fucking matter

>>16189466
So if the book is wrong, what is the limit in >>16188586 ?

>>16189473
obviously 0

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>>16189478
oh dear, you poor summer child.

>>16189473
The book is likely not wrong.
Post the definition of a limit from your book. It likely uses the non-deleted limits rather than deleted limits which is the better definition anyway.

>>16189480
>take any infinite sequence of y-values that converges to y=0
>output converges to g=0
wow sure looks like the limit is 0 to me

>>16189488
Take the sequence
0,0,0,0,0,...

>>16189484
>>16189488
It should be obvious from the epsilon delta definition of a limit one does not exist for this function.

>>16189480
I have a stupid question: what is the appeal of azur lane?
I see it on here somewhat often and it's making me feel out of touch.

>>16189499
No idea. I just saved it because it was a funny reaction image.

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>>16189478
I don't even know who's baiting who anymore.

>>16189503
I don't think it's a bait, he actually seems to believe his answer is right.

>>16189496
Which epsilon delta definition?
The burgerland one where
[eqn] \lim_{x \to a} f(x) = L \text{ iff } (\forall \varepsilon >0)\,(\exists \delta >0)\,(\forall x\in \mathbb {R} )\,(0<|x-a|<\delta \implies |f(x)-L|<\varepsilon ) [/eqn]
or the one used in the rest of the world where
[eqn] \lim_{x \to a} f(x) = L \text{ iff } (\forall \varepsilon >0)\,(\exists \delta >0)\,(\forall x\in \mathbb {R} )\,(|x-a|<\delta \implies |f(x)-L|<\varepsilon ) [/eqn]

Hint: The limit exists for exactly one of those definitions.

>>16189496
guess the same is true of any removable discontinuity then, yeah?

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>>16189508
Genuinely concerning post.
Give me one source for the second definition. It can be in any romance language or in German.

>>16189513
And by source I mean a textbook or a lecture notes pdf from a reputable source.

>>16189513
The Amann-Escher book that keeps getting shilled here uses the second definition for example.

It's the better definition because with it you get that if [math]y_0 = \lim_{x \to x_0} f(x) [/math] and [math]z_0 = \lim_{y \to y_0} g(y)[/math] then
[eqn]\lim_{x \to x_0} g(f(x)) = z_0[/eqn]
which is wrong for the first definition.

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>>16189517
CTRL+Fed through Analysis I and couldn't find it. Closest thing was this definition of *continuity* (which is entirely correct). If anything it's weird that, if they're using your definition, they don't just define a continuous function as one that has a limit everywhere.

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>>16189517
>>16189523
Found confirmation in page 242 of Analysis I that they aren't using your definition, otherwise pic related is trivial.
The pdf I'm using: https://library.lol/main/2F7E3AAC611CDDD93D55D6B529DC724C

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>>16189527
It's trivial. That's why the proof is so short.
Look one page earlier where the limit is actually defined. Amann-Escher does allow the sequences (x_n) to take the value x=a.
It's the same in Dieudonne's analysis book too if you want a french example.

Those non-deleted limits are the standard in Europe.

>>16180594
I want a math book which covers high school level mathematical concepts but going deeper and exploring more. Someone recommended me vygodsky's higher mathematics mathematical handbook but it's not available for sale at my location. Please suggest a similar book.

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>>16189533
>It's trivial. That's why the proof is so short.
I don't mean trivial as in its easy, I meant trivial as in it's not saying absolutely anything. Your definition is literally just "f has a limit at a if f is continuous at a".
>the pic you attached
Notice how [math]a \in \overline{A}[/math], the sequence is of points is in [math]A[/math] and the limit is with respect to [math]A[/math]. It's completely different from what you're talking about and obviously a generalization of the basic use case, which is [math]A = \mathbb{R} \setminus \{ a \}[/math].

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>>16189533
It might have been better to post the acutal definition and epsilon-delta criterium from Dieudonne.

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>>16189513
Here is a part from Bartle's Analysis book that compares the two definitions.

>>16189484
>which is the better definition anyway.
I'm curious why you think so.
I can think of examples where the deleted limit is useful, but none where the non-deleted limit is.

>>16189610
very helpful, nice

>>16189534
Higher Algebra by Henry Hall and Samuel Knight

Does the t suppressors found in seminal fluid negatively affect a fetus after coitus during pregnancy?

I need to calculate the functional derivative (or the differential) of the functional:
[eqn]F \left[ \rho(\vec x ) \right] = \int \left( \vec\nabla \rho(\vec x ) \right) ^2 d\vec x[/eqn]It should turn out to be:
[eqn]\frac{\delta F}{\delta \rho}=-2\nabla^2\rho(\vec x)[/eqn]But I can't get that result. Does anyone know how to do it or some resource where this calculation is done?

By the way, the definition I was given for [math]\frac{\delta F}{\delta \rho }[/math] is:
[eqn]F[\rho +d\rho] -F[\rho] = \int \frac{\delta F}{\delta \rho } \delta \rho d \vec x [/eqn]And I only can get as far as writing:
[eqn]F[\rho +d\rho] -F[\rho] = \int \left[ \left(\vec\nabla \delta \rho \right)^2 -\nabla^2\rho \delta\rho \right]d \vec x [/eqn]
Thanks in advance

>>16190474
Well, ur first and second equation definitely do not imply each other since their units aren't even the same.

Your first equation doesn't even make sense either.
p is a map of a vector into a scalar. The gradient Dp is then a vector. What is a the square of a vector? Do you mean the magnitude squared scalar (so the Laplacian of p)? Or is this a bi-vector with x_i*x_J 's.
The RHS is also an integral over the vector d(X). If the square if Dp is meant to be a scalar Laplacian, is the RHS supposed to be a vector? Are you saying that F, a function of p, is a vector and not a scalar?
Or do you mean to integral over the length of the path across d(X), so dL = |d(X)|?
Or do you mean the RHS to be a dot product of the vector d(X) and the square of Dp as a vector?

When u fix ur equations, for functional analysis it's easier to replace dp or dL with a n or eta, so ur treating dp as a variable. This would make d/dx(n) = d/dx(dp)

>>16190663
the second dL i mention at the end i meant to be the Lagrangian, not the displacement length dL, my b

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Goldstein chapter 13.3. How does eq 13.33 follow from 13.32? I'm confused what I think [math]T_\mu[/math] is and what is claimed in the book. Looking at 13.32 and the LHS of 13.33, I can read off that [math]T_\mu[/math] is a 3-"vector" of the form [math]\left<T_\mu^1, T_\mu^2, T_\mu^3 \right>[/math] that has the divergence applied to it, i.e. [math]\left<\frac{d}{dx},\frac{d}{dy},\frac{d}{dz} \right>\cdot \left<T_\mu^1, T_\mu^2, T_\mu^3 \right>[/math], but the text suggests that [math]T_\mu[/math] contains components of the form [math]T_\mu^0[/math].
Assuming that I'm right, isn't there also supposed to be a minus sign next to the integrals in eq 13.35, because [math]\frac{dT_\mu^0}{dt} = -\nabla \cdot T_\mu[/math] from eq 13.33? Also, what's up with the random ass factor of c in 13.33 but not 13.32?

>>16190733
T_u is explicitly stated as a set of 4-vectors. Spacial div is prob meant to be (0, d/dx, d/dy, d/dz). You need the c in order to keep the units the same. Unit analysis is good to tell if there was a typo or not. When two numbers equal 0, it doesn't matter if you multiply or divide by a finite number like c or -1, 0 stays 0 so who cares.

>>16190663
I think the square means taking the dot product with itself:
[eqn]F \left[ \rho(\vec x ) \right] = \int \left( \vec\nabla \rho(\vec x ) \right) ^2 d\vec x = \int \left( \vec\nabla \rho(\vec x ) \right) \cdot \left( \vec\nabla \rho(\vec x ) \right) d\vec x [/eqn] As for the integration, [math] \vec x = (x_1,x_2,x_3) [/math], so:
[eqn]\int \left( \vec\nabla \rho(\vec x ) \right) ^2 d\vec x = \int \int \int \left( \vec\nabla \rho(x_1,x_2,x_3) \right) ^2 dx_1 dx_2 dx_3[/eqn] I hope it makes sense now. Basically I need the functional derivative of a functional that takes the gradient of a function, multiplies it by itself and then integrates over volume.

>>16191037
Looks like you almost got the result here
>>16190474
You're only missing a factor of two in the last line and you can drop the term which is quadratic in [math] \delta \rho [/math] because it's negligible.

>>16191058
Ok, the factor of 2 was my mistake. So indeed if I neglect [math]\left(\vec\nabla \delta \rho \right)^2 [/math] I get the result I need. It's not obvious to me why I can neglect it though. If it was just [math]\left( \delta \rho \right)^2 [/math] I'd have no problems, but it's its gradient. How would I justify it?

>>16191108
One way is to compute the derivative of the ordinary function [math] t \mapsto F[\rho + t \delta \rho] [/math] at t = 0.

>>16191037
Yeah now the units are even worse. They simply are not equal, this isn't ignorable
Also, jesus that notation is so bad. dX is obviously meant to be the vector d(X)/dt * dt
Why are you not writing it as
[math] \Vert \vec{\nabla} \rho \Vert^2 \ dV(\vec{x})[/math]

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>>16191108
>It's not obvious to me why I can neglect it though.
Good instincts. You can cook up functions that are very jagged and such that, although they are very close to [math]\rho[/math], the contribution of the derivative squared is non-trivial.
There are formal outs for this later on but in this context IIRC you just ignore it.

>>16191270
>in this context IIRC you just ignore it.
Correction: you can just restrict the possible paths to >>16191120 like anon said.

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How would you solve for 'x' if the equation involves an infinite series like picrelated?

>>16191388
depends on the series
in this case it's pretty easy. use the substitution [math]u = \frac {1} {x^2} [/math] to rewrite your infinite series as a basic geometric series [math]\sum_{k=0} u^k[/math]
there are a trillion different resources out there on how to evaluate a series like this, but it comes out to [math]\frac{1} {1-u}[/math], though importantly it only converges if [math]|u|<1[/math]
substituting x back in and rewriting the ratio turns your original equation into [math]x= \frac {x^2} {x^2-1} [/math], which is easy enough to solve algebraically and has three roots: [math]x=0[/math] and [math]x= \frac { 1 \pm \sqrt{5} } {2}[/math]

but because [math]|u|=| \frac{1} {x^2} |<1[/math] the only one of these for which the series converges, and thus the only valid solution, is [math]x= \frac {1 + \sqrt{5} } {2} [/math]

>>16191388
1. recgonize trivially that the RHS is the taylor series for 1/(1 - x^-2)
2. do algebra

Can you guys tell me how the constanrs are calculated. Like F=Gmm/r2. How did they calculatr the exact value of G. Does it have something to do with ratios? Sorry might be silly but bo one ever told me about this

>>16191417
Look up cavendish experiment. Lots of good utube vids on it, Steve moulder is good and fairly recent.

Guys, I think I've found a simple derivative formula to calculate squares(tested up to 100000 steps, returns accurate) where most complicated operation is a simple *2. Where do I poast it to get grant monay

Square = 1 + last square found + (2*iteration number)

1 + 0 + 2*0 = 1 = 1*1
1 + 1 + 2*1 = 4 = 2*2
1+ 4 + 2*2 = 9 = 3*3
etc

But I'm no math autist so this may already be known or trivial.

>>16191574
trivially, the nth square among the positive integers is [math]n^2[/math], so your formula can be rewritten as
[math]1+n^2+2n[/math]
[math]=n^2+2n+1[/math]
[math]=(n+1)^2[/math]
it works, but it's not really interesting

Question for oncology enthusiasts and experts. I just read this post here >>>/news/1297864 and as someone whose mother died to cancer and whose cousin lost her uterus to cancer, it makes me wonder if this avutometinib and defactinib combination therapy is something that can actually work or not. I'm worried that my female children if I ever manage to reproduce might be affected by cancer since it's very likely a genetic thing in my family.

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What software were these graphs made with? Or

What the fuck are the rules for permutations and combinations Just give some formulae and some further reading.
Say I want a combination where I pick r things from a set of n objects with n_1 of one kind, n_2 of another, n_3, and so on to n_k where they all sum to n obviously. How do I compute what that should be?

>>16191120
>>16191270
Thank you anons

>>16191156
I really don't understand. It's the integral of a scalar over a volume. Why have others understood and answered my question if it's all wrong? Also many books use that notation

>>16192792
NTA but tbqh writing something like [math]F[\rho +d\rho] -F[\rho][/math] is pretty goofy, but I don't really know what does he mean.

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>>16192661
I dunno the exact specifics of this image but similar graphs can be done with Matplotlib.
https://matplotlib.org/stable/gallery/mplot3d/index.html

>>16192661
might be Maple

>>16192889
It aint that goofy, it's just dF

am i range banned

>>16193197
no

>>16193197
Your interesting meter went up 0.02

>>16192901
>>16192935
Thanks. It does look like Maple.

>>16180594
What books should i pick up if i am struggling with vectorial calculus on my current college semester if i have a hard time factorizing.
I just need to have better fundamentals i guess.

>>16193392
factorizing? give an ex

>>16193392
Vector calc I think is fairly common online. Just google stuff and look at pdfs from university professors.

>>16180594
Stupid question: Anyway to estimate something like potential horizontal run speed or initial movement from resting based on the height achieved by a vertical jump? Say 100 meters(lol) vertical for simplicity.

Why does superglue stick to hands faster than to actual object I'm gluing?

What is avarage themal effectivity of fridge?

>>16193578
Ur asking if giving information about vertical tells you anything about horizontal speed? Do you really not see the issue in this if no other info is needed?

Rule of thumb: n unknowns need n equations. Knowing this now, about how much new information do you need to figure out ur problem?

>>16194258
>no other information is needed
*is provided

>>16193886
U probably aren’t using as much in ur skin as ur object. Also, ur skin is exposed to the air instead of being between two surfaces

>>16194034
Don’t know how to Google huh?

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>>16193578
If you make the (kinda ridiculous) assumption that your vertical speed when jumping from inertia equals your horizontal speed when starting to run from inertia then you can do a basic [math]mgh = mv^2/2[/math] estimate.

Adult brainlet here who forgot pretty much everything math-related in school:

I've been trying to figure out the formula for the XP curve in a game I've been playing for awhile now. Unfortunately, I didn't think to try and do this until Level 47, so I only have a little data so far.

Here's what I have:

> Level - XP Needed
> 47 - 72703
> 48 - 79973
> 49 - 87970
> 50 - 96767
> 51 - 106443

When I plug these into a graphing function, it changes the equation slightly with each new datapoint:

> 2 Points
> 7270x − 268987

> 3 Points
> 7633.5x − 286193

> 4 Points
> 8018.9x − 304563

> 5 Points
> 8427.4x − 324171

Do I have enough information to determine the real equation here? Or do I need to go back and get the data for the first few levels to "connect the dots" so to speak?

>>16194576
could be a quadratic, could be exponential, could be cubic, who knows?

>>16194576
Not enough data points to answer that.

>>16194576
As the others said, not enough data points to figure it out conclusively.
For a good demonstration as to why that is, I fed your values to WA and asked it to give me a polynomial that describes them; it spat out [math]\frac{x^4}{4} - \frac{109 x^3}{3} + \frac{8557 x^2}{4} - \frac{343213 x}{6} + 587917[/math].

This actually does perfectly fit your data... but the problem is that the minimum value it takes is between 29 and 30, so unless you mean "amount of experience needed from the previous level" and not "amount of experience needed total", you'd need negative experience to level up at lower levels than that

>>16194576
It's impossible to find the real equation for certain from a finite amount of data points.

Either way it looks exponential so you can try the ansatz
f(n) = a * b^n

Plug in the first and the last point
106443 = a * b^51
72703 = a * b^47
Divide the first by the second equation to find that
b = (106443/72703)^(1/4)
and then use this to calculate
a = 106443 * (72703/106443)^(51/4)

If you round the end results then this formula does indeed give the correct values for levels 48-50 too.

What is the curvature of a parabola as a functon of X where X is the x-coordinate of the tangent point of the osculating circle and how do you find it? Curvature is one divided by the radius of the osculating circle.

>>16194638
The curvature of the graph of a function at the point (x,f(x)) is
[eqn] \frac{|f''(x)|}{(1 + (f'(x))^2)^{\frac{3}{2}}} [/eqn]
The proof is in literally every introductionary differential geometry book.

Do physicists think dark matter/energy unambiguously exist or are they just on the fence if it's an issue with the model or not?

>>16195056
> Do physicists think dark matter/energy unambiguously exist
Yes. They are observations, multiple of them. No one is saying those are false. What you are get your panties in a twist over is the explanations for what has been seen, the cause for what astronomers have measured.

>>16194588
>>16194591
>>16194602
>>16194603
All great information, thanks so much Anons!

I'm guessing exponential as well, I'm going to start over at Lvl 1 on another account and get the first ten levels to close the gap.

>>16194602
Oh also, yes, important point of clarification, this is "amount of XP to level up from the previous level" NOT total XP needed.

>>16188106
bad news: might be months away from vyv now

What is the difference between making traditional balsamic vinegar and wine?
Everywhere i search, the process seems identical
1. Crush grapes
2. Fement grapes for a couple days
3. Store fermented grapes in barrels for years
4. Wine/Vinegar magically reads your intentions and becomes what you want it to be

>>16195430
oxygen = vinegar
co2 = wine

>>16195434
This answer is confusing but it led to me finding out it was a difference in the microbes used so its all good
Oxygen = What acetic bacteria needs to ferment
Co2 = What yeast shits out during fermentation

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I need help with something, I'm a complete retard and retard extraordinaire when it comes to statistics. I'm running multivariable regression for a paper, and the results are mostly normal (I think?) except for one variable that has absurdly high coefficient. I later eliminate that variable from the study entirely, but I'm still worried about this. And I don't think there's any error calculating that variable.

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Is this correct? This isn't a geometric series, is it?

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I am supposed to determine both speed and direction of each component if I am given angular velocity ω1 and each distance rₐ. How do I do it? Honestly, I'm not even sure what is shown on this picture (bars, wheels, ...?) and how should I imagine it working.

>>16194264
>effectivity
Because in google, they say 500%, therefore we could have perpetual energy just cooling the air.

Why do poltards and schizos congregate in /sci/?

>>16195842
That's not stupid question, try another thread.

Lets say there are 100 flowers in a box, 50 yellow and 50 red, so Ω={w1,w2,...,w100}, is A- picking a red flower an elementary event, I'm thinking it is, but in Ω there are 50 different omegas, so I'm not sure.

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>>16195885
Depends. The usual interpretation is that an event is "something you can tell happened." If all of the red flowers are interchangeable then yeah, the event is basically elementary (but it might also not be if the definition you're using demands it be a singleton).

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>The cart is moving without slipping on a steep incline with an angle α. An inextensible rope, CA, is passed over the pulley B and tied at one end to the cart C and at the other end to mass A. At the initial moment, the velocity of mass A is v0=1m/s. The mass of the cart mC=80kg, the mass of one wheel (there are 2 in total) is mD=20kg, and the mass of A is mA=120kg. The mass of the pulley and the rope can be neglected. Determine the height h through which mass A has descended at the moment when the magnitude of its velocity is v=5.9m/s.
Just a general idea on how to solve this is enough. If I am correct, this is a trick question and mC, mD and α play no role.

>>16196005
Suppose a = 90 degrees and mC+mD is very heavy. Now suppose a = 0 degrees and mC+mD is very light. Are they really ignorable?

>>16196005
• Consider the forces on the cart C and mass A separately (resolve weight on C parallel to the incline). Tension in the rope is the same for both A and C.

• Once you have expressions for the resultant forces on A and on C, you can use Newton's 2nd law to relate them to the acceleration of the two objects (acceleration is the same for both).

• Now you have a system of simultaneous equations you can solve to find the tension in the rope and the acceleration of A and C. Because the mass of A is the same as the total mass of C in this case, these should be fairly easy to solve.

• Once you know the acceleration, use equations of motion for constant acceleration to find the change in height.

>>16196005
Problems like these, you outta intuitively think about using the conservation of energy. Also understand that this is a constrained problem. There's a thread in the catalog about a ball falling in between two blocks, and a bunch of people couldn't get it because they didn't understand that it was a constrained problem. In this case, the velocity of A will always be the velocity of mC. Then you also have to consider the wheels. If there is no rolling, the problem is easier, but if they are rolling, then some of the energy is being used to rotate the wheels.

No other information is given about the wheels, so you should ponder that

Can someone spoonfeed me how to find the orientation of a parameterization of a closed curve?
I understand that it's the orientation of the basis of {normal vector pointing inside of the area enclosed by the curve, vector tangent to the curve} with respect to the standard basis, but I can't understand how I'm actually supposed to determine the normal vector that points inside the curve. Is there a way except literally drawing the curve and the vector?
(I know I can use Green's theorem to find the area within the curve and the orientation is right IFF it is positive, but that seems kind of laborious).
I'm having a hard time understanding all this differential forms stuff so much appreciate any answers

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>>16196535
Afaik there is no way.
Consider that orientation is not a local property (two curves with opposite orientations can share a segment of their parametrization) so because it's a global property you'll automatically have to calculate some sort of integral.

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>>16196552
Funny drawing to complement my point.

>>16196552
>>16196557
I see, I was hoping there's some sort of simpler method than just computing [math]-\frac{1}{2} \int _{\gamma} {xdy - ydx }[/math] (or a similar differential form integral) and seeing if it's positive or negative, since it takes me a long time to do these with some of these curve parametrizations.

From Goldstein:
>While a Hamiltonian formulation can thus be introduced in a straightforward
manner for classical fields, note that the procedure singles out the time variable
for special treatment. It is therefore in contrast to the development we have given
for the Lagrangian formulation where the independent variables of time and space
were handled symmetrically.
How exactly does the Hamiltonian formalism single out time?

>>16197150
Well Hamilton's equations are differential equations only with respect to time.

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Anyone familiar OS? I'm having trouble with this past paper question. Please help.

What is the thermal conductivity of silver sulfide?
I ask because sterling silver should be one of the best materials to use for cookware (other than solid diamond but who the hell is using diamonds for pans?) due to its very high thermal conductivity and toughness however its surface slowly degrades into silver sulfide. The difference this makes is probably negligible but i still wanna know how much theoretically worse it becomes

>>16197355
extremely low, less than 1 W/K.m compared to 429 W/K.m for silver
supposedly heavily anisotropic also
but it's still OK if the layer is thin, teflon coating also has very low conductivity but is still used
silver sulfide is also fairly easy to remove with normal cleaning products
silver cookware actually exists as a commercial product: https://duparquet.com/products/solid-silver-cookware

>>16197403
Thanks and that exact store was what got me thinking about silver sulfide to begin with. By the way, where did you find that information about its thermal conductivity? I looked all over to no avail so it would be nice to know for future reference

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>>16197150
They both single out time if you're talking about the [math]L(q, \dot{q})[/math] formulation (there's also a literal time differential in the Euler-Lagrange equation), but it's fairly simple to adapt Lagrangian mechanics to relativity while in Hamiltonian mechancs the situation is completely different.

>>16180594
Is it necessarily true that for a function [math]f : \mathbb{R}^n \to \mathbb{R}^n[/math] that is differentiable with differentiable inverse is [math]C^1[/math]?

>>16197817
No.

>>16197849
How would you construct a counterexample?

Let [math]f: \mathbb{R} \to \mathbb{R}[/math] be bounded and Borel. True or false: for every [math]\epsilon > 0[/math] there is a simple (not necessarily integrable) [math]s: \mathbb{R} \to \mathbb{R}[/math] such that [math]\int_\mathbb{R} |f - s| dx < \epsilon[/math] ?

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How can I prove that the polynomial in pic rel is orthogonal on the interval [-1,1] wrt to the weight function ϕ(t)=(1−t^2) ^ (λ - 1/2)

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>>16197933
False as fuck, consider [math]f(x) = \sin x[/math], prove that, for all simples functions [math]s(x)[/math] with at most [math]n[/math] terms [math]\int_0^{2 \pi} |f - s| dx[/math] has a lower bound larger than zero, done.

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>First we scale the container by 0.5 on each axis and then rotate the container 90 degrees around the Z-axis.
it's been literal years since i've actually thought about matrices, why is the order like this again? isn't multiplication associative? did he just happen to list what's done in the code out of order

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>>16197946
1) i think you mean "commutative", not associative.
2) in general, matrix multiplication is not commutative.
3) scale and rotating *is* commutative, so it doesnt even really matter.
4) his code and description is correct, matrix transformations are "FIFO", i.e. you do the first one last.

>>16197956
excuse me, that would be FILO no FIFO

>>16197956
>3) scale and rotating *is* commutative, so it doesnt even really matter.
fuck me, UNIFORM scaling and rotating is commutative

>>16197956
whoops i did mean commutative lol
and thanks for the ordering clarification
after thinking for a bit (and more specific googling) i think the specific ordering is just a thing that only *really* matters when going between object and world space
>>16197959
very much noted lol

>>16197959
>>16197961
wait now i get the importance of order w/ non-uniform matrices
fuck i'm out of practice

>>16197971
theres a normal order that seldom changes:
scale -> rotate -> move -> viewport
the rotation one is weird and involves quaternions and shit but as long as you stick to that order you shouldnt get any weird results.

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>>16197933
>>16197943
>prove that, for all simple functions s(x) with at most n terms [math]\int_0^{2 \pi} |f - s| dx[/math] has a lower bound larger than zero, done.
Just hit me that this part of the proof is kind of nontrivial, so broad proof strategy:
[math]s[/math] having n components means it can take on n + 1 values tops. Dividing f's amplitude by n + 1 tells us that two points in the image are at least [math]\dfrac{2}{n + 1}[/math] apart. We'll call these two [math]a, b[/math] for convenience. We split the interval [math]a, b[/math] into three equal parts so we get [math]a < a + c < a + 2c = b - c < b[/math]. It's clear that the along the preimage of [math][a + c, b - c][/math] we always have [math]|f - s| > c[/math], so you have to determine the optimal choice of such a pre-image (which is going to be around 0 and have a *minimal* length) and glue together the entire lower bound.

>>16197975
gotcha, i'll write that down
also yea i vaguely remember mention of quaternions in a kinematics class i took but i absolutely didn't get it at the time lmao.......

>>16197982
>so you have to determine the optimal choice of such a pre-image (which is going to be around 0 and have a *minimal* length)
Correction: [math]|\sin' x| \leq 1[/math] so [math]\mu (\sin^{-1} ([a + c, b - c])) \geq \mu([a + c, b - c]) = c[/math]

https://doi.org/10.1117/12.2655671
https://doi.org/10.1364/AOP.468066

>>16197993
sorry, didnt know if DOI links were filtered.
can anyone get either of these papers? my school doesnt have access to those journals and they arent on scihub :(

>>16197920
[eqn]f(x) = \begin{cases} 4x + x^2 \sin(1/x) & x \neq 0 \\
0 & x=0\end{cases}[/eqn]

>>16197933
Only works if you work in L_1. Otherwise you run into problems with non-integrability

>>16197982
If [math]\int _{0} ^{2\pi} |f - s| = 0[/math] then f is almost everywhere equal s.
Since s is a simple function, then there exists a set with positive measure A such that [math]s(A) \equiv \text{ const}[/math]. But we know that sin(x) is never constant on a set with positive measure on [math](0,2 \pi)[/math]. So the integral must be separated from 0.

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>>16197933
>>16197943
Simpler counterexample:
[math]\displaystyle f(x) = \dfrac{ \chi_{ [1, \infty) }}{x}[/math]
For whatever [math]s[/math], let [math]a[/math] be the smallest element in [math]s[/math]'s image bigger than zero.
Then [math]\displaystyle \int |f(x) - s(x)| d \mu (x) \geq \int_{[2/a, \infty)} |f(x) - s(x)| d \mu (x) \geq \int_{[2/a, \infty)} \dfrac{1}{x} d \mu (x)[/math], which diverges.
>>16198228
Yeah but you can't prove that [math]\displaystyle \sum_{k = - \infty}^{\infty} \int _{2 \pi k}^{2 \pi (k + 1)} |f(x) - s(x)| dx[/math] diverges just by arguing that every individual term is non-zero.
Hence the necessity for a global lower bound.

In my understanding, at least.

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What's a generic "operator" symbol; a symbol that indicates any operation being done? I mean just for notes, meaning "if x <generic operator> y, then this happens/is true/is the case". I just mean something that can stand for multiplication, modulo or whatever you'd like, really.

>>16198537
[math]\ast[/math] is pretty commonly used to represent a binary operation in group theory.

>>16198543
Is there something more unique that wouldn't be taken for something else, like multiplication in your example? btw, yes, binary please; binary generic operator.

>>16198602
I've seen people use symbols like [math]\oplus\ \otimes\ \odot[/math] as a generic operator.

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>>16198638
hm, yea, also thought of using ⊙, or rather the Sun symbol () which is similar and represents the Monad and moreover supposedly "everything" or something, so I thought "everything operator", you know what I mean?, didn't know the 'Odot' used for this sorta thing; very epic; tysm, anonnete; lol; anyway, sending a virtual hug right now 2u!

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>>16198672
>()
meant to insert '' (the Sun symbol) in-between
"fix'd", as it were
anyway here's a rare Sun

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>>16198676
>"
i mean this fells in picreçl, 4chin does not allow speciaL chars like that, lol!
anyways, bye!

>>16198237
Thanks remi. I eventually came up with my own counterexample using the function [math]f = \sum_{n=1}^\infty \frac{1}{n} \chi_{[n, n+1)}[/math], but my proof was rather convoluted. Your argument is much neater.

Are there any frequencies of electromagnetic radiation produced by typical appliances that can penetrate the head and reach the brain? AKA could some of those studies saying they might be dangerous be true?

What are the best refreshers out there to prepare someone for Calculus that has been out of school for some time and is returning? I don't know how much HS math I remember, but it doesn't feel like much at times. I am good with mental math and am reasonable good with math puzzles, however.

whats the limit of sqrt[2k+1] {k*(3^k)}

>>16199056
Let
[eqn]a_k = \sqrt[2k+1] {k(3^k)}[/eqn]
Note that this is just a subsequence of the sequnece
[eqn] b_k = \sqrt[k] {\frac{k-1}{2}\left(3^{\frac{k-1}{2}} \right)}[/eqn]
So if you can prove that [math](b_k)[/math] converges against [math]L[/math] then [math](a_k)[/math] converges against [math]L[/math] too.

The limit of [math](b_k)[/math] can be calculated with Stolz-Cesaro
[eqn]\lim_{k \to \infty} \sqrt[k] {\frac{k-1}{2}\left(3^{\frac{k-1}{2}} \right)} = \lim_{k \to \infty} \frac{k 3^{\frac{k}{2}}}{(k-1) \left(3^{\frac{k-1}{2}} \right)} = \sqrt{3} \lim_{k \to \infty} \frac{k}{k-1} = \sqrt{3}[/eqn]

So
[eqn]\lim_{k \to \infty} a_k = \lim_{k \to \infty} b_k = \sqrt{3}[/eqn]

>>16199056
>>16199142
You could also let [eqn](1+h)= \sqrt[2k+1] {k(3^k)}[/eqn], then [eqn](1+h)^{2k+1}= k(3^k)[/eqn], then find an interesting binomial coefficient within the binomial expansion.

>>16199056
[math]\displaystyle \lim_{k \to \infty} \sqrt[2k + 1]{3^k k} = \lim_{k \to \infty} 3^{k/(2k + 1)} k^{1/(2k + 1)} = \lim_{k \to \infty} 3^{k/(2k + 1)} = \sqrt{3}[/math] where the last step is just the continuity of [math]x \to a^x[/math]

How do you measure slipperiness. Is it just the absence of friction? Is I generally accepted that less of a substances, say a shallower pool of water, is always necessarily less slippery?

This is more of a science question than math question that I got the idea for from a numberphile video. The idea is that there's two cars side by side, and they suddenly need to break to avoid hitting an obstacle. One of the cars is driving 100 mph and the other 70 mph, and if the 70 mph car barely stops before hitting the obstacle, the other car hits the obstacle at 71.4 mph. This assumes that both cars lose the same amount of kinetic energy and they start breaking at the same time for the same distance.

Does the speed at which you are breaking actually affect the energy that the breaks absorb even if both cars use the breaks for the same distance (and so the break discs also make the same number of rotations, but in the faster car it happens quicker)? Assumging also that they are using the breaks with the same force.

>>16199960
The charts you see that equation speed to stopping distance are an approximation. Friction (breaking) does vary with speed but I doubt it's a large variable. Then there is drag, which does depend on velocity, and probably various other factors too. tl;dr There is no simple way to calculate the exact numbers.

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What triggers a neuron to fire? Before you answer action potential depolarization, I want to know what stimulates even that? What sets it all in motion? Additionally, when I move my arm, what is the exact biochemical (metaphysical??) mechanism involved whereby my neurons fire to elicit arm movement? How does "will" connect with the material in the form of neuronal firing, causing ion channels to open and neurotransmitters to be released? Where does the crossover connection occur, if separate mind and matter is assumed? [spoiler]The Big Bang is the trigger isn't it?[/spoiler]

Very stupid question but bear with me. I'm a physics undergraduate, 4th year second semester. We have a project this semester which is basically "choose a specific subject out of this list and write a 5 page article about it using scientific literature". We've been told that we can also suggest to write an article about a subject that's not on the list. As retarded as this sounds, I want to ask permission to write an article about UFO study. Thing is, obviously the subject is heavily stigmatized and antagonized. I don't know how serious is the literature, and even if there are any conclusions in these studies. Should I ask permission or will I just get called a clown? The subject list is pretty mundane as anything in modern scientific study.

I'm a bit confused regarding the bounds of a function, why doesn't the function [math]e^{2-x^2}, x \geq 1[/math] not have the upper bound of e and a lower bound 0? Am I misinterpreting the definition perhaps?

>>16200545
>Thing is, obviously the subject is heavily stigmatized and antagonized.
You could make a cool article about theoretical spacecrafts but I genuinely don't get how UFOs would even be physics.

>>16200620
>You could make a cool article about theoretical spacecrafts
Decent idea.
>but I genuinely don't get how UFOs would even be physics.
Physicists are the only ones who research this kind of stuff. Its mostly astrophysicists and a touch of meteorologists.

>>16200592
Those bounds are correct. What makes you think they aren't?

>>16200592
>why doesn't the function e2−x2,x≥1 not have the upper bound of e
[math]x = 0 \implies e^{2 - x^2} = e^2[/math], which is the actual upper bound.
>lower bound 0?
0 is the correct lower bound tho.

>>16200697
Google Gemini, usually when he's wrong I can actually use my knowledge to practice and correct him, it's like he's a human study buddy. If I can't then that means that I need to study something a bit further
>>16200704
Thanks but the function had a domain of x≥1

>>16200778
>Thanks but the function had a domain of x≥1
Oh, my bad then.
>Google Gemini
LLMs are still atrocious at maths tbqhwy. I can't get them to solve basic tasks without thoroughly spoonfeeding them the proof strategy.

>>16200778
dont rely on AI chatbots for math stuff.

>>16200785
>>16200850
I don't want them to solve anything for me, only as a form of discussion and to explain some concepts, it has helped me I think, if I'm not happy with what he says I just default back here

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If you put a random infinitely long line on the Cartesian plane, what is the probability that any integer coordinates are on that line? By an integer coordinate I mean any point (a, b) where "a" and "b" are integers.

If you need specification how the "random line" is drawn, let's just say you select two uniformly random points inside a unit circle centered at origin and then draw the line through those points.

So 0.999... = 1
Like this is a proof that works out fine. I get that. I also get the image of the infinite limit where it eventually approaches 1 (or maybe I don't because I'm here asking about it). But is there ever any situation where you would want or need to distinguish between the two, or is that impossible/unreasonable because they're the same number by definition(?)

>>16201229
> random and infinitely long
Ask yourself how many possible such lines there are.

> is that impossible/unreasonable because they're the same number by definition
Correct. You are confusing the value of the number to i's representation. Each are the same value, but different representations.

>>16201229
Zero.

>>16201243
>is that impossible/unreasonable because they're the same number by definition(?)
So when you're in middle school your teacher explains to you something like "real numbers are these infinite strings of digits, but the ones that end with 999... are actually the same as the ones that end with 000..." or something like that.
That's not what real numbers are. Real numbers are usually constructed with Dedekind cuts or Cauchy sequences and the essential thing you need to know is that real numbers need to be separated by rationals. 0.999... = 1 because there are no rationals between them.
>But is there ever any situation where you would want or need to distinguish between the two
You can do stuff with infinitesimals for stuff like that.
You can also directly operate on strings of digits, but then you have the issue with arithmetics that your teacher has already proven pops up.

Is there a word for "set containing at least n elements"?

>>16180594
Planning on doing a summer course for Linear Algebra in order to do Quadratic Equations next semester.
Thing is i struggle a lot with integration and have very shoddy math fundamentals.
Any tips as to how to reinforce my math in the next couple of months in order to not get ass raped next semester?

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>>16202136

>>16201456
Forgot to reply earlier but thx for the explanation anon