/sqt/ /qtddtot/ - stupid questions thread

[Anonymous No.12399674]

Previously >>12387042

>what is /sqt/ for
Questions regarding math and science, plus related advice requests.
>where do I go for other SFW questions and (advice) requests?
>>>/wsr/ , >>>/g/sqt , >>>/diy/sqt , >>>/adv/ , etc.
>carreer advice?
https://sciencecareergeneral.neocities.org/
>books?
https://spoon.wiki/Books
https://stitz-zeager.com/
>articles?
sci-hub.st
>book recs?
https://sites.google.com/site/scienceandmathguide/
https://4chan-science.fandom.com/wiki//sci/_Wiki
http://math.ucr.edu/home/baez/physics/Administrivia/booklist.html
>help with calculus?
https://spoon.wiki/WolframAlpha
>how do I post math symbols?
https://imgur.com/MDiglsS.png
>a google search didn't return anything, is there anything else I should try before asking the question here?
https://scholar.google.com/
>where do I look up if the question has already been asked on /sci/?
>>/sci/
https://boards.fireden.net/sci/
>how do I optimize an image losslessly?
https://trimage.org/
https://pnggauntlet.com/

Question asking tips and tricks:
>attach an image
>if a question has two or three replies, people usually assume it's already been answered
>ask anonymously
>check the Latex with the Tex button on the posting box
>if someone replies to your question with a shitpost, ignore it

Stuff:
Meme charts: https://imgur.com/a/JY6NNeL
Serious charts: https://imgur.com/a/0qDEgYt (Post any that I've missed.)
Verbitsky: https://pastebin.com/SmBc26uh
Graphing: https://www.desmos.com/
Tables, properties, material selection:
https://www.engineeringtoolbox.com/
http://www.matweb.com/

[Anonymous No.12399684]

>>12399674
Are there any good organic chemistry lectures on youtube?

[Anonymous No.12399691]

So we have the given problem: "For an unfair coin toss, the probability it lands heads is p=0.6. Find the probability that in 20 coin tosses it lands heads AT MOST 5 TIMES (no more than 5 times)".

I thought I should approach this using the binomial distribution, for n=20 and p=0.6 I looked up the tables of cumulative function for the binomial distribution (we don't need to actually integrate analytically), and for 20 tries under p=0.6 and for r=5 successes it gives me a probability of 0.001. Is that correct? I get that with a 60% chance of landing heads it is unlikely you only get 5 or under in 20 tosses, but 0.001 seems wayyyy too small to me. Any clarification would be greatly appreciated

[Anonymous No.12399699]

I am a physics major currently taking my first statistics course. We're covering chapters 1-12 from the OpenStax Introductory Statistics textbook. I want to get another book to use for reference, after I finish the course. Below is a list of things I would like to have in it (these are preferences, not requirements):

Calculus. The OpenStax book aims to be (largely) accessible to students who have not done any calculus. While I understand the necessity of omitting the calculus, I find it dissatisfying.
Detail. This has some overlap with the first point. The way the OpenStax text explains some things feels shallow. Sometimes my intuition often tells me that there must be more to a topic than what the book explains. Chapter 7 (The Central Limit Theorem) is a good example of what I am describing.
Applications. I want to learn more about how the statistics is used in experimentation, data analysis, and physical models. I think the OpenStax textbook does a good job showing the relationship between statistics, data, and experiments. I would love to have a book that takes concepts from statistics and probability and connects them to physics (or even chemistry).
Content. Too much information is better than too little. I welcome extra topics/content, so long as the math is manageable. I am comfortable with differential and integral calculus, sequences, series, parametric functions, and a little linear algebra. I learned some complex algebra in high school, so I know what imaginary and complex numbers are and did some graphing on a complex plane. I have been exposed to some differential equations (which I will take a course in next semester) and multivariable calculus (not taking that course until spring 2022) through physics.

[Anonymous No.12399704]

>>12399691
[math]P(k\leq 5)=\sum_{m=0}^{5}P(k=m)[/math]
Is this correct?

[Anonymous No.12399710]

If A is a subset of B, is always true that B is a super set of A?

[Anonymous No.12399713]

>>12399704
Yes.

[Anonymous No.12399722]

>>12399710
Yes. Two sets a,b can never be supersets of each other but two classes c,d can be superclasses of each other

[Anonymous No.12399733]

Is 12 decimal?

[Anonymous No.12399742]

Had this question in the last thread, but still don't get it. Say I have a hula hoop like object that equations a) and h) of pic related apply to. Say this hula hoop is rolling down an inclined plane of 20 degrees. Which of the equations a) or h) would I apply?

I guess I don't really understand the difference in motion between a) and h). Is a) rolling how I'd expect a hoop to roll, while h) is 'flopping' or 'clunk-clinking' like how a crossfit person would move a tire? If so, obviously in my scenario I'd choose a).

[Anonymous No.12399744]

My prof glossed over really quickly that the commutator subgroup of A4 (the alternating group) is equal to V (the Klein 4 group). The containment of A’4 in V I have but the other direction I’m lost on. How do I show this?

[Anonymous No.12399752]

In the first episode of Jojo's Bizarre Adventure Stardust Crusaders, Star Platinum Catches a bullet at point-blank range. The revolver was a Nambu Model 60. How fast would Star Platinum have to be to catch it?

[Anonymous No.12399757]

Trying to figure out the exact percent of our lives watch spent watching TV

The average American watches for... 4 hours per day.

Average American lives to 78.54.

Average American lives somewhere around 692,040 hours.

What would be the best way to figure what percent our lives spend watching a bunch of Kardashians buy things for high prices?

Thank you!

[Anonymous No.12399758]

>>12399742
>Is a) rolling how I'd expect a hoop to roll, while h) is 'flopping' or 'clunk-clinking' like how a crossfit person would move a tire?
Yes, exactly.

[Anonymous No.12399769]

In a graph network defines by an adjacency matrix, is there any meaningful way to assign an angle to two paths or edges that intersect at a node? It feels like something similar to assigning distances and angles in different vector spaces. If anyone could point me in the right direction, it would be appreciated.

[Anonymous No.12399774]

Say I am creating a random number generator to randomly assign numbers from 0-99 to a baseball team of 26 people. However, I forget to take a number out once it is assigned. What are the chances I assign the same number to 3 different players.

[Anonymous No.12399782]

Given I have a set of numbers x = [1,2,3,4,5] and I want every subset of n combinations, how would I find that? For example, if n was 1, I would want the set to look like:

[1],[2],[3],[4],[5]
If n was 2 I would want the set to look like:

[1,2] [1,3] [1,4], [1,5], [2,3], [2,4], [2,5], [3,4], [3,5], [4,5]
And so on. What is the formula I would use to find the number of combinations?

[Anonymous No.12399790]

if tests are 30 percent of my grade, and i have 3 tests, are they 10% individually?

[Anonymous No.12399796]

What Level of Calculus is Differential Equations?

[Anonymous No.12399802]

You are dealt five cards from a standard deck of 52 cards. How many of these hands have at least one king and at least one heart.

[Anonymous No.12399809]

so we bought 85 dollars worth of food one person paid 11 out of 55 other paid 6 out of 30 and we slip with 5 people in total how much does each person get?

[Anonymous No.12399878]

>>12399758
thanks!

[Anonymous No.12399880]

Let X and Y be a random variables that are not necessarily independent. If U is the conditional distribution of Y given X = u, V is the conditional distribution of Y given X = v where u and v are two different values in the support of X, how do we check if U and V are independent? Or because they are conditioned on different values, U and V are, in a sense, mutually exclusive?o

[Anonymous No.12399892]

>>12399880
U,V are distributions so there is no sense in thinking about independence. Question is poorly worded

[Anonymous No.12399904]

>>12399782
Combinatorics 101. Answer is nCk

[Anonymous No.12399909]

What does it mean when this thread has 25 replies and 5 posters?

[Anonymous No.12399914]

i have to do physics lab online, so it can be hard for me to guage uncertainties and stuff since everything is technically a supplied measurement (i.e, no uncertainty).

but today I have this thing, which spins when it is hit with a piston and we move the purple objects to adjust the rotational inertia and therefore acceleration. my question relates to the uncertainties present:

I place the objects along the axis, so I assume it's proper to assign some uncertainty value, say [math]\pm 0.01[/math]m. If I knew radius of this circle I could get the circumference, and apply some of that uncertainty to the angular speed value, but I can't. so now considering the speed value, I thought some appropriate uncertainties might be randomly applying something like [math]\pm 0.1^{\circ}[/math] and [math]\pm 0.1[/math]s (seconds).

does any of this make sense, or am I best to have no uncertainties in this situation? my prof is a bit of a stickler for them.

[Anonymous No.12399917]

>>12399909
How do you know

[Anonymous No.12399933]

>>12399909
Someone is either shitposting or wants us to do their math homework for them.

[Anonymous No.12399934]

Is it bad that I want a PhD so I can be a part of the nuclear weapons program, because of repressed murderous rage?

Also, would it be possible to be a fighter jock and get a PhD?

[Anonymous No.12399972]

>>12399909
There are questions science just can't answer.
BTW tally ETA is ~6 hours, because I'm estimating I'm going to be in the mood for doing it around then.

[Anonymous No.12399989]

when will technology get to the point where i could become an anime girl for real?

[Anonymous No.12400019]

>>12399674
what do u guys think of climate change research as an academic field? Im a strong math undergrad at a top university, and since i worked a co-op at a government environmental agency, I am receiving lots of interest and opportunity to work with climate research profs. Im looking to pivot from math to more computational/data/statistics research areas because i dont see myself staying in academia long term, but im curious what you guys think of climate change research in general. im not a climate change greta doomer, nor am i a conservative oil sands boy, i just want to do interesting data-oriented and statistics research, and the opportunities available seem fun to work on, and the profs are very nice sociable people (a good break from math autists). just wondering if u guys think climate research is a shitty field or something to get into. the actual opportunities are climate physics, atmospheric modelling, glaciological modelling, and the profs are in physics or earth/ocean sciences departments. to clarify, the opportunities are undergrad research opportunities, not grad school. what do u anons think? im thinking i should do climate physics so that im set to either do physics/applied math grad school

[Anonymous No.12400023]

For YEARS my brother and dad have argued over this hypothetical issue, and I want somebody to weigh in.

The argument: If you flip a coin for eternity, it is impossible to flip tails every single time for infinite time. Eventually, you will HAVE to flip heads.

My father says that eventually you WILL flip heads. My brother says that there is no guarantee you will flip heads, and for eternity you can flip tails.

I'm just tired I'd hearing this argument, can somebody help me lay it to rest?

[Anonymous No.12400047]

>>12400023
both eternal tails and any kind of sequence to infinity have probability zero (think head tails alternating or whatever). All zero probability. This does not mean impossible, but almost surely won't happen.

[Anonymous No.12400059]

>>12400047
I have to add that I have no formal proof of this so I welcome a measurebro providing proof or counterexample

[Anonymous No.12400088]

>>12400019
Boom of funding in this field lately, mostly gibs from guvvie and shady ngos. It's a fad. If you specialize in that, take into account that once a new fad comes up you'll have no funding and a hardly transferable set of knowledge. You're a math major so you could sell yourself, but the pigeonhole risk is high.

[Anonymous No.12400157]

Shamefully reposting my unanswered question from previous thread

Let [math](X, \Sigma, \mu)[/math] be a measure space. Suppose [math]\mu(E_n) < \infty[/math] for all [math]n[/math] and suppose that the indicators [math]\chi_{E_n}[/math] converge in the [math]L^1[/math] sense to some [math]f[/math]. Show there exists [math]E \in \Sigma[/math] such that [math]f = \chi_E[/math] almost everywhere.

My attempt: Let [math](\chi_{E_{n_k}})_{k=1}^{\infty} [/math] be a subsequence that converges a.e. to [math]f[/math]. Suppose this convergence takes place on some full measure set [math]A[/math]. Let [math]x\in A[/math]. If [math]x \in \liminf_{k} E_{n_k}[/math] then surely [math]f(x)=1[/math]. Otherwise, since [math]\lim_{k} \chi_{E_{n_k}} (x)[/math] exists, we must have [math]f(x) = 0[/math]. This implies that [math]f = \chi_{\liminf_{k} E_{n_k}}[/math] on [math]A[/math] (hence a.e.).

Does this seem right to you? I have qualms because a nearly identical argument can be used to show that [math]f = \chi_{\limsup_{k} E_{n_k}}[/math] on [math]A[/math].

[Anonymous No.12400168]

>>12399914
Do you get different values when you do the simulation with the same initial conditions?

[Anonymous No.12400203]

This is my last attempt on getting some information on how to sole Project Euler #735.

By using prime factors, finding the number of factors for a given number is easy. But how would I go about doing this for the number of factors for 2n^2 that are below n?

According to this: https://math.stackexchange.com/questions/58426/number-of-factors-less-than-a-number
I must take the number of factors, subtract one, half it, and then add one. This works fine for most numbers but not for 2n^2 = 72 and 450.

Any help would be appreciated!

[Anonymous No.12400284]

I'm having an online exam in a few days. What is the best free solution for solving integrals, something that breaks it down similarly like I would do it mechanically on my own.

[Anonymous No.12400293]

>>12400284
Learn your integrals fag

[Anonymous No.12400301]

>>12400293
I have less than two days anon

[Anonymous No.12400317]

>>12400301
symbolab. but learn your integrals

[Anonymous No.12400355]

>>12400023
I think your brother is right here. He's only saying that there is (NO GUARANTEE) that you will flip heads and I feel like that is true. As the number of coinflips approach infinity, the chances of not flipping heads approach zero, but that's all that happens. It approaches zero, and for all intents and purposes, it would be considered zero, but I don't think it's truly ever zero, just arbitrarily close to zero.

Let's consider it on a per flip basis. Every time you flip it, you have a 50/50 chance of getting tails. At no point will that ever not be true. At no single flip will you be guaranteed to flip heads. Your dad claims that you are GUARANTEED to flip heads at some point. If you're not guaranteed to flip heads at any single point, then at what point will you be guaranteed to flip heads?

I'm not sure that's correct. It's just what I think. t. undergraduate.

[Anonymous No.12400389]

>>12400317
Thanks

[Anonymous No.12400620]

>>12399757
Just divide the 4 hours of watching TV with 24 hours in a day and you get 4/24 or 1/6, which means it is a huge waste of your time.
I no longer have a TV.

[Anonymous No.12400624]

Why can't ax+In(bx)+c=0 be solved algebraically?

[Anonymous No.12400790]

>>12399674
Does the CMB rest frame pick out a "special" location in the universe? Since galaxies are accelerating away from each other, there has to be one region of the universe with exactly the same reference frame as the CMB rest frame. Would it not make sense to call this the "center" of the universe? Or at least a special location within it? All observers would agree that the spot with a co-moving frame identical to the CMB rest frame is special.

[Anonymous No.12400942]

>>12400790
There is no center to the universe, the "location" of the CMB is a sphere with (You) as its center.

[Anonymous No.12400957]

Unsanswered questions:

There's a typo somewhere in this post.

Math questions:
>>12390171
>>12392416 [He probably took my suggestion and solved it on his own, but it still goes here.]
>>12396260 [Something something naturals are integrally closed in the rationals something something if p and -p are roots f(0) would need to be divisible by f(0) twice.]
>>12398997
>>12399226
>>12399444
>>12399455
>>12399460
>>12399499
>>12399502 [I have like, no idea what's he doing.]
>>12399503
>>12399509

Physics questions:

Engineering questions:
>>12390816
>>12393076

Chemistry questions:
>>12394907 [If it were just the drinkable part it would go in stupid, but he leads it with a serious question.]
>>12396831

Psychology questions:
>>12398187

Stupid questions:
>>12388244
>>12395130
>>12397806 plus >>12397914
>>12399026
>>12399044
>>12399492 [What?]

[Anonymous No.12400977]

Do you lads think that once robotics and AI have advanced enough we'll be able to use machine learning to feed AIs data so they have the personalities of specific people, and I'll be able to get a yukariposter robot maid gf?

[Anonymous No.12401010]

>>12400942
But there is a CMB rest frame, right? So that picks out a special reference frame. So change your speed until you are in that reference frame. Then look out at the universe and find the galaxy which is stationary relative to you.

Wouldn't all observers, regardless of their location in the universe, agree on which galaxy (or cluster of galaxies or whatever) that is?

[Anonymous No.12401072]

>>12401010
no there isn't

[Anonymous No.12401090]

Hello /sci/
Could one of you please recommend me a book, website, video series or anything of the sort as a definitive guide on limits.
I'm currently studying electrical engineering and some of the limits they make us solve are giving me some trouble.

pic rel, an example, pls no bully

[Anonymous No.12401095]

>>12401090
you're looking for l'hopital's rule
any calculus 1 book should have a "guide to limits," it's not a standalone topic

[Anonymous No.12401100]

>>12401072
Yes there is.
>https://en.wikipedia.org/wiki/Cosmic_microwave_background
From the CMB data, it is seen that the earth appears to be moving at 368±2 km/s relative to the reference frame of the CMB (also called the CMB rest frame, or the frame of reference in which there is no motion through the CMB.). The Local Group (the galaxy group that includes the Milky Way galaxy) appears to be moving at 627 ± 22 km/s in the direction of galactic longitude l = 276° ± 3°, b = 30° ± 3°.[83][10] This motion results in an anisotropy of the data (CMB appearing slightly warmer in the direction of movement than in the opposite direction).[84] From a theoretical point of view, the existence of a CMB rest frame breaks Lorentz invariance even in empty space far away from any galaxy.[85] The standard interpretation of this temperature variation is a simple velocity red shift and blue shift due to motion relative to the CMB, but alternative cosmological models can explain some fraction of the observed dipole temperature distribution in the CMB.

[Anonymous No.12401107]

>>12401100
hm I didn't know this.

[Anonymous No.12401126]

i get it doesn't really matter but is the 3(n+1)+1 right? shouldn't it be 3(n+1)+4?

[Anonymous No.12401135]

>>12401010
The rest frame matches with all points in the observable universe from which photons were emitted during the recombination 370k years after the Big Bang.
Because the Universe is isotropic and homogeneous, it must look the same regardless of your observation point.
Therefore, the frame is merely a sphere with the observation point at its center and its radius determined by how long light has traveled.

[Anonymous No.12401156]

>>12401135
I don't understand this. Aren't those points all moving away from each other? So therefore they have different velocities. So how can they all be the same reference frame?

[Anonymous No.12401182]

Does anyone how that I can learn mathematics to speed up my brain?

[Anonymous No.12401200]

>>12401182
install gentoo

[Anonymous No.12401209]

>>12401156
Those points are moving away from you.

[Anonymous No.12401228]

>>12401209
Yes I agree. So they aren't in my reference frame, right? They have a different reference frame.

[Anonymous No.12401240]

the implications of covid has had effects on supply chains across the world
>food
>medicine
>personnel
probably more

have these effects had an impact on deaths unrelated to covid?

[Anonymous No.12401260]

>>12401240
>have these effects had an impact on deaths unrelated to covid?
Of course, but how much is a matter of debate and we may not have decent answers for years.

[Anonymous No.12401385]

As you gain more knowledge, do you feel the world get more boring because you now "know how it works"?

[Anonymous No.12401397]

>>12401385
no because we still don't know how things work on a fundamental level. there are a lot of mysteries
and philosophy still exists

[Anonymous No.12401456]

>>12401385
as a programmer my biggest gripe is that all of the problems i encounter at work are manmade
i do not solve problems, i fix bugs

[Anonymous No.12401499]

Hello, I posted this circuit a few weeks ago and many helpful anons told me it probably was a common, unity gain, low output impedance amplifier. I agree, and doing the math yields results that support that. However, I am told that this circuit has a special use, and hence a special name, something that maybe has something to do with load curves. Has anyone ever used it or seen it and know where this might be used? or what name it could have? Thanks for the help

[Anonymous No.12401596]

[math]13x \equiv 5 \mod{21}[/math]

A really noob question, but I've never had congruence before and the teacher didn't explain it at all and gave us this homework. We're supposed to solve it with Euclides' algorithm, so we need to put it into a form like

[math]13^{-1}\times13x \equiv 13^{-1}\times5 \mod{21}[/math]

but idk what number i'm supposed to put Euclides' algorithm to

[Anonymous No.12401631]

>>12401596
Nvm, I found this https://www.york.cuny.edu/~malk/mycourses/math225/euclideanalgorithm.html

[Anonymous No.12401763]

Continuing from a previous post.
>>>12398867
>Low-level data monkey. Requires knowledge of databases, data cleaning, not that much programming. Once you know enough math you can move to junior data analyst.

Advice on any online courses and skills to develop to become this low level data monkey. I guessing Excel would be required? Anything else?

[Anonymous No.12401784]

The correct answer is D. I'm can't really say why. Can someone fill in the gap in my understanding?

Initial velocity was the same in both cases. Acceleration on earth is 6 times acceleration on the moon. This means it should take 6 times as long to reach a velocity of zero (at which point, it would be at its max height). Why does this also mean that the max height is 6 times the max height on earth?

[Anonymous No.12401794]

>>12401784
conservation of energy
maximum height is where all the kinetic energy is converted to potential energy
[math] K= \frac{1}{2} m v^2 \rightarrow mgh [/math]
since K is the same starting on the earth and the moon (same velocity and same mass) then you get
[eqn] mg_{E}h_{E}=mg_{M}h_{M} \\
h_{M}=\frac{g_{E}}{g_{M}} h_E \\
h_M=\frac{g_E}{g_E/6} h_E \\
h_M=6 h_E [/eqn]

[Anonymous No.12401854]

>>12399674
Tried putting in the values but I can't figure it out. Some help?

[Anonymous No.12401869]

I have a question regarding CS/Data Science internships. I'm just about to finish Linear Algebra, I've done single-variable Calc, discrete math and stats. Do you think I can get an internship in a CS or Data Science related field while I'm studying for my bachelor's, or should I just focus on my studies?

I don't consider doing menial webdev work as a good use of my time, and would like to avoid it as much as I can.

[Anonymous No.12402209]

>>12401794
Thanks. I wouldn't have thought about using conservation of energy because this was in the kinematics chapter.

[Anonymous No.12402221]

>>12401869
I think it might be better to focus on your studies right now. Specifically because of the pandemic, getting internships might be tougher. Not only that, but the quality of the work experience you get may be lower since you won't have as much interaction with your superiors and your workplace.

I'm not a CS guy though. Maybe working from home will not be that different from the work you do outside the pandemic. I'd say just increase your course load and grind harder in school.

[Anonymous No.12402252]

Im panicking a little because all of the sudden I have no idea what the fuck what is going on in this physics chapter (static equilibrium). For one example, I've realized I have no idea why it's assumed that these two angles are the same.

[Anonymous No.12402261]

>>12400019
Did some climate research (econ). It was nice and it feels like the field is moving up. You'll probably be doing climate scenario modeling or investigating geoengineering, both interesting topics in my opinion. Stay away if you don't like uncertainty because there's a lot of it.
>>12401126
Looks like it to me, probably a typo.
>>12401240
Hard to know so early into the pandemic, but it's a great natural experiment (in the social sciences meaning of the word) so expect loads of papers to be published on the topic in the future.

[Anonymous No.12402274]

>>12401854
Any help with this?

[Anonymous No.12402301]

>>12402252
You can form a right-angled triangle by drawing lines along the directions of f and w. Then remember what the angles of a triangle add up to.

[Anonymous No.12402755]

Let [math]D_m[/math] denote the dihedral group of an [math]m[/math]-gon (i.e. has order [math]2m[/math]). How can I show that for all even [math]n[/math], we have [math]D_{2n} \ncong D_n \times \mathbb{Z}_2[/math]?

I've been stuck on this for a while now. I know that since [math]n[/math] is even, [math]\mathbb{Z}_2 \cong \langle R^{n/2} \rangle[/math] (where [math]R[/math] denotes some rotation in [math]D_n[/math]), but I'm not sure how to put this to use

[Anonymous No.12402852]

Ok bros real analysis time

Assume [math]f_n \to f[/math] uniformly. Prove that [math]|f_n| \leq M \Rightarrow |f| \leq M, M>0[/math].

My attempt:

Assume by contradiction that [math]|f(x)| > M \ \forall x \in A[/math].
Therefore [math]||f(x)|-M|=\varepsilon_0>0[/math].
This implies [math]||f(x)|-|f_n(x)||\geq||f(x)|-M|=\varepsilon_0>0[/math].
Hence [math]|f_n(x)-f(x)|\geq||f(x)|-|f_n(x)||\geq \varepsilon_0[/math].
But uniform convergence implies that there exists [math]N \in \mathbb{N}:\forall n \geq N,|f_n(x)-f(x)|<\varepsilon_0,\forall x \in A[/math].
This contradiction implies [math]|f(x)|\leq M[/math].

Is this argument sound? Any feedback appreciated

[Anonymous No.12402868]

>>12402852
There is a mistake in your first line - you would need, for contradiction's sake, to assume that there exists an x s.t. abs(f(x)) > M.
In the second line you need to drop the outer norm bars in order to make your argument in the third line. Other than that it is correct.
An alternative way would be to use the triangle inequality:
[math]\vert f \vert = \vert f - f_n + f_n \vert \leq \vert f-f_n \vert + \vert f_n \vert \leq M + \vert f-f_n \vert[/math]
The second term in the last equality can be uniformly (in x) estimated by [math]\epsilon[/math] for any [math]\epsilon[/math] by choosing n large enough, and this yields the assertion.

[Anonymous No.12402875]

>>12402868
Thank you!

[Anonymous No.12402931]

>>12401854
Sum identity: sin(α+β)=sin(α)*cos(β)+cos(α)*sin(β)
a^2+b^2 = (sin(α)+sin(β))^2 + (cos(α)+cos(β))^2
= (sin(α)^2+2*sin(α)*sin(β)+sin(β)^2) + (cos(α)^2+2*cos(α)*cos(β)+cos(β)^2)
= sin(α)^2+cos(α)^2 + sin(β)^2+cos(β)^2 + 2*sin(α)*sin(β) + 2*cos(α)*cos(β)
= 1 + 1 + 2*(sin(α)*sin(β) + cos(α)*cos(β))
= 2*(1+sin(α)*sin(β) + cos(α)*cos(β))
2*a*b = 2*(sin(α)+sin(β))*(cos(α)+cos(β))
= 2*(sin(α)*cos(α) + sin(α)*cos(β)+cos(α)*sin(β) + sin(β)*cos(β))

sin(α+β)*(a^2+b^2) = (sin(α)*cos(β)+cos(α)*sin(β))*2*(1+sin(α)*sin(β) + cos(α)*cos(β))
= 2*((sin(α)*cos(β)+cos(α)*sin(β))
+ (sin(α)*cos(β) + cos(α)*sin(β))*sin(α)*sin(β)
+ (sin(α)*cos(β) + cos(α)*sin(β))*cos(α)*cos(β))
= 2*(sin(α)*cos(β) + cos(α)*sin(β)
+ sin(α)*cos(β)*sin(α)*sin(β) + cos(α)*sin(β)*sin(α)*sin(β)
+ sin(α)*cos(β)*cos(α)*cos(β) + cos(α)*sin(β)*cos(α)*cos(β))
= 2*(sin(α)*cos(β) + cos(α)*sin(β)
+ sin(α)^2*cos(β)*sin(β) + sin(β)^2*cos(α)*sin(α)
+ cos(β)^2*sin(α)*cos(α) + cos(α)^2*sin(β)*cos(β))
= 2*(sin(α)*cos(β) + cos(α)*sin(β)
+ sin(α)^2*cos(β)*sin(β) + cos(α)^2*sin(β)*cos(β)
+ sin(β)^2*cos(α)*sin(α) + cos(β)^2*sin(α)*cos(α))
= 2*(sin(α)*cos(β) + cos(α)*sin(β)
+ (sin(α)^2 + cos(α)^2)*sin(β)*cos(β)
+ (sin(β)^2 + cos(β)^2)*sin(α)*cos(α))
= 2*(sin(α)*cos(β) + cos(α)*sin(β) + sin(β)*cos(β) + sin(α)*cos(α))
= 2*a*b

=> sin(α+β) = 2*a*b/(a^2+b^2)

[Anonymous No.12402935]

>>12402931
I feel so glad I'm past trigonometry.

[Anonymous No.12402941]

For jobs IT, is it better to have a math degree or a CS degree?

[Anonymous No.12402945]

>>12402931
bruh

[Anonymous No.12402949]

best free online source to learn basic analysis?

[Anonymous No.12402993]

>>12401763
Any answers?

[Anonymous No.12403008]

>>12399674
Question regarding QM. Can a superposition of coherent states be a pure state? And if not was the effect of the ladder operators on a pure state?

[Anonymous No.12403042]

>>12401763
>>12402993

Excel, but most importantly some SQL + queries. Then you can move to R/Python for data analysis

[Anonymous No.12403183]

can someone help me please.
im trying to find a pre jordan basis and I have (x,-x,z) for x,z in Complex Numbers.
my lecturer has the basis as (1,-1,-1) and (0,0,1). can someone explain this to me, i thought it would be (1,-1,0) and (0,0,1)

[Anonymous No.12403210]

I have a lot I should be doing but I just procrastinated for 3 hours and now it’s 1am. What do?

[Anonymous No.12403223]

>>12403210
Sleep. Do better tomorrow.

[Anonymous No.12403229]

>>12403042
Thank you mate.

[Anonymous No.12403335]

The fags on stack exchange have failed me on this one. See pic related for the setup and disregard part a.

>Define a weak exchange Bayesian Nash equilibrium (WEBNE) as a Bayesian Nash equilibrium in which each student [math]i[/math] chooses [math]s_i(g_i) = X[/math]exactly when

[math]\mathbb{E}(v_i(X,s_{-i}(g_{-i});g_i) | \text{ envelope for student [math]i[/math] contains [math]g_i[/math]})[/math]

[math]\geq \mathbb{E}(v_i(H,s_{-i}(g_{-i});g_i) | \text{ envelope for student [math]i[/math] contains [math]g_i[/math]})[/math]

>Find all the symmetric (where both students use the same strategy) WEBNE of this game.

We have an action for each type the players can take on and we have 5 types, thus we are looking for equilibria that look like [math](s_1(g_1)s_1(g_2)s_1(g_3)s_1(g_3)s_1(g_4)s_1(g_5),s_2(g_1)s_2(g_2)s_2(g_3)s_2(g_3)s_2(g_4)s_2(g_5))[/math] where [math]s_1(g_i) = s_2(g_i) \forall i[/math]. From my understanding, a potential candidate solution could be something like (HHXXX,HHXXX). However, it seems like a lot of work testing random candidate solutions if they satisfy the inequality. Is there a more intelligent way to find these symmetric WEBNE solutions?

I know this is a lot of text, so special shoutouts to any anons who help

[Anonymous No.12403354]

>>12403335
Consider the strategy "offer to trade if and only if you get an F".
If you know the opponent will only offer to tade when he gets an F, you have literally no incentive to offer to trade if you get any other grade or above, so it should satisfy the Nash thing conditions.

[Anonymous No.12403361]

>>12403354
Is this a unique solution? If not, is the best way to find other equilibria to simply rationalize like you just did?

[Anonymous No.12403364]

>>12399674

[Anonymous No.12403389]

>>12403361
>Is this a unique solution?
Doubt it. Probably the only deterministic equillibrium tho. Does bayesian shit admit non-deterministic equillibria?
>is the best way to find other equilibria to simply rationalize like you just did?
Probably.

[Anonymous No.12403429]

>>12403389
>Does bayesian shit admit non-deterministic equilibria
If you are referring to something like this: https://www.dmtcs.org/pdfpapers/dmAF0106.pdf, then I have not learned it in class so I imagine it would not hold in this context.

[Anonymous No.12403430]

>>12403361
>>12403389
Actually, on further thinking, it might be the only solution.
For a proper equillibrium that isn't an autistic corner case like >>12403354 , you'd imagine that the expected grade given that you trade needs to equal the expected grade given that you want to trade. Except it's constantly that plus one.
Hence, the issue.

[Anonymous No.12403533]

>>12403430
>you'd imagine that the expected grade given that you trade needs to equal the expected grade given that you want to trade. Except it's constantly that plus one.
Wouldn't that give an incentive to trade or am I misunderstanding your argument? If it's that payout plus one, that gives a higher payout.

[Anonymous No.12403564]

>>12403533
>Wouldn't that give an incentive to trade
That's the broad issue.

[Anonymous No.12403630]

>>12403564
Ah I see now thank you

[Anonymous No.12403824]

Did I do this problem correctly?
[math]F_{net} = \mu_k(M+m)g[/math] The net external force is the force of kinetic friction only.
[math]W = Fd [/math] W = Fd because force and displacement are parallel
[math]W = -\mu_k(M+m)gd [/math]

[math] .5mv_{ci}^2 = \mu_k(M+m)gd [/math] The change in mechanical energy is equal to the work done
[math] v_{ci} = \sqrt{\frac{2\mu_k(M+m)gd}{m}} [/math] solve for initial velocity of the wad of clay

[Anonymous No.12403860]

>>12403824
The speed of the clay before impact is not the same as the speed of the clay + block after impact. What you've determined is the latter, use conservation of momentum to find the former.

[Anonymous No.12403954]

>>12403335
>>12403354
Fuck, offering to trade if you get an F or a D should also be an equillibrium. Logic is the same as earlier for it.
I had thought about how swapping D didn't give any utility loss, but I kind of just assumed that it spiralled off unstably.
Anything above is loss tho.

[Anonymous No.12403973]

>>12403860
Is this correct?
[math] mv_{ci} = (m+M)v [/math]
[math]v_{ci} = \frac{ (m+M)v}{m} [/math]
[math]v_{ci} = \frac{ (m+M)\sqrt{\frac{2gd\mu_k(M+m)}{m}}}{m} [/math]

[math]v_{ci} = \frac{ (m+M)\sqrt{2gd\mu_k(M+m)}}{m^{3/2}} [/math]


I don't really understand how I wound up finding the final velocity in my initial derivation.

[Anonymous No.12403983]

>>12403973
Almost. Swap [math]v_{ci}[/math] and [math]v[/math], [math]v[/math] is what you're looking for in the end.

[Anonymous No.12404011]

>>12403983
Thanks for the help. I think I got the right answer now. I think I'll read the chapter again then reattempt this. I kind lost track of the physics and was just doing algebra after some point.

[Anonymous No.12404016]

This is false but could someone give me an example function/sequence.

[Anonymous No.12404049]

>>12404016
The constant zero function.

[Anonymous No.12404050]

>>12404016
any constant function will do

[Anonymous No.12404057]

Scientifically speaking, what are some good feeds to add to my RSS?

I honestly don't know where I stand on keeping up with anything. I check HN (Hacker News) sometimes to keep up with table talk stuff. I tried subscribing to comp security papers (and a few other sub fields of interest) on ArXiv but it was way above my level and not very practical.

[Anonymous No.12404064]

>>12404049
>>12404050
good one thanks

[Anonymous No.12404066]

>>12399691
>AT MOST 5 TIMES
2%

[Anonymous No.12404096]

>>12399691

[Anonymous No.12404114]

>>12404096
>Excel
gtfo business major

[Anonymous No.12404123]

>>12404114
tourist

[Anonymous No.12404260]

Where does 1/58 come from?

[Anonymous No.12404274]

>>12404260
sqrt 2 * sqrt 29 = sqrt 58. sqrt(58)^2=58

[Anonymous No.12404318]

>>12404274
thanks. i gotta stop thinking of |x + y|^2 as |(x + y)^2|

[Anonymous No.12404438]

What is the residue of a complex function? I understand how to calculate it, but what does it represent, if anything? For example, I'm working with synthetizing RC dipole impedance functions, and what I do is look at the poles and find the residue. But what is the residue in this case? Like the limit in a sort of neighbourhood of the singularity? Or is it wrong to try to assign a sort of physical meaning to it?

[Anonymous No.12404568]

>>12404438
Imagine you have a meromorphic function [math]f[/math] with a pole at zero.
We then have the formula
[eqn]f = g + \frac{Res(f, 0)}{z}[/eqn] which decomposes [math]f[/math] as a canonical function with a pole at [math]0[/math] plus a function [math]g[/math] with no residue at [math]0[/math] (this is all in wikipedia btw).
So in essence, the pole gives you a clean canonical decomposition of the function.

[Anonymous No.12404588]

How do I tell if a solution to the Euler-Lagrange equation is a maxima or a minima?

[Anonymous No.12404715]

>>12404588
jacobi something, it's in gelfand fomin

[Anonymous No.12404728]

>>12404588
>maxima or minima
>implying it can't be a saddle point
Anyhow, you can't do hessians for functions, give up.

[Anonymous No.12404733]

>>12404728
When I say "you can't" I don't mean literally impossible btw, I mean "if it works it works by coincidence."

[Anonymous No.12405428]

How does a digital computer do what it does with electricity.
Like lets say we have a microprocessor doing basic calculations and sending the results to a basic display. It has to get binary input first to know what to do which travels to it through electro magnetic waves or something and a bunch of transistors do logic on that before it goes to the display. Like I'm barely sure what I'm asking here but is what's happening that electricity "pushes" em waves encoded as binary electrons through a bunch of logic transistors switching and moving the binary around until until you add for example 10 to 10 and get the binary equivalent of 20 that gets pushed to the output screens transistors that decode the 20 as a visualization of the number 20?

[Anonymous No.12405439]

>>12405428
Like goth shit?
Like vampires?
Like hiphop/rap
Then listen to this amazing mixtape made by ELEVEN it is fire as fuck if you don't your mother will die in her sleep tonight thanks!
https://www.youtube.com/playlist?list=PLi-nstDpMFxcNWB59MsvAQrNSZVTaiR9_

[Anonymous No.12405455]

>>12405439
Take the pills anon

[Anonymous No.12405792]

A weightlifter stands on a bathroom scale. He pumps a barbell up and down. What happens to the reading on the scale as he does so? What if he is strong enough to actually throw the barbell upward? How does the reading on the scale vary now?

Am I on the right track here?

When the weightlifter is at rest, the scale reads his weight + the barbell's weight.

When he exerts an upward force to lift the barbell, the barbell exerts an equal and opposite force downward. The scale now has a higher reading.

If he lifts it to some maximum height and keeps it there, the scale will display its initial reading.

Is this right so far?

What happens when he lowers the barbell? Does he have to exert a force to lower it or is it just gravity?

[Anonymous No.12405812]

>>12405792
reading on the scale is measuring a force
force is a combination of your force due to gravity and the force due to [math] F= \frac{dp}{dt} [/math]

[Anonymous No.12405844]

>>12405792
If he lets the barbell accelerate downwards as much as it would if he wasn't holding it, the reading will decrease to just his own weight. If he applies a force to slow the descent, the reading on the scale will be higher, his own weight + that force. If he applies a force to make the barbell descend faster, the scale reading will be lower, his own weight - that force

[Anonymous No.12406043]

I get to the point [math] \int_{0}^{1} \int_{x/2}^{1} \sqrt{16 y^2 + 17} dy dx [/math] but I obviously am not supposed to integrate that. What am I missing?

[Anonymous No.12406075]

>>12405812
I don't understand.

>>12405844
I think I understand these parts

>If he lets the barbell accelerate downwards as much as it would if he wasn't holding it, the reading will decrease to just his own weight.
the barbell is essentially in free fall

> If he applies a force to slow the descent
then the barbell applies a force down on him equal to the upward force he applies

>If he applies a force to make the barbell descend faster, the scale reading will be lower
This one, I don't understand at all. What's making this happen?

[Anonymous No.12406104]

>>12406075
Good old newton iii. By pushing down on the bar, he's pushing himself up, just as if it was a fixed bar.

[Anonymous No.12406151]

>>12406104
That makes much more sense now. Thanks.

[Anonymous No.12406159]

>>12406151
Like goth shit?
Like vampires?
Like hiphop/rap
Then listen to this amazing mixtape made by ELEVEN it is fire as fuck if you don't your mother will die in her sleep tonight thanks!
https://www.youtube.com/playlist?list=PLi-nstDpMFxcNWB59MsvAQrNSZVTaiR9_

[Anonymous No.12406360]

Let G be a topological group such that H is a closed subgroup. Suppose G/H is finite. Why is G/H discrete? I've been super stuck on this for a few hours and I don't really know how to prove each coset is open.

[Anonymous No.12406364]

>>12406360
A set is closed iff its complement is open. A finite union or intersection of open sets is open

[Anonymous No.12406529]

>>12406364
I've thought about this a little bit but I don't really see what you are getting at. Could you please elaborate?

[Anonymous No.12406554]

>>12406529
Do you know how to prove that if you partition a space into finitely many disjoint closed sets, they're all clopen? Can you see why the cosets of H in G satisfy those conditions?

[Anonymous No.12406871]

My uni has started registration for the spring semester.
Has anyone here taken a quantum computing course? Is it interesting? How hard would it be for a mathlet (but I'm good at physics/quantum mechanics).

[Anonymous No.12407019]

>>12406871
how the hell are you a mathlet but good at QM? Humblebrag

[Anonymous No.12407034]

In my first semester of analysis, my prof showed us a class of complex functions with [math] f(z) = \frac{az+b}{cz+d} [/math]. They had a name, but I forgot what they were called, can anyone help me?

[Anonymous No.12407081]

>>12407034
Möbius transformations

[Anonymous No.12407084]

>>12407019
No idea. Wasn't meant to be a humblebrag
It just "clicked" and I had to put in minimal effort to understand it.

[Anonymous No.12407236]

Can someone please explain how you solve the last two?

[Anonymous No.12407242]

i am a bit dumb, what is the relation/difference between centripetal force, centrifugal force and angular momentum?

[Anonymous No.12407244]

>>12407236
hint: remember that sin(x)/cos(x) = tan(x)

[Anonymous No.12407247]

>>12407236
GONIOMETRISCHEVERGELIJKINGEN

[Anonymous No.12407250]

>>12407236
[math]0 = \cos 2x +2 \sin x = 1 - 2 \sin ^2 x + 2 \sin x[/math]>
Then we have [math]\sin ^2 x - \sin x + 0.5 = 0[/math].
This is a quadratic equation and can be solved with Baskhara.

[Anonymous No.12407257]

>>12407250
The signs are wrong but you get it.

[Anonymous No.12407263]

>>12407236
For 5), consider [math]t = \tan\left(\frac{x}{2}\right)[/math] which you can use to obtain a quadratic equation.

[Anonymous No.12407276]

>>12407236
4. Use the double angle formula cos2x=1-2*(sinx)^2 and than you have a 2nd degree polynomial in sinx which you can solve to sinx=...
5. Divide both sides by cosx (when we have a solution we have to check this isnt 0). Than you have an equation for tanx which we can solve (and than see x is not pi/2 so cosx is not 0)

[Anonymous No.12407314]

>>12407081
Thanks

[Anonymous No.12407363]

>>12407250
It's allowed to just put the whole equation on a denominator of 2?
Don't you also have to multiply the numerator?

[Anonymous No.12407367]

>>12400157
Your augment is ok, but I don't see how you get the part with f being the limsup a.e.

[Anonymous No.12407377]

>>12407276
For the fifth one.
When you divide the equation cosx ( 5 cosx/cosx + 13 sinx/cosx = 0/cosx) you then get 13 tanx = -5?
Like i didn't know you could just divide the whole equation without adding anything.

[Anonymous No.12407504]

is it better to say sqrt(x^3) or x^(3/2)

[Anonymous No.12407549]

>>12407377
> Like i didn't know you could just divide the whole equation without adding anything.
a=b => a/c=b/c
If the RHS is literal zero, you can multiply or divide the LHS by whatever you want.
More generally, a=b => f(a)=f(b) for any f. I.e. you can do whatever you want to one side provided that you do exactly the same thing to the other side.

[Anonymous No.12407824]

>>12407367
ok, I see it, it warks also for limsup since ch-_E_k(x) converges for x in A, hence limsup=liminf=lim there.

[Anonymous No.12408029]

>>12407019
QM math is babby shit. if you can pass first year math you're qualified for QM
>>12406871
In my experiences, QC courses depend a lot on the instructor. The math will not be your problem though, assuming it's an intro course.

[Anonymous No.12408038]

>>12407504
depends on the context but I'd say the 2nd option is clearer
if you want to emphasize that you're taking the square root of an x^3 term then the first could be better (say as an intermediate step for a derivation)

[Anonymous No.12408050]

>>12408029
I see.
It's a relatively new course at this university so it's not like I have a massive repertoire to examine but the final exam from last year looked managable even now without knowing much.
And yes, it's an introductory course.

[Anonymous No.12408207]

>>12399674
Is there a site that searches through all free pdf sites at the same time?

[Anonymous No.12408300]

>>12408207
No, but if it's not on libgen you're very unlikely to find it somewhere else.

[Anonymous No.12408456]

I was reading this Schauder's fixed point aplication, but how can they say M is a closed subset? M is a closed ball, but L^2 is infinite dimensional so 'closed' means nothing here or I'm mistaken?

[Anonymous No.12408565]

>>12408456
M is a closed 'ball' of square-integrable functions and a subset of the set of all square-integrable functions. What's not clear here?

[Anonymous No.12408619]

>>12408456
Infinite - dimensional spaces can still have topologies

[Anonymous No.12408764]

is plasma wakefield acceleration a meme?

[Anonymous No.12408896]

> >>12406755 is still up from yesterday
Is this a Christmas miracle? Did janjan die and/or give up?

[Anonymous No.12408978]

>>12408896
deleted lol

[Anonymous No.12408982]

>>12408978
This was all part of my master plan to figure out if janjan posted here.

[Anonymous No.12409010]

Hi /sqt/

Is it do-able to take first semester physics without any highschool knowledge? I'm browsing for electives I want to take next year's summer, and physics is something I've always wanted to learn.

Some math stuff I've learned by that time are Calc I/II, discrete math, and linear algebra.

[Anonymous No.12409021]

How can light be both a particle and a electromagnetic radiation?

[Anonymous No.12409079]

>>12409010
you should be fine doing an intro course as long as you're prepared to read the book for concepts. intro physics profs are notorious for not explaining the concepts well enough, even though they're simple. the math isn't that hard and if you've done that level of math you'll survive

[Anonymous No.12409159]

>>12409010
Sure
iirc, first semester physics is pretty much the same thing as high school physics anyway. Well, a few concepts are expanded upon, usually sneaking in some three dimensional stuff as opposed to the typical 2d workspace in high school, but it's pretty much the same thing, you should be fine.

[Anonymous No.12409206]

I'm sure this has been asked before but suppose I get the big C vaccine, and after a month, the actual virus enters my system. Can I still pass the virus onto other people or will the immune response be fast enough to kill the viruses before they can multiply and be spread to my surroundings?

If the risk for contagion remains, there is no point in getting vaccinated unless the disease would be life threatening due to your age or other conditions.

[Anonymous No.12409211]

WHATs the final redpill on naps? Scientifically speaking, of couse

[Anonymous No.12409272]

>>12409206
you should not pass it on because your body will attack it upon first entry.
unless you're coughing out the virus particles that you just breathed in. otherwise, the virus shouldn't be able to replicate enough to become transferrable.

[Anonymous No.12409316]

>>12409021
Because it's neither. Depending on how you measure it that dictates what you observe.

[Anonymous No.12409547]

What does [[ ]] denote here?

[Anonymous No.12409562]

In this phasor diagram, it compares the phase angle between Eo and the voltage across the load.

Does the diagram say that the voltage across the load is lagging Eo by 36.9 degrees?

[Anonymous No.12409595]

>>12408456
With infinite-dimensional spaces, compactness is no longer equivalent to closedness + boundedness, but like the others have already pointed out, you can certainly define closed balls and closed sets more generally in infinite-dimensional spaces.

[Anonymous No.12409642]

Dumb question: effective date of hire means I won't work before that date?
For example 1/4/2021 for effective date of hire. If I accept the position now, I wont work until next month? I want to finish my degree before anything, which should be completed in 3 weeks.

[Anonymous No.12409696]

>>12409642
Yes.

[Anonymous No.12409759]

>>12409547
That's the Iverson bracket (heavily underrated notation imo):
If [math]\phi( \mathbf{x})[/math] is a logical formula, i.e. a truth-valued expression depending on a vector of variables [math]\mathbf{x}[/math], then [math] \left[ \left[ \phi( \mathbf{x}) \right] \right] [/math] is a {0,1}-valued function of [math] \mathbf{x} [/math] according to whether [math]\phi( \mathbf{x})[/math] is true or false at [math]\mathbf{x}[/math]. So it behaves kind of like an indicator function.

For your expression specifically, that Iverson bracket is simply telling you to sum only over those n for which [math]y_n = +1[/math], by setting the other summands to 0.

[Anonymous No.12410057]

>>12409759
Ah, that makes sense, thanks.

[Anonymous No.12410297]

>>12399674
I'm trying to solve this equation for [math]x \text{ where } x = \cos \theta[math]. Pic should be the same equation in case I fucked up 4channel latex.
So far I came up with a quartic manually and apparently I messed up somewhere along the way. Is there a program that will solve it for me symbolically? [math]v,g,R,\mu[\math] are all known.

[eqn]\frac{v^2}{gR} = \frac{\sqrt{1-x^2} + \mu x}{x - \mu \sqrt{1-x}}[/eqn]

[Anonymous No.12410300]

Ok. Sorry. This is fucking stupid, but I have to ask. If somehow a not-insignificant portion of the world was sliced off, would you feel as if you were walking on a level surface, or up/down an incline? Let's assume that this doesn't destroy the world. Or imagine it's another planet with life on it.

[Anonymous No.12410310]

>>12410300
Up an incline

[Anonymous No.12410369]

>>12410297
Damn I hate myself. The reason it was wrong is because I forgot the x^2 on the bottom root. Question still remains though, is there software I can use to solve for x symbolically?

[Anonymous No.12410406]

How does Null hypothesis work? Im trying to wrap my head around it but im confused on how to write the H0 and Ha.
For example, I have a problem that says
>In a blind taste test would more people prefer national brands or store brands? (experiment)
would the H0 just be
>People do not have a preference
or
>People prefer name brand
please help anon

[Anonymous No.12410638]

So what do you do when p=0.049?

[Anonymous No.12410718]

>>12410406
"People prefer name brand" isn't one hypothesis, it's lots of them, because there's lots of different strengths of preference that are compatible with it, while "no preference" is fully specific. So you have to use "no preference".

[Anonymous No.12410846]

>>12410638
Accept the null hypothesis under [math]\alpha = 0.05[/math] level of significance

[Anonymous No.12410851]

How do I deal with the overpowering desire to give up

[Anonymous No.12410913]

>>12410851
Give in.
What are the detriments of swapping hormones?
I'm like 50% of the way there and I'm not sure the benefit outweighs the harms.

[Anonymous No.12410998]

Recommend me a solid state physics textbook please.

[Anonymous No.12411170]

>>12399674
Hello, im trying to do exercise 6.A.4 of Axler's Linear Algebra, which goes like this:

Suppose [math]V = C[-\pi,\pi][/math] is an inner product space with an inner product given by [math]\langle f,g \rangle = \int_{-\pi}^{\pi}f(t)g(t)dt[/math]
Suppose $n \in \mathbb{N}$, Prove that the list given by:
[eqn]\left\{ \frac{1}{\sqrt{2\pi}} , \frac{\cos(x)}{\sqrt{2\pi}} , \dots , \frac{\cos (nx)}{\sqrt{2\pi}} , \frac{\sin (x)}{\sqrt{2\pi}} , \dots , \frac{\sin (nx)}{\sqrt{2\pi}} \right\}[/eqn]
Is an ortonormal list on [math]V[/math}

Now the problem itself isnt hard, you just need to compute a few annoying integrals and verify its ortonormal. So what I would like to know is if theres a more elegant and slick way of proving this than computing a bunch of ugly ass integrals, I tried to use the pythagorean theorem but that assumes the list is orthonormal so its no use.

[Anonymous No.12411244]

>>12411170
One shortcut that comes to mind is through even and odd functions. Since the interval of the integral is symmetrical, odd functions over it will come out as 0. So that takes care of [math] \langle \sin, \cos \rangle [/math] at least.

[Anonymous No.12411248]

>>12411170
You just have three integrals to compute.

[Anonymous No.12411280]

>>12411244
Ohh I didn't think about this, I like it, thanks!!

>>12411248
Yeah but computing integrals is boring

[Anonymous No.12411427]

Fellow goyim,

If I have the number of divisors for 2n^2 (using the divisor function with prime factors), how would I find the number of divisors less than or equal to n?

[Anonymous No.12411571]

>>12411427
Just use the relationship between [math]\sigma_0(z)[/math] and the [math]a_i[/math] components of [math]z = \prod_{i=1}^{k}p_i^{a_i}[/math]

[Anonymous No.12411776]

Hello bros. Worked out a proof of Weierstrass M-Test. It is a corollary for the Cauchy criterion for uniform convergence of series of functions but I didn't use it.

Statement:
[math]\forall n \in \mathbb{N}, f_n:A\subseteq\mathbb{R} \to \mathbb{R}[/math]
[math]M_n>0,M_n \in \mathbb{R}:|f_n|\leq M_n ,\forall x \in A[/math]
[math]\textrm{If }\sum_{n=1}^{\infty}M_n \textrm{ converges } \Rightarrow \sum_{n=1}^{\infty}f_n \textrm{ converges uniformly on }A[/math]

My attempt:
[math]0\leq\bigg|\sum_{k=1}^nf_j\bigg|\leq\sum_{k=1}^n|f_j|\leq\sum_{k=1}^nM_j[/math]
Now the second series is increasing and bounded, so it converges [math]\forall x \in A[/math].
[math]a_n(x)=\sum_{k=1}^n|f_j| \textrm{ converges } \forall x \in A \Rightarrow b_n(x)=\sum_{k=1}^nf_j \textrm{ converges } \forall x \in A[/math]

Is this legit? I feel like I proved pointwise convergence and not uniform convergence. feedback appreciated

[Anonymous No.12411785]

>>12411776
fucked up the indices but it's understandable

[Anonymous No.12411839]

>>12411776
> I feel like I proved pointwise convergence and not uniform convergence.
That's also what I'm reading.

[Anonymous No.12412375]

I graduated HS with good grades months ago but now i'm a neet due to corona. If I want to study math for my own enjoyment and remain sharp where should I dig around?

[Anonymous No.12412520]

is there a maximum theorical efficiency of a computation machine? is there a way to measure the amount of "energy" a computation takes, or maybe the amount of energy the computation itself "is"?

[Anonymous No.12412564]

>>12412375
Start with Terence Tao's Solving Mathematical Problems, and then check out Stephen Abbott's Understanding Analysis. I wish I'd done that if I could go back to when I was your age.

[Anonymous No.12412608]

I'm insecure about an exercise from Folland's Real Analysis book (Chapter 2, Problem 36).

Let [math](\Omega, \mathcal{F}, \mu)[/math] be a measure space, and let [math]\{E_n\}_{n \geq 1}[/math] be a sequence of measurable sets with finite measure.

Further assume that [math]\chi_{E_n} \to f \text{ in } L^1[/math]. Then [math]f[/math] agrees almost everywhere with the characteristic function of a measurable set.

Here's what I think:

We can find a subsequence of [math]\{\chi_{E_n}\}_{n \geq 1}[/math] that converges almost everywhere to [math]f[/math]. Then for every point in [math]\Omega[/math], said subsequence must be either converging towards [math]0[/math] or converging towards [math]1[/math], since the pointwise a.e. limit exists.

How do I make this proof less handwavy and more formal? Is it correct? Thanks in advance.

[Anonymous No.12412615]

Is [math]x\in\mathbb{Z}[x][/math] irreducible because there are no non-unit elements such that [math]x=gh[/math]?

[Anonymous No.12412654]

>>12412615
Verily

[Anonymous No.12412660]

>>12412654
thanks. i'm losing my mind here

[Anonymous No.12412696]

I accidentally saw my girlfriends sisters totally nude and I saw her ass. My girlfriend had told me before that her sister had this, but I thought it was an exaggeration or just some joke. BUT, she really did have an bump right over her BUTT. It was not a hole, it wasn't a dimple, it was just a simple bump. I've tried SO FUCKING MUCH to find an identical ass online but I just can't. I've searched so many times for this with all the terms that I've thought, both in English and in my mother language and I just can't find it. So please, if someone here can actually shed some light on this new fetish of mine I would be grateful for the rest of my life.

[Anonymous No.12412719]

>>12412608
Looks good to me. We have convergence in [math]L^p[/math] implies convergence in measure by https://math.stackexchange.com/questions/1281421/convergence-in-lp-implies-convergence-in-measure , and convergence in measure implies we have such a subsequence.
>How do I make this proof less handwavy and more formal?
You have that [math]f[/math] equals a.e. to either [math]1[/math] or [math]0[/math]. You can then give the characteristic function explicitly by considering [math]g = \chi _{f^{-1}(1)}[/math].

[Anonymous No.12412722]

>>12412719
Shitty source for the second result.
https://math.stackexchange.com/questions/1006091/convergence-in-measure-implies-convergence-almost-everywhere-of-a-subsequence

[Anonymous No.12412731]

>>12412719
Awesome, thanks for the tips!

I'm still trying to understand why finite measure is required for each of the [math]E_n[/math]. Where did I (implicitly) rely on that fact?

[Anonymous No.12412815]

>>12412731
You didn't use it, the problem statement of "[math]\chi_{E_n} \to f \text{ in } L^1[/math]" only makes sense if all the sets have finite measure.
Folland asked for it to be formal and propa.

[Anonymous No.12413189]

>>12412815
Got it. The thing that's bothering me now is this: I've managed to then show that [math]f[/math] is indeed the characteristic function of *a* set; but how do we make sure that it is a *measurable* set?

[Anonymous No.12413205]

>>12413189
Actually, given the explicit formula we have for [math]f[/math], I can just use the argument that since [math]f[/math] is measurable and the Borel [math]\sigma[/math]-algebra contains all the singletons, their inverse image is again a measurable set. Is that it?

[Anonymous No.12413209]

>>12413189
Pre-image of a measurable function at a single point is always a measurable set.

[Anonymous No.12413213]

>>12413205
Yes.

[Anonymous No.12413269]

>>12413209
>>12413213
Awesome. Thanks, guys!

[Anonymous No.12413630]

Can someone give me a hand
I can find the first two points but I can’t figure out the third point of intersection
x^2(x+1)=(x+1)

[Anonymous No.12413638]

>>12413630
there are only two points where that's equal

[Anonymous No.12413650]

>>12413638
They are two separate functions
F(x)=x^2(x+1)
G(x)=(x+1)
And the question says there are three points of intersection of these graphs of functions but I can only find two

[Anonymous No.12413662]

Can I assume that the two blocks will meet at the center with equal velocities? The only thing acting on them is gravity so I just assumed that.
Then I used conservation of energy
[math]m_1g_h + m_2g_h = .5m_1v^2 + .5m_2v^2[/math]

[math]v = \sqrt{\frac{2gh(m_1+m_2)}{m_1+m_2}}=\sqrt{2gh}[/math]

Did I do that correctly? Assuming that's not completely wrong, what would be the next step?
I figured momentum would be conserved, but I didn't know how to proceed.
[math]vm_1 + vm_2 = m_1v_1 + m_2v_2[/math]

Do I just solve for v_1 and plug into another conservation of energy equation?

[Anonymous No.12413685]

>>12413650
then the book is incorrect
[eqn] x^2(x+1)=x+1 \\
x^2(x+1)-(x+1)=0 \\
x=-1 \rightarrow 1(0)-0=0 \\
\text{ for other solutions (since this is a cubic equation so there are at most 3 solutions), divide by x+1 } \\
x^2-1=0 \rightarrow x= \pm 1 [/eqn]
the only solutions are x=1, x=-1

[Anonymous No.12413686]

>>12413650
I think there must have been an error in the question.

[Anonymous No.12413695]

>>12413685
>>12413686
See that’s what I thought so I just threw in a bogus (0,1) as a third point

[Anonymous No.12413753]

>>12413695
>doesn't get the expected answer so just makes something up even though he knows it's wrong
are you an engineer by any chance?

[Anonymous No.12413764]

NASA lists the power output of the first stage of the Saturn V as 120GW. How the hell did they get that? It doesn't equal the fuel flow times the energy density of the fuel, it doesn't equal the work per second done on the rocket.

[Anonymous No.12413771]

>>12413764
I'm not an expert, but this is just an idea. Since power is given by energy per unit time, and energy of the rocket is given by kinetic and potential energy (loosely), could they just measure how high/fast the rocket gets during the first stage and divide that by how long it took?

[Anonymous No.12413817]

>>12413771
At specifically say right after liftoff. One second after liftoff the rocket is only 1.4m above ground, at 2.7Mkg that's 37MJ of potential energy. Velocity is 2.8m/s so that's 10.5MJ. Total: 47.5MJ in 1second, so 47.5MW.

Fuel flow is 20,000kg/s. Energy density is about 15MJ/kg (accounting for the mass of the liquid oxygen.) So that is 300GW total energy released. NASA counts 40% of that as the value.

[Anonymous No.12413908]

>>12399674
If microwaves can heat by putting atoms in motion can't they also cool by wave interference (cancelation)?

[Anonymous No.12413916]

>>12413908
theoretically, but you'd need much more advanced methods. and your understanding of why microwaves heat won't really make that much clear

[Anonymous No.12413926]

>>12413916
Then I wonder if it could remedy global warming...
I know energy can only be transformed so where would the heat energy go?

[Anonymous No.12413928]

>>12413926
the atmosphere, the average temperatures of everything on earth. the energy would not make it to space. you'd just be heating earth more

[Anonymous No.12413941]

>>12413928
But if wind energy could be but into cooling ocean streams or polar air for more snowfall it could maybe be a net positive...

[Anonymous No.12413966]

>>12413753
this wasn't even for me I was just helping out my younger brother with his math

[Anonymous No.12414044]

how do i solve for x

-4 = 20 log (x over 0.775)

[Anonymous No.12414068]

>>12414044
Ask yourself what is the inverse of log.

[Anonymous No.12414098]

>>12414044
[math]10^{\log{x}}=x[/math]

[Anonymous No.12414249]

Literal retard here struggling with my precalculus course in community college. I wanted a proof check for one problem and I needed help on the second.

>If a,b are coprime, then (a+b)^m and (a-b)^m have at most a GCM of 2^m.

Case 1: one is odd, one is even -
It is obvious that a+b is coprime to a,b since
with a = pb+c, where a,b,c,p are all integers, the GCM of b and c is the GCM of a and b.
Similar logic is applied to a-b.

So then, we have a+b = (1)(a-b) + 2b. Since a-b is odd, it cannot have a common factor with 2b, so 2b and a-b are coprime, and hence a+b and a-b are coprime. Their powers are also coprime, as a result.

Case 2: Both a and b odd:
Proceeding similarly and back to a+b = (1)(a-b) +2b, we see that a-b has a common factor of 2 with 2b, so a+b and a-b have a common factor of 2. So, let a+b and a-b be 2d and 2k, where d and k are some coprime ints, and take both to the mth power. It is obvious that the common factor here is 2^m.
So, the max GCM is 2^m.

Second problem:
>Assume two fractions are in their lowest forms. Show that their addition or difference cannot be an integer, unless their denominators are equal.

I tried doing this by contradiction with a/b + k/m = (am+kb)/bm.
So am + kb must be exactly divisible by bm. Originally I thought it was a simple case of "neither am nor kb have bm in them, so b and m must be equal" but that seems to be wrong.

[Anonymous No.12414264]

>>12414098
yes. now think.

[Anonymous No.12414318]

>>12412696
https://www.allodocteurs.fr/maladies/peau/quest-ce-quun-kyste-pilonidal_899.html

or generic lipome
https://www.linfo.re/magazine/sante-beaute/le-lipome-ou-l-apparition-d-une-boule-sous-la-peau

[Anonymous No.12414321]

>>12409206
>Can I still pass the virus onto other people or will the immune response be fast enough to kill the viruses before they can multiply and be spread to my surroundings?
nobody knows

[Anonymous No.12414496]

>>12413650
> And the question says there are three points of intersection of these graphs of functions but I can only find two
In general a cubic equation has three roots, i.e. it can be written as a(x-r1)(x-r2)(x-r3)=0, but roots can be repeated. In this case the equation is equivalent to (x-1)(x+1)(x+1)=0 so x=-1 is a repeated root (with multiplicity two). If it's asking you for three answers, give 1,-1,-1.

A repeated root occurs when the graph is tangent to the x axis (in the case of f(x)=0) or the two graphs are tangent to each other at a point (in the case of f(x)=g(x), as in >>12413686 . Notice that if you were to move the x+1 line down even slightly, you'd get two distinct points of intersection rather than a single point.

[Anonymous No.12414515]

How many genes do we have to modify to make a human with six fingers/toes at each limb?

[Anonymous No.12414519]

>>12414098
Only for [math]x>0[/math]

[Anonymous No.12414559]

>>12414249
> GCM
ITYM GCD.

For the second part, a/b+c/d = (ad+bc)/bd.
Assume bd | ad+bc
=> d | ad+bc
=> d | bc (because clearly d | ad)
=> d | b or d | c
=> d | b (d | c is excluded by c/d being in lowest common form).
But also bd | ad+bc
=> b | ad+bc
=> b | ad (because clearly b | bc)
=> b | a or b | d
=> b | d (b | a is excluded by a/b being in lowest common form).

d | b ∧ b | d => b = d

[Anonymous No.12414677]

>>12414559
Thanks, this makes perfect sense!

[Anonymous No.12414706]

>>12414559
Goddamn, this makes perfect sense. Thank you.

[Anonymous No.12414930]

I'm dumb. please help. thank you.

[Anonymous No.12414941]

>>12414930
nvm got it.

[Anonymous No.12415041]

Is it ok to reference figure 2 before figure 1 in an article? I would like to switch them for space reasons.

[Anonymous No.12415115]

>>12415041
Why would you even think it was not okay?

[Anonymous No.12415118]

>>12415115
Well, they would not be in order... Maybe I'm autistic

[Anonymous No.12415129]

>>12415118
There is no maybe about it.

[Anonymous No.12415148]

>>12415129
:-(

[Anonymous No.12415235]

[Anonymous No.12415243]

>>12415041
...it's an article, space doesn't matter.

[Anonymous No.12415571]

I understand all the calculations etc in this and I understand why 2/7 is a lower bound but I don't understand why the n>3/7e-1 is the infinitum? Please help.

[Anonymous No.12415630]

>>12415571
What happens if epsilon is very very tiny (which means you are approaching the bound)?

[Anonymous No.12415659]

Chembros, what's the best way to find out what acids or bases dissolve a particular compound and what the solubilities are?
In particular, I need to find this out for MnWO4 and In2O3.

[Anonymous No.12415688]

>>12415630
If epsilon is very very tiny then n will be very very big?

[Anonymous No.12415694]

>>12415571
[math]n > 3/7\epsilon -1[/math] isn't the infinitum. It's the value of n which gives the infinitum.

So put it back into the original equation and take the limit that [math]\epsilon[/math] approaches zero to prove the statement.

[Anonymous No.12415697]

it's not the infimum, it's just a proof that 2/7 is a least lower bound as long as there exists such an n

[Anonymous No.12415706]

>>12415571
they want to show that any number larger than 2/7 cannot be a lower bound. this means exactly that 2/7 is the LARGEST lower bound. 2/7+eps is just a general number larger than 2/7. this number is not a lower bound if there is at least one element in your which is smaller than it. that's exactly what they do.

[Anonymous No.12415712]

>>12415697
I thought in general a lower bound does not have to be the infimum? For example for the set {2,3,4} the lower bound is 1 but the infimum is 2.

[Anonymous No.12415743]

>>12415571
> I don't understand why the n>3/7e-1 is the infinitum?
The infimum is 2/7. Do you understand what that word means? Any number <= 2/7 can be shown to be a lower bound, meaning that the value of the expression is never less than that value. But the infimum is unique; it's the value to which you can get arbitrarily close but never less than.

So to prove that 2/7 is the infimum you have to prove that you can get arbitrarily close to it. I.e. for *any* positive ε, however small, there's some n such that (2n+5)/(7n+7)<2/7+ε. Which pic related does by rearranging the expression to show that (2n+5)/(7n+7)<2/7+ε is equivalent to n>(3/7ε)-1. IOW, for any given ε, *all* values of n greater than (3/7ε)-1 result in the expression being less than 2/7+ε.

The rearrangement is essentially the same as solving the equation (2n+5)/(7n+7)=2/7+ε for n, except that with an inequality you have to keep track of whether it's < or >.

[Anonymous No.12415751]

>>12415694
>>12415743
Thank you, I actually understand what is happening now.

[Anonymous No.12415914]

Why are there so many Schrodinger's equations?

I'm using one book but then I read something else and I get a completely different version.

[Anonymous No.12415949]

>>12415914
They are all secretly the same

[Anonymous No.12415964]

>>12415914
Some of those have potentials and some don't.
Also, some of those are one-dimensional and others are arbitrary dimensional, and others are just the abstract functional analytic version.

[Anonymous No.12415978]

>>12415964
Also some are time dependant others not.

[Anonymous No.12416018]

>>12415914
Two different equations are commonly referred to as the Schrodinger equation: the time dependent Schrodinger equation describing the dynamics of a wave function
[eqn]
H(t)|\psi(t)\rangle=i\hbar \frac{\text d}{\text dt}|\psi(t)\rangle,
[/eqn]
and the eigenvalue equation describing the energy eigenvalue [math]E[/math] associated to a certain state [math]|\psi\rangle[/math]
[eqn]
H|\psi\rangle = E|\psi\rangle.
[/eqn]
If you then write them in the position [math]\mathbf q[/math] basis, you get
[eqn]
\langle \mathbf q|H(t)|\psi(t)\rangle=i\hbar \langle \mathbf q|\frac{\text d}{\text dt}|\psi(t)\rangle
\implies \left(-\frac{\hbar^2}{2m}\nabla^2 + V(\mathbf q)\right)\psi(\mathbf q, t) = i\hbar\frac{\text d\psi(\mathbf q,t)}{\text dt}
[/eqn]
and
[eqn]
\langle \mathbf q|H|\psi\rangle = E\langle \mathbf q|\psi\rangle
\implies \left(-\frac{\hbar^2}{2m}\nabla^2 + V(\mathbf q)\right)\psi(\mathbf q) = E\psi(\mathbf q)
[/eqn]
If you have a free particle, then [math]V(\mathbf q)=0[/math], and if you are in one dimension you replace [math]\mathbf q[/math] with [math]x[/math] and [math]\nabla^2[/math] with [math]\frac{\text d^2}{\text dx^2}[/math].

[Anonymous No.12416243]

>If A and B are two sets such that A is countable and |A|<|B|, then B is uncountable.

Wtf does this even mean and how would one answer if it is true or false. I did not receive a single lecture on the subject and now I have a bunch of similar questions on an assignment.

I don't get it, if B has higher cardinality could they not just both be finite and countable?

[Anonymous No.12416298]

>>12416243
Whatever text they got that problem from probably uses "countable" to mean countably infinite.

[Anonymous No.12416312]

what's the cardinality of the set of all cardinal numbers

[Anonymous No.12416315]

>>12415914
Sometimes I rejoice thinking there's people even stupider than me

[Anonymous No.12416329]

>>12416298
But then isnt it still false if considering N and Q? Both would be countable but I assume not of the same cardinality?

[Anonymous No.12416338]

>>12416315
To be fair maths is kind of hard, especially for physicists.

[Anonymous No.12416342]

>>12416329
They do have the same cardinality.

[Anonymous No.12416346]

>>12416329
Those two have the same cardinality.
Any two countable infinite sets biject.
Proof left to the reader, and from it the result follows immediately.

[Anonymous No.12416446]

Circuits question
Is it do-able to study everything from nodal/mesh analysis to operational amplifiers in like a week or am I fucked? I'm about to start crying hahahaahahaha

[Anonymous No.12416497]

>>12416346
Ok thanks I think I found this in the textbook, it was in a different section than where I was looking. So since any infinitely countable set has the same cardinality and A is infinitely countable then |A| < |B| implies B is uncountable? (My understanding of the textbook is that there is no set S with cardinality between the cardinality of N and R).

So the statement:

>If A is an uncountable set, then |A|=|R|. (R is the set of real numbers).

Would be true for similar reasons that there is bijective function f: A -> R and both sets have the same cardinality?

[Anonymous No.12416523]

>>12416497
Nvm i think the second statement is false. Ill just try my luck.

[Anonymous No.12416569]

>>12416497
>My understanding of the textbook is that there is no set S with cardinality between the cardinality of N and R
No, that would be the continuum hypothesis which is still unsolved (and in fact it's proven that it is impossible to solve).
There are infinitely many kinds of uncountable infinites, you don't need to fixate on [math]\mathbb{R}[/math]'s cardinality. You just need to prove that, whatever the cardinality of B may be, as long as its cardinality is strictly greater than that of A, there can't possibly be a bijection between B and [math]\mathbb{N}[/math].

[Anonymous No.12416578]

40 students are doing a multiple choice test. None of the forty knows anything about the test's subject, but since it's a multiple choice test, they'll each choose randomly, uniformly and independently on each question between the four alternatives given.
What is the class's expected highest grade?

[Anonymous No.12416584]

>>12416578
Forgot to mention: The number of questions in the test is twenty.

[Anonymous No.12416596]

>>12416578
I don't think you can define an expected highest grade... You have the expectation value, which is the average grade, but I can't see what expected highest grade would mean.

[Anonymous No.12416613]

>>12416578
Define 'expected'.

[Anonymous No.12416625]

>>12416578
>>12416584
For the love of god, put the one relevant info in it!
How many possible answers per question???

[Anonymous No.12416629]

>>12416625
>they'll each choose randomly, uniformly and independently on each question between the four alternatives given.
>four alternatives given.

[Anonymous No.12416674]

>>12416596
>>12416613
I'll use [math]\mathbb{Z}_n[/math] to denote the set [math]\{ 1, 2 \ldots , n \}[/math].
Then, the sample space is the set of maps [math]f[/math] from [math]\mathbb{Z}_{40} \times \mathbb{Z}_{20}[/math] to [math]\mathbb{Z}_4[/math].
So essentially, [math]x \in \mathbb{Z}_{40}[/math] represents student number x, and [math]y \in \mathbb{Z}_{20}[/math] represents question number y, and we say that [math]f(x, y) =z [/math] just means "student x selected alternative z in the question y".
We define the "function's alternative is correct" by [math]g(y, z)[/math], which equals [math]1[/math] when z is the correct alternative in question y, and 0 otherwise.
We put the uniform probability on this sample space, and we ask for the expected highest grade in the class, that is, [eqn]\mathbb{E} \left [ \max _{x \in \mathbb{Z}_{40}} \sum_{y \in \mathbb{Z}_{20}} g(f(x, y), y) \right ][/eqn]

[Anonymous No.12416683]

>>12416674
[math]g[/math] is swapped, but whatever.
Also forgot to mention that you can assume, for all practical purposes, that [math]g[/math] equals the Kronecker delta.

[Anonymous No.12416688]

>>12416674
Ok, thanks for the explanation. I'm afraid I can't help you, however, since I am not very good at statistics.

[Anonymous No.12416709]

>>12416629

What if I told you that I fucked up even harder than it seems, I didn't not see the 4, but rather asked for the wrong thing.
--not the answer--
I wanted to know how many students there are per class but my brain was somewhere along the way.
You need to know, how the test works, how many points for how many questions, then now many points equal which grade and then somehow calculate the most generic outcome per class with the number of students and their grades from the tests and then determine what you would call a "expected grade". Like the likelihood of that grade occurring. Is it everything over 50%I'd guess you'd barely make it a 4- in a class of 20.

[Anonymous No.12416726]

Is there a book or website that can teach me the fundamentals of machine learning? I don't want shit like "how to use tensorflow/pytorch", since I already know how to use them. I just want to know more about the process of machine learning, like what are tensors, how neural networks work, what exactly does a convolutional neural network mean, etc.

[Anonymous No.12416729]

I'm taking topology 1 and I am havin trouble with this stupid question.
Does the isolated points of a set in a finite product topology equal the product of the isolated points in the proyections?

[Anonymous No.12416740]

>>12416726
I've read Deep Learning with Python by Francois Chollet and it explains the theory along with the Keras implementation. Not in the most mathematical way (in fact, it doesn't even use mathematical expression, which in my opinion is a little unfortunate), but for example it explains how a convolutional NN works, how its input is transformed into the output etc. If you want something more mathematical and theoretical, then I don't know.

[Anonymous No.12416744]

>>12416729
Think of a line in R2 union a point not on the line

[Anonymous No.12416766]

>>12416744
Thanks!

[Anonymous No.12416854]

Imagine two black holes rapidly orbiting each other and on a path to merger.
I've been hearing as objects approach the event horizon, to an external observer, they appear to slow down, become red shifted and stop, never actually falling in the black hole.
If that's the case, how is it possible for us to detect a black hole merger?
I obviously misunderstood something so thanks for clarifying.

[Anonymous No.12416904]

>>12416854
We detect the gravity waves produced by the merger but we don't directly see them collide. Similar to how you don't have to see a bell strike to hear it chime.

[Anonymous No.12416905]

>>12416497
Any countably-infinite set has a bijection with the natural numbers, so they all have the same cardinality. The reals are uncountably infinite (Cantor's diagonalisation proof). For finite n, R^n has the same cardinality as R (there are space-filling curves which map R<->R^n). There are sets with cardinality greater than that of R, e.g. the powerset (set of all subsets) of R.

[Anonymous No.12416920]

how the FUCK does this make any sense?

[Anonymous No.12416927]

>>12416854
it usually takes a long time before they fall into each other's event horizon and until then they emit crazy gravitational waves

[Anonymous No.12416950]

>>12416920
[math](f(g(c))'=\lim_{x \to c}\frac{f(g(x))-f(g(c))}{x-c}=\lim_{x \to c}\frac{f(g(x))-f(g(c))}{g(x)-g(c)}\frac{g(x)-g(c)}{x-c}=f'(g(c))g'(c)[/math]

[Anonymous No.12416953]

>>12399674
wtf is MMd/b its an oil measurement unit but what the hell does it mean?

[Anonymous No.12416963]

>>12416950
I know, I've seen the proof a million times at this point but it doesn't help me make any sense of this
it gives me trigonometry flashbacks, "yeah i guess it's true but good luck coming up with that"

[Anonymous No.12416971]

>>12416963
what do you mean by sense? the chain rule is just a trick

[Anonymous No.12416972]

>>12416953
its million barrels per day but why is it mm fucking stupid

[Anonymous No.12416974]

>>12416963
https://www.youtube.com/watch?v=mdbjV48ZjSk&ab_channel=MichelvanBiezen
fantastic video series on calc

[Anonymous No.12416989]

>>12416920
What doesn't make sense about it? It's just the chain-rule.

The derivative of a function of a function is the derivative of the outer-function times the derivative of the inner-function.

[math]\frac{df}{dx} = \frac{df}{du} \frac{du}{dx} = \frac{d}{du}f(u) \frac{du}{dx}[/math] where [math]u = g(x)[/math]

[math]= f^\prime(u) g^\prime(x) = f^\prime(g(x)) g^\prime(x)[/math]

So derivatives of trig functions are easy, [math]\frac{d}{du} sin(2x) = 2cos(2x)[/math], etc.

[Anonymous No.12416997]

>>12416974
will it help me make sense out of it or will it just do the proof like all other videos?
>>12416971
nothing in math is just a trick
>>12416989
ok but why? why isn't it just f'(g(x)) like any other derivative?

[Anonymous No.12417012]

>>12416997
> why isn't it just f'(g(x))
Because f isn't a function of x, it is a function of g

[Anonymous No.12417014]

>>12416997
his entire series on math helped me go from a 60% in calc 1 to 95% in calc 3. he has a lot of practical solutions not so much for theory

[Anonymous No.12417037]

>been doing somewhat okay in my physics quizzes and homework
>realize that most of the time I know what formulas/concepts to apply because the quiz/homework is on a specific chapter
>realize the finals is going to be comprehensive
bros oh no
how the fuck do i figure out which problems to use kinematics or conservation of momentum/energy for?

[Anonymous No.12417077]

>>12417012
f is still a function whose value ONLY depends on x, hence it's indirectly still a function of x
f(x) = 2x, g(x) = x^2 => f(g(x)) = 2x^2 => (f(g(x)))' = 4x = f'(g(x))
you could make reasoning analogous to >>12416989 and it would be equally sound
"What doesn't make sense about it? It's just the chain rule.
The derivative of a function is just the derivative of the function like in the case with f(x) = 2x => f'(x) = (2x)'. Therefore the derivative of any function is just the derivative of the function no matter what's inside. So for f(g(x)) => f'(g(x)) = (g(x))' = g'(x)."

[Anonymous No.12417080]

>>12417037
nigga gonna get blasted

[Anonymous No.12417089]

>>12417080
ohnonono bro say it ain't so

[Anonymous No.12417108]

>>12417077
> f is still a function whose value ONLY depends on x
Not true. If you want to be more exact you should write f=f(g,x) but no one ever uses that notation. What you have done is substitute x=y^2 into 2x where y=x. So f(g(x)) becomes f(x), a standard single parameter function.

You could do exactly the same with something like f=sin(x^2+1), use the taylor series for sin but replace x by x^2+1 but the chain-rule method is obviously simpler.

[Anonymous No.12417127]

>>12417108
>Not true.
but it's true, that's why it's called the chain rule
the evaluation of f is dependent on whatever the evaluation of g is dependent on, which is x
hence the evaluation of f is dependent on x in an entirely predictable and deterministic way
that's why the chain rule doesn't make any logical sense

[Anonymous No.12417152]

>>12417127
f depends only on g but g depends on x. so f does depend on x but not directly, not the same thing at all.

if you know coding its like the quicksort() method where one of its parameters is the function that does the item comparison.

[Anonymous No.12417161]

>>12417127
f(g(x)) does depend on g(x) in a determistic way, but it's still a different way than it depends on x.

[Anonymous No.12417163]

>>12417127
>the evaluation of f is dependent on whatever the evaluation of g is dependent on, which is x
And here you just pointed out yourself why it's not true. It is primarily dependent on g.
>f is still a function whose value ONLY depends on x
If that were true then the intermediate function would be completely irrelevant. If it ONLY depended on x then it wouldn't matter if g(x)=sin(x) or g(x)=x^3 or whatever it may be. But alas, it's not true. Changing x slightly in either of those functions drastically changes the values in their images, which has a direct impact on the value of the derivative which is precisely the rate of change (and the images might not even be the same to begin with). So it is also directly dependent on the image of the function g, and that may change from function to function even if the values of x remain the same across all functions.
>hence the evaluation of f is dependent on x in an entirely predictable and deterministic way
But ultimately not independent of the function g, which is what matters for the chain rule.

[Anonymous No.12417196]

>>12417152
>>12417161
okay, I know it's true, you're just not making any argument and saying "nah bro it's like this because it's like this trust me"
>>12417163
>And here you just pointed out yourself why it's not true. It is primarily dependent on g.
no, I pointed out it's true, the argument just gets passed after one more step but it's still x in some form
>If that were true then the intermediate function would be completely irrelevant. If it ONLY depended on x then it wouldn't matter if g(x)=sin(x) or g(x)=x^3 or whatever it may be.
no, you misunderstood
by saying it only depends on x I didn't meant that g(x) = x, only that the value of f depends on the value of g which depends on x
so for g(x) = sin(x) we would just have (f(g(x)))' = g'(x) = (sin(x))', that's why it matters what g(x) is
>But ultimately not independent of the function g, which is what matters for the chain rule.
yup, so (f(g(x))' = g'(x) or (f(g(x))' = f'(g(x)) are still possible

[Anonymous No.12417210]

>>12416315
you mean there are people who are learning something for the first time? and you make yourself feel better about yourself by pretending they're dumb not new

[Anonymous No.12417222]

>>12417163
And also to complement, that's why you always need to specify what the variable you are differentiating w.r.t. is. If you wanted to take the derivative w.r.t g then you'd actually be correct, you are just evaluating how the function would change if the value of g changed (as if that were your x), regardless of what changes x would need to achieve that. But when you want to take it one step further and find the rate of change when you take x as the independent variable instead, the rate changes.

Think about it like this, if g is a function that increases really fast (faster than the identity) then differentiating w.r.t x instead of g would actually have some sort of "magnifying" effect, as opposed to just finding the derivative w.r.t. g, because the change of x implies an even more drastic change of g to begin with. It'd be like the derivative w.r.t. g, but even more magnified. Same when g is a function that increases really slowly, differentiating w.r.t. x actually would have some sort of "dampening" effect, because the change of x that would cause a change of f is getting held back by how slowly g changes, so f would also change more slowly by changing x as opposed to directly changing the value of g.
Those "magnifying" and "dampening" effects are what's being represented by the constant g'(x)

[Anonymous No.12417233]

>>12417196
> so for g(x) = sin(x) we would just have (f(g(x)))' = g'(x) = (sin(x))', that's why it matters what g(x) is
> yup, so (f(g(x))' = g'(x) or (f(g(x))' = f'(g(x)) are still possible
I don't think you know what you are typing because that all reads like gibberish.

[Anonymous No.12417294]

>>12417196
>only that the value of f depends on the value of g which depends on x
That is correct. It IS dependent on x, which is precisely why the derivative of f w.r.t x is dependent on x as well. But the important part is that it doesn't EXCLUSIVELY depend on x. Let's see, the formulas you were proposing were f'(g(x)) and g'(x):

The former implies that the rate of change of g has no change whatsoever in how f changes. So imagine g(x)=99999x (or some other very steep function). If you differentiate f with respect to g, as if it were some independent variable, you'd get some value, say k. But if you do the same w.r.t x, what happens is that if you change x JUST AS MUCH as you changed g, the effect it will have on g is going to be massive because how steep g is. And now the change in the value of f is going to increase a lot, because the change in g that was caused by x (which was a change of the same magnitude as the one we used for g) is much more accentuated than just k, the one we found when we took g as an independent variable. By how much exactly? By about 99999, or g'(x), times k.

The latter implies that f doesn't even have any effect whatsoever in the value of its derivative so it should be obvious why that doesn't make much sense.

[Anonymous No.12417296]

>>12417233
>that all reads like gibberish
exactly, it's meant to sound like gibberish because it applies the same reasoning as all the attempts at explaining the chain rule in this thread, which are unfounded gibberish when you break them down

[Anonymous No.12417321]

>>12417294
okay that made it click for me after some thought, why couldnt anyone just say from the beginning that g'(x) is just meant to be interpreted as a scaling (stretching) factor for the new axis g(x) which f(g(x)) is defined on?

[Anonymous No.12417364]

>>12417321
At least from personal experience, it seems that for whatever the fuck reason that fact rarely ever gets mentioned, even in textbooks and stuff. The chain rule is almost always stated as an entirely numerical result, the proof using the definition is presented without much context other than it looking like a neat little trick, and then it's mostly only used for calculations and stuff, to the point where I think most people already forgot what it was supposed to represent (if they were ever taught in the first place). Which means that even most professors teach it like that, and the cycle repeats.

[Anonymous No.12417419]

>>12417364
having it finally click got me so excited I think I'm gonna stay up all night
I can literally explain it to anyone intuitively now and there is absolutely no way I will ever forget it now, it just required a different way of thinking and then it's completely obvious
and when asked why it works, whoever starts doing the algebraic proof should be banned from doing math forever

[Anonymous No.12417546]

The radius and the mass of a sphere doesn't matter when calculating the velocity it will roll down a smooth surface right?

[Anonymous No.12417798]

new
>>12417796
>>12417796