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Board
/sci/ - Science & Math

Previously >>12536145

Ignore the other one, deleting it in a second.

>what is /sqt/ for?
Questions regarding math and science, plus related advice requests.
>where do I go for other questions and (advice) requests?
>how do I post math symbols (Latex)?
https://imgur.com/MDiglsS.png
>a plain google search didn't return anything, is there anything else I should try before asking the question here?
>where can I look up if the question has already been asked here?
https://warosu.org/sci/
https://boards.fireden.net/sci/
>how do I optimize an image losslessly?
https://trimage.org/
https://pnggauntlet.com/

Where can I get:
>books?
https://spoon.wiki/Books
https://stitz-zeager.com/
>articles?
sci-hub.st
>book recs?
https://4chan-science.fandom.com/wiki//sci/_Wiki
https://sciencecareergeneral.neocities.org/
>help with calculus?
https://spoon.wiki/WolframAlpha
>charts?
https://imgur.com/a/JY6NNeL
https://imgur.com/a/0qDEgYt
>tables, properties and material selection?
https://www.engineeringtoolbox.com/
http://www.matweb.com/

>attach an image
>check the Latex with the Tex button on the posting box
>if someone replies to your question with a shitpost, ignore it
>avoid arguing with Yukarifag
>do not tell us you came from whatever the fuck board, /pol/ in particular
>do not mention how [other place] didn't answer your question so you're reposting it here
>If you use j for the complex unit, put a ¿ somewhere in your post or use emoticons I will automatically ignore your question. I don't actually know about everyone else, but you shouldn't assume they're too far off about whatever random things they dislike
>>

Math questions:
>>12543143
>>12544363
>>12546108
>>12548385
>>12550572
>>12550908
>>12564609

Physics questions:
>>12541128
>>12565475

Chemistry questions:
>>12556040

Computer Science questions:
>>12536799
>>12566223

/g/ questions:
>>12537293
>>12546201
>>12561704
>>12564588

Engineering questions:
>>12566254

Stupid questions:
>>12541985
>>12544331
>>12547678
>>12549815
>>12552976
>>12559053
>>12564653
>>12568960
>>12569818
>>12570365
>>
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Why do pajeets have a monopoly on non pop-sci lectures/videos on youtube?
>>
Does anyone want to start an aerospace engineering book club with me?
>>
Is there a based website to learn calculus? I'm stuck at implicit differentiation and related rates. I can solve it, but it's weird as fuck for now. I would not mind giving it a little more time, but I don't have it.
>>
>>12570535
Indian culture has a huge emphasis on sharing as much knowledge you have and respecting teachers.
>>
>>12570568
openstax.org/subjects/math
>>12570577
>1.4 billion people
>one homogenous culture
>>
>>12570568
https://tutorial.math.lamar.edu/
>>
What's a good way to study for the GRE?
>>
>>12570620
archive.org
>>
>is there a site(or app ?) like wolframalpha or symbolab but with all steps being free?

bump
>>
>>12570620
not be a retard
take the practice one they offer online, note any math topics that you've forgotten, and refresh on them until you can take another practice test and get 100%. if you can't get 100% you should be ashamed, the test is piss easy
for english as long as you're not ESL then it's easy. it's just SAT 1.5, not even 2.0
>>
I don’t completely understand the proof in example 20. How does this map to the positive integers? He says we arrange them to arrange them we start with p/q such that p+q = 2, but how does this exactly work? For example if we had f(1) = 1/1, f(2) = 1/2, f(3) = 2/1, doesn’t this fall apart immediately? F(4) = 3/1, but how about f(5)? We can skip 2/2 since it was already listed, but when we reach 1/3, that p+q doesnt = 5, it equals 4 again. So how does this work as a one-to-one correspondence? Doesn’t this violate f(n) = f(m) -> n = m? 3/1 and 1/3 both add to 4.
>>
>>12570776
Obviously he's just not counting the repeats.
>>
>>12570624
there are videos showing step by step solutions for almost every imaginable undergrad math problem on youtube
>>
>>12570776
>>12570842
It actually says so right there:
>Whenever we encounter a number p/q that is already listed, we do not list it again.
>>
>>12570847
I see, I misinterpreted that we had some function where f(4) is equal to the rational number such that p+q is equal to 4, but I realize that isnt exactly the case. We aren’t saying f(x) is necessarily gonna be a rational number such that p+q = x, just that we would eventually hit every possible rational number and it would have some positive integer assigned to it. I’m retarded
>>
How did the >>12566900 meme thread template actually succeed at taking off when it only produces constant repetition of one (1) joke with actual variations like >>12567553 once in a blue moon?
>>
How do I into CS and Quantum Computing?
I'm a second year math undergrad.
>>
>>12570535
because they have no infrastructure to profit from so they must sell out knowledge for a pittance. High quality knowledge isn't shared because it would be too dangerous.
>>
I can't understand how the fuck this applies someone please explain. Like what are the values of a and b in (-1)(-1).
>>
>>12570998
a is 1, b is -1
swap the first two terms in line 2 and they are equivalent to the first two terms in line 3
>>
>>12570624
Do you want to use them for a particular reason? Use derivative-calculator.net for derivatives and integral-calculator.com for integrals.
>>
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>>12571258
>>12570843

>Do you want to use them for a particular reason?
Is there a way to identify intervals without substituting into an inequality ?

the
>>
>>12570998
a and b can be any value though as a proof its not very clear to me at all. I prefer something like,

$(-a)(-b) = (-a)(-b) + a(-b + b) \\ = (-a)(-b) + (a)(-b) + (a)(b) \\ = (-a + a)(-b) + ab \\ = ab$
>>
>>12570353
Why the fuck aren't their $\LaTeX$ courses at uni, or at least included in uni courses?
>>
>>12571939
In general you don't have to write Latex until you get to MSc or PhD level and by that point you are expected to learn things by yourself if required. There are enough tutorials online a basic Google search will find.
>>
>>12571939
Latex is a true intellectual's signal because it's never taught
>>
>>12571585
wolfram alpha and others just brute force it if the solution isn't hardcoded in, step by step won't give you the answer you seek.
>>
>>12572003
Ok is there a way for human to identify intervals without substituting into an inequality, that is not brute force?
>>
Where did this force come from? How is it so high if they're 30m apart I dont get it.
>>
>>12572058
It's a bad analogy and badly explained. What he's trying to say is one of those grains of sand was just protons (and they didn't repel each other) and the other was just the same number of electrons that would be the force between them. Gravity is really really fucking weak.
>>
>>12572110
Oh I see the assumption now. Thanks, that's a much better explanation.
>>
How do I prove that ln(1-x)/x is integrable over [0,1]? I'm pretty sure it's something with the dominated convergence theorem.
>>
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>a new texstudio update
>ok why not
>update miktext as well while I'm at it
>5 packages were updated
>try to compile my thesis
>it errors at \begin{document}
The fuck do I do now... I can't downgrade
>>
>>12572338
Have you tried looking at line 41 to see what control sequences you use?

If you have a screenshot of that I might be able to help.
>>
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>>12572364
Line 41 is just the \begin{document}
>>
>>12572376
Dang. Looks like it could be some option clash between packages? Try commenting out cosmetic packages like color or switching the order to see if the error position changes.
>>
>>12572338
>>a new texstudio update
>ok why not
>update miktext as well while I'm at it
>5 packages were updated
>try to compile my thesis
>it errors at \begin{document}
>The fuck do I do now... I can't downgrade
Try to compile it with LuaLatex or whatever the fuck.
>>
>>12572395
I tried all kinds of commenting out earlier, but I just found out one thing:
removing the siunitx package and all of its uses throughout my thesis makes it copile without errors
I'll take it I guess, just have to manually typeset all the units but luckily I'm not using many.
Do you think it's likely to be fixed in 3 days, or should I prepare for it to stay broken and seek alternatives?
>>
Physics question I suppose. Is there a 'good enough' supersonic drag equation out there that I can use to figure out the external ballistic performance of relatively basic shapes (bullets mostly). It doesn't have to be perfect or good, just good enough. I spent some time looking for something in the past but I couldn't find anything, just lots of "it's an empirical science you need to measure the bullets :^)"
>>
>>12572444
I don't think so since at hypersonic speeds geometry starts to increasingly matter, temperature and aerodynamic heating becoming important, air flow properties can be radically different at faster speeds. That's why using powerful (super) computers to numerically solve Navier Stokes to some precision is the only option with practical experiments to confirm.
>>
>>12572427
If you have to hand in your thesis in three days, just manually input the SI units and try to fix it later, it's not a good idea to risk it.

I guess my only other suggestion is that you update your (La)TeX distribution if you haven't already; often times it's some problem with your Linux (Mac, Windows?) distro being behind because maintainers haven't updated their repositories yet. If you use TeX Live and haven't updated in a while, that might just work.
>>
Can someone explain what does P=dF/dA represent? I mean, if P=F/A represents an amount of force per unit of area, then dF/dA certainly can't present a "change" in force for a "change" in area? I know it's supposed to mean an infinitesimal force per infinitesimal area unit, but that's because I learned this through watching youtube videos. How do I learn more about this geometrical distinction vs change distinction? Or am I wrong?
>>
>>12570353
Stupid question: is the OP Pic supposed to be a trap Hong Hai Er from journey to the west? The bottle and bull horns make me think so.
>>
>>12572869
a derivative is a quotient of infinitesimals, it's the same thing, in mechanics you just use the more literal definition of the term
>>
>>12572920
Yeah I get that, so in this sense they represent a more tangible, physical thing? Like if I were to cut out a micron*micron of some material and say it's got a certain force?

On the other hand, I've learned to think of ds/dt(t) as, if I plug in t, I know how much much change in S I can expect if I move a unit t.

Do you understand my dillema? One's supposed to be a "physical", albeit it's still an abstract thing, a tangible area, or a volume, or a strip or whatever, a "physical" piece of geometry, and the other is supposed to be a slope. I know there is a difference between those two concepts, but I can't for the love of god find any information on google that goes into detail on making a clear distinction between the two.
>>
>>12572875
>not a crop
>didn't even change the filename
It's just Suika.
>>
Can lava make a splash? This has been bugging me and I can’t find an answer
>>
>>12573156
No clue who that is sry, not a weeb
>>
>>12573627
https://en.touhouwiki.net/wiki/Suika_Ibuki
>>
>>12572946
> so in this sense they represent a more tangible, physical thing? Like if I were to cut out a micron*micron of some material and say it's got a certain force?
No, that's just force per unit area. The derivative is a measure of the amount by which the force would change if the area increased or decreased by a small amount.
From the definition of the derivative:

[eqn]
\begin{align} {dF \over dA} & = \lim \limits_{\delta A \to 0} \frac {f(A+\delta A)-f(A)} {\delta a} \\ & \approx \frac {f(A+\delta A)-f(A)} {\delta a} \\ f(A+\delta A) & \approx f(A) + {dF \over dA} \delta A \end{align}
[/eqn]
>>
I'm doing some work on degree-3 polynomials in four variables. In notation, if I write x^3 before x^2y which is before xy^2, which is before y^3, and I write y^3 before z^3 before w^3, what's the correct order of terms out of x^2w, xz^2 and yzw? I want my homework to not lose marks for being formatted incorrectly, and the guy marking is a douche.
>>
>>12573828
there is no convention for this. I would only advise you to group terms with shared variables (make sure xw^2 and x^2w are next to each other so the retarded grader doesn't think you forgot one)
>>
>>12573968
Are you sure there's no convention?
>>
>>12573828
Increasing element orders and then alphabetic is standard.
So $x + y + x^2 + xy + y^2$, for example.
>>
>>12574001
Order doesn't matter because the terms in polynomials are added.
>>
What are some fields of math I should look into specialising in if I really enjoy analysis but want to do a master's/PhD and go straight to industry? I have connections to the laser and photonics industry so if it could somehow be related to that that would be awesome... I'm a third year math undergrad 3.9gpa at a hard top school and realllly enjoyed analysis, diff geo, pdes, complex analysis. I didn't really like number theory or abstract algebra or set theory or math logic. I have no research experience though , so I'm basically looking for research experience to get the summer after this one (since I'm taking year long internship break). Sorry for the stream of consciousness but basically looking for subfields I can look into that might fit all my extremely narrow criteria, i.e. analysis based, connected to industry, especially if it is connected to laser/photonics. Thanks.
>>
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I've never solved one of these before, and don't quite get it. Taking a) as the example, I should be integrating the left side w.r.t y and the right side w.r.t x?
>>
>>12574575
Both sides wrt $x$ so that the LHS integrates as a function of $y$
>>
>>12428826
It worked out nicely thanks to everyone lending me their luck.
>>
>>12574012
>increasing element orders
??????
>>
>>12573828
Use the lexicographic order.
>>12574018
An order on monomials must be imposed before you implement polynomial division to find the minimal Groebner basis
>>
>>12572253
ln 1 = 0
ln 2 = .693
All intermediate values are between thase two
>>
>>12574416
Signal processing is basically analysis
>>
>>12572253
I feel that
$\frac{\ln(1-x)}{x} \leq \frac{1}{\sqrt{1-x}}$
and the function is increasing and continuous. What do you think
>>
>>12575301
forgot a minus
$-\frac{\ln(1-x)}{x}$
>>
What is the best way to learn SQL? Every fucking data science job seems to require it.
>>
>>12575327
SQL makes me want to kill myself out of boredom every time I think about it so I'm reluctant to help you, but youtube videos are always the best for data monkey topics.
>>
>>12572483
So if you had to do it, how would you?
>>
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Brainlet here. I don't get it... How do you prove this?
>>
>>12575327
You learn the very basics from pretty much any tutorial ou there and the rest on the job.
>>
>>12575327
The same way you learn everything else, open libgen, throw the subject name in there, download some textbook, internalize the material.
>>
I keep seeing this form

$e^{ikx}$

What does it mean? I don't know any math btw
>>
>>12576424
It's the coordinates on the circle of radius 1, given that you have travelled distance kx on it, starting from (1,0) and going counterclockwise.
i.e. (cos(kx), sin(kx))

As, to why "exponentiating" results to this, watch this video:
https://youtu.be/v0YEaeIClKY
>>
>>12576442
isn't kx two variables? What do they represent?
>>
>>12576424
>>12576456
You'll see equations of that form in wave equation where k is the called the 'wave number' which is related to the frequency. x is just the postion. As for why e, it is just a quicker way of writing lots of cos and sin formula.
>>
>>12576424
It's a complex valued wave function. By Euler's identity, its real part is a cosine and its imaginary part is a sine. If you plot them one against the other, you get a unit circle.
>>
>>12576459
>>12576460
So let me check I understand this
e and i are constants that are used to create an imaginary circle
x and k are variables that specify what the circle is like
x is the x-axis coordinate and k is related to the wave
the 'real' part of this imaginary circle is an actual wave rather than a circle
>>
>>12576456
You interpret k as a constant and x as a variable.

If you have exp(i 2x) you go around the circle twice as fast exp(i x) does.
If exp(i 5x), the five times faster, etc

Think of k as predefining the velocity with which you travel on the circle.
>>
>>12576469
No, the circle is always the unit circle. This is because the amplitudes of the cosine and sine are equal to 1. k represents how fast both oscillate (so how fast you circle around) and x is the spatial coordinate along which the waves move.
>>
>>12576475
Ah I see. If k velocity where is the amplitude?
>>
>>12576484
The amplitude is a constant by which you multiply the wave. In this case it's 1.
>>
>>12576484
The amplitude is the radius of the circle.
In our case it was 1.

To change the radius from 1 to r, just scale all the coordinates by r
i.e. r * exp(i kx)
>>
>>12576502
Btw, note that the velocity now has magnitude r*k.
>>
>>12576502
>>12576490
>>12576482
>>12576475
Thanks for your help I get it now
I've also seen this sometime, what it wt and what extra finformation does it encode?
$e^{(ik - wt)}$
>>
>>12576510
exp(ikt - wt) =
= exp(-wt) * exp(i kt)

Interpret exp(-w t) as a radius, that also varies (decays) with time with exponential speed (speed predetermined by constant w)

So, you move circularly, while going down to the origin (0,0) exponentially fast, thus tracing a cool-ass Spiral.
>>
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>>12576519
Is there any way I can plot it so I can see what it looks like?
(in wolfram alpha)
>>
>>12576527
Yes

ParametricPlot[Re(Exp(i*t - 0.3*t)), Im(Exp(i*t - 0.3*t)), {t,0,10}]

Pretty cool that these stuff interest you and you understand them without having much background.
Keep going fren
>>
>>12576533
Awesome thanks. And yeah I am definitely going to learn some math properly now.
>>
>>12576533
Btw you can use ReIm to be more concise
ParametricPlot[ReIm[Exp(i*t - 0.3*t)], {t,0,10}]]
>>
>>12576519
https://en.wikipedia.org/wiki/Logarithmic_spiral
>>
>>12575899
Any ideas?
>>
>>12573776
Ok, but why would I be interested in knowing how much the force would change? Wouldn't I be more interested in knowing the exact amount of force per area? Like, what does this derivative even represent then? So dF/dA isn't the same as F/A?
>>
>>12577259
You can deduce the total force from infinitesimals.
[eqn]dF = PdS \\ F = \int dF = \int PdS[/eqn]
>>
>>12577130
Prove what? The red underlined section? If so then there's nothing to prove. It is just from the notation definition above.
>>
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>>12577340
I don't see how it is guaranteed not to be [k (p/q)] + 1 instead.
In fact if k > q, this can happen.
See pic for sqrt(2) with the convergent 7/5.
>>
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>>12577413
oops, bad example. sqrt(2) > 1
here's for sqrt(2) - 1 which is < 1
>>
>>12577413
The definition states that $\alpha = \frac{p_n}{q_n}$ so trivially $k\alpha = k\frac{p_n}{q_n}$
>>
>>12577463
a is an Irrational number in (0,1)
p_n / q_n is its n-th convergent

https://en.wikipedia.org/wiki/Continued_fraction#Infinite_continued_fractions_and_convergents
>>
>>12577463
>>12577473
Also, note that [x] denotes the integer part of x, and is equivalent to x when x is positive.
>>
>>12577259
> Ok, but why would I be interested in knowing how much the force would change? Wouldn't I be more interested in knowing the exact amount of force per area?
Either or both of those may be relevant. But they're different things.

> Like, what does this derivative even represent then?
The rate of change of force with respect to area. If you plot a graph of force against area, at any given point dF/dA is the slope of the tangent at that point while F/A is the slope of the line through that point and the origin.

> So dF/dA isn't the same as F/A?
Not necessarily. If the pressure (which is just F/A) remains constant as the area changes, they're the same.
>>
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Can someone explain to me what is being said here? I'm reading it as "if it doesn't satisfy the first constraint then it satisfies the first constraint" which makes absolutely zero sense to me
>>
>>12578286
Looks like some sort of gimmicky analogue of Walras's law.
"If all but one constraint are satisfied, then all constraints are satisfied."
>>
Do generalized eigenvectors have to be put in a specific column of the matrix? Like say I have two ordinary eigenvectors and a generalized eigenvector obtained from one of them. Would there be a specific order to put them in the matrix?
>>
>>12578493
u1 is eigenvector, u2 is generalized obtained from u1, and v is eigenvector, then

v, u1, u2 is fine
u1, u2, v is fine
u2,u1,v is not fine
u1,v,u2 is not fine

u1 and u2 must come successively
>>
Would it make sense for a university to combine matrices and linear algebra into one course? Because I think that's what my uni did
>>
>>12571192
I see that now, I thought he was going to apply the rule exactly as stated but it was exemplified by it's actual meaning, not it's proposal.
I should take these rules more so by what they propose rather than their literal meaning from now on.
>>12571933
Yeah, that kind of proof makes is easier to understand, you can't get lost like I did if you're using variables.
>>
>>12578856
"matrices" is not a course. it is a tool in linear algebra
that's like asking "would it make sense for a university to combine integration with calculus into one course?"
>>
I was reading articles on compact objects and accretion and most the studies use a software program called SpEC (Spectral Einstein Codes) to solve the equations. The software is 'private', how can these results be trusted? Is this good science?
>>
>>12579048
the course title is literally just "matrices"
and my university doesn't have a course called "linear algebra"
so I assume I'm in a linear algebra course
>>
>>12579065
What theorems are you learning?
>>
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>>12579067
here's from the syllabus, I don't know what any of this shit means since I didn't start the course yet
>>
>>12579098
Is that the entire course? Or just the first week?!
>>
>>12579108
It's a shortened course, doesn't last the entire semester
>>
>>12579122
Linear algebra covers that and more. It seems like a "linear algebra for engineers" type course, i.e. only the stuff that has immediate application.
>>
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why doesn't it work like this?
>>
how the fuck do I pay attention in class with heavy accent chinese professor?
>>
>>12579271
First, a mask doesn't form an airtight seal. Second, the mask stops droplets, which eventually evaporate. The virus particles are too small to have a noticeable effect.
>>
If you give a person 5 sets of 2 pictures and they have to select the correct one of the two pictures, whats the probability they get them all correct? Would you use a combination?
>>
Is there a website that lets you see the orbital position of the planets at various years? Preferably as far back as the 1800s.
>>
What is the matrix form of the surreal numbers ϵ and ω?

I know the dual number ϵ = [0 1] [0 0]
and imaginary number i = [0 1] [-1 0]

but have the surreals ϵ and ω been defined?
>>
>>12579487
Binomial distribution
>>
also I found the reciprocal of the dual number $\epsilon$
it's:
$\frac{1}{\epsilon} = \begin{bmatrix} a & \frac{b}{0} \\ 1 & -b \end{bmatrix}$
where $a, b \in \mathbb{R}$

How many cookies do I win?
>>
>>12579059
No answers to this? I should also add that you can't even download/buy the software. It's just provided to certain researchers it seems. Not something I could ever get.
>>
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>>12570353
I'm interested in reading pic related. I don't study physics in uni, but in the subject a got an A in GCSE and a B in A-levels, I forgot most of the A level stuff, and I forgot nearly everything about calculus. Will I understand University Physics if I study it?
>>
>>12580398
*Also, you could advise me to just start reading it for myself and see if I understand it, but I'm worried about putting in effort understanding the earlier chapters and then I get perplexed at the later chapters, will I understand everything in the book if I put in the effort to study it? Yes, I know I'm lazy.
>>
>>12580398
I looked through it. It looks equivalent to a first year course of physics in the US. Not sure how that correlates to the UK. For example it doesn't show lagrangian mechanics or hamiltonian. The E&M avoids the use of vector calculus and has simplified problems. The QM section is just bolted on as an afterthought to give you a taste. It would be fine to teach you an intro to the subject, but I wouldn't say it's all of 'university physics' just the first year.
>>
>>12580398
>>
>>12575899
:/
>>
I'm learning Linear Algebra.
The assigned text Linear Algebra and It's Applications by Lay.
I love this subject. What are a couple other good Linear Algebra texts both application and theory oriented?
Thanks!
>>
>>12580613
Axler is S-tier
Also, watch 3blue1brown's videos.
>>
>>12580613
If you want applications & theory Hoffman & Kunze is the best. Lots of good material in there. Axler might be too concise, but it is well written (less dry).
>>
>>12580616
This has to be a meme
>Axler
Good luck generalizing half the proofs to anything other than R or C
>3blue1brown
Complete waste of time. There is no royal road.
>>
Hello bros, analysis time! What do you think:

Let f be integrable on any interval in [a,inf). Prove that $\int_{a}^{\infty}f$ converges iff for $\epsilon > 0,\exists M>a:d>c\geq M$

$|\int_{c}^df|<\epsilon$

I will ask your opinion on this proof on the reverse implication.
Assume $\epsilon > 0,\exists M>a:d>c\geq M$

$|\int_{c}^df|<\epsilon$

Consider the sequence $M_1>M_2>...>M_n>...$ such that

$|\int_{M_n}^{M_{n+1}}f|<\frac{\epsilon}{2^{n+1}}$

Then

$|\int_{a}^{\infty}f|\leq|\int_{a}^{M_1}f|+|\sum_{n=1}^{\infty}\int_{M_{n}}^{M_{n+1}}f|<A+|\sum_{n=1}^{\infty}\frac{\epsilon}{2^{n+1}}|<A+\epsilon$

Since epsilon is arbitrary the improper integral converges. Does this work?
>>
i have Phenibut HCl and Acetyl-L-Carnitine HCL

The capsules are sold as Phenibut 200mg and Acetyl-L-Carnitine 250mg respectively, but since I dont know the ratio of substance:HCL and the mass them individually, I dont know what to expect if I weigh them. Because one capsule of each weighs 290 and like 360 respectively
>>
>>12580829
>Consider the sequence M1>M2>...>Mn>... such that
You can do that, right.
But you can't actually assume that $M_n \rightarrow \infty$, so it doesn't prove anything.

Really look at that condition. It should instantly make you think of a Cauchy sequence. You should look at the problem, analyse it, and conclude that it's some sort of continuous form of the Cauchy sequence criterion for convergence, and then prove it based on that.
>>
>>12580899
>But you can't actually assume that Mn∞Mn∞
But why? As the errors get smaller, the Mn elements increase necessarily because they can't remain constant, otherwise I guess the condition that is assumed is not met?
>>
>>12580907
Oh man, I get it, it's not the case, it just suffices for a function to become 0 after a certain point for the Mn to become eventually constant
>>
I don't understand. When did they prove that zero is natural number in mathematical induction?

Yes, I'm giant stupid. And now I'm very confused about induction. I can't find the proof? Is it taken for granted, then?
>>
>>12581255
zero is not a natural number lmao
>>
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How tf do I whiten my teeth? It's yellow as fuck.
>>
>>12581380
prove it
>>
If X is 75% of n, how can I find what 100% of n is?
E.g. X = £2,500
>>
>>12581380
Well why is it then used in proofs/axioms about natural numbers? like succ(0) being nat 1?
>>
>>12581392
proof by definition

>>12581405
Many just axiom 0 up by saying that 0 is a natural number or just consider $\mathbb{N} \cup \{0\}$. Unless you shoehorn 0 in, 0 is not a natural number.
>>
>>12581398
$X = 75\%n$
Using the identity $\% = 0.01$, we can rewrite that as $X = 0.75n$, and then $100\%n=n=X/0.75$
>>
>>12581420
yeah the axiom shoehorning is throwing me off I guess, reading taos Analysis 1
>>
Can someone help me with this
I am trying to solve something but I need to work out the expectation of a (sum)^2

I.e. E[(sum of x)^2]. How do I work this out? I cant write it properly so I hope it's clear
>>
>>12581420
> Unless you shoehorn 0 in, 0 is not a natural number.
Is this a US thing? I have a CS degree from the UK, which involved a fair number of discrete maths courses, and the term "natural numbers" always included zero.

The second paragraph of the wikipedia entry says:

> Some definitions, including the standard ISO 80000-2,[4][a] begin the natural numbers with 0, corresponding to the non-negative integers 0, 1, 2, 3, ... (often collectively denoted by the symbol $\mathbb {N}$, $\mathbb {N}$, or $\mathbb {N}_{0}$ for emphasizing that zero is included), whereas others start with 1, corresponding to the positive integers 1, 2, 3, ... (sometimes collectively denoted by the symbol $\mathbb {N}$, $\mathbb {N} _{1}$, or $\mathbb {N} ^{*}$ for emphasizing that zero is excluded).[5][6][b]

If you remove zero, you end up with a set which lacks an additive identity, so it isn't particularly useful. In terms of the Peano axioms, the natural numbers are defined as ℕ={0}∪{S(n):n∈ℕ}, i.e. zero is a natural number.
>>
>>12581695
$E[X]=\sum_i P(X=x_i) x_i$
IOW, the expected value is the weighted average of the squares of the sums, weighted by the probability of each sum.
>>
>>12581695
[eqn]\left(\sum_{i=1}^n X_i\right)^2 = \sum_{i=1}^n X_i ^2 + 2\sum_{1<i \leq j < n} X_i X_j[/eqn]
>>
>>12581695
Y : = sum of x

V(Y) = E(Y^2) - E(Y)^2

E(Y^2) = V(Y) + E(Y)^2
>>
>>12581849
Also E(Y) = Sum E(X_i)

And if the X_i's are uncorrelated
V(Y) = Sum V(X_i)
>>
Why is space vacuum so cold? Why does it hurt us? I mean it is literally nothingness, how can nothingness be harmful?
>>
>>12581695
$E[(\sum_nX_n)^2]=V[\sum_nX_n]+E[\sum_nX_n]^2=\sum_nV[X_n]+2\sum_{n \neq k}\textrm{Cov}[X_n,X_k]+E[\sum_nX_n]^2$
>>
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actual stupid retard question here, i'm completely brain sharting about how to solve this with non-constant acceleration and getting the t variable in there
>>
>>12582021

$x(T)=x_0+\int_0^Tv(t)dt$
$x(T)-x_0=\int_0^Tv(t)dt$
$dx(t)=v(t)dt$
$\frac{dx(t)}{dt}=v(t)$

Does this make sense?
>>
Can anyone explain to a brainlet why the Maximum Likelihood Estimator is not suited to estimating binomial distribution when both n and p are not known?
>>
>>12581954
your body requires the pressure of Earth's atmosphere to work. you're basically a flesh balloon.
what happens when balloons get really high in the atmosphere (where there's less pressure)? they get big and pop
that would be your body in space. the pressure inside your body would be much greater than the ambient pressure, and would start pushing your skin out until you rupture
>>
Like, you have the total number of successes but and want to estimate n and p, or you have the fraction of successes and want to estimate n and p?
Because those are both stupid simple. Think for 2 seconds plus.
>>
>>12582175
>>
>>12575899
Ok, now I think I finally fucking figured it out.
It holds for any irrational a, not just for 0<a<1.

This inequality is true:
$|a - \frac{p}{q}| < \frac{1}{qq'}$ where q' is the denominator of the next convergent ($q < q'$ holds).
and we're also given that $k \leq q$

So we get $|ka - \frac{kp}{q}| < \frac{k}{qq'} < \frac{1}{q'}$ (*)

Case 1: $\frac{p}{q} < a$
(*) becomes $\frac{kp}{q} < ka < \frac{kp}{q} + \frac{1}{q'}$
Thus, it suffices to show that $\frac{kp}{q} + \frac{1}{q'} < [\frac{kp}{q}] + 1$
Equivalently, show $\{\frac{kp}{q}\} < 1 - \frac{1}{q'}$ where {x} is the fractional part of x. (Notice that $\{\frac{kp}{q}\} = \frac{(kp) \% q}{q}$ where % is the modulo operation)
Equivalently, show that $(kp) \% q < q - q/q'$ which is true since $(kp) \% q < q - 1< q - q/q'$

Case 2: $\frac{p}{q} > a$
(*) becomes $\frac{kp}{q} - \frac{1}{q'} < na < \frac{kp}{q}$
Thus, it suffices to show that $[\frac{kp}{q}] \leq \frac{kp}{q} - \frac{1}{q'}$
Equivalently, show that $\{\frac{kp}{q}\} \geq \frac{1}{q'}$, which is true since $\{\frac{kp}{q}\} \geq \frac{1}{q} > \frac{1}{q'}$
>>
>>12582076
i mean those are the general equations yeah but my shortcoming is how to use that to get v(t) and v(x) when acceleration has v(t) in it
>>
>>12582163
The maximum likelihood estimator does not perform well on a nontrivial range of the parameter space. In particular, if both $n$ and $p$ are unknown, and $p < \frac{1}{2}$, then your estimator will be both biased and inefficient (its variance will be large).
>>
If you were to bang two pieces of uranium against each other would it create a nuclear explosion ?
>>
>>12582258
No. You would cause a spike in radioactivity if the combined mass was over criticality but not an explosion.
>>
>>12582268
how does it explode then ?
>>
>>12582271
The uranium needs to be compressed together for long enough for super-criticality to occur. In the original atomic bombs they used standard explosives to create an implosion. That inward force is needed to ensure enough of the material undergoes fission before it blows itself apart.
>>
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I am going to kill myself.
>>
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>>12582345
These should be x, y and z
>>
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>>12582403
Praise be to anon, who shows kindness to the disabled.
>>
>>12582436
>>
>>12570353
for equations of the form x^p - 1 = 0, where p is some natural number I can re-write them in terms of the complex pth roots of 1.
For example, x^4 - 1 = 0 can be re-written as
(x-1)*(x-i)*(x+1)*(x+i) = 0.

But this doesn't work if x is some non-natural number. For example if I use a rational number like 5/2. Is there some generalization or correction I can make to this method that works for all possible exponents p?
>>
>>12583317
typo in my post.

>But this doesn't work if x is some non-natural number.
But this doesn't work if p is some non-natural number.
>>
Does anyone else problem solve by thinking out loud? I find that I can contextualize the problem much better by speaking my thoughts rather than internalizing them.
>>
>>12583317
x^(5/2)-1=0 => x^(5/2)=1 => (x^(5/2))^2=1^2 => x^5=1.

IOW, the number of solutions is determined by the numerator.
>>
Why is a^2 = (p - a)^2 mod p?
>>
>>12583756
(p - a)^2 = p^2-2ap+a^2. p^2 and -2ap are multiples of p and thus ≡0 (mod p). Also, (p-a)≡-a (mod p) and (-a)^2=a^2.
>>
Tell me the science reason why I want to smell feet of cute grills
>>
>>12584219
Either evolutionary mismatch or you're just a degenerate.
>>
What is the purpose of the siphon mechanism in a soxhlet extractor? Wouldn't a continuous percolation of hot solvent added dropwise acheive the same effects?
>>
>>12584219
There is plenty of literature out there than explains why fetishes are a thing.
>>
>>12583708
I get that the solutions for x are the same, but the equation isn't. If you plot

f(x) = (x-1)*(x-Exp[i*2*pi*1/5])*(x-Exp[i*2*pi*2/5])*(x-Exp[i*2*pi*3/5])*(x-Exp[i*2*pi*4/5])

it looks like f(x) = x^5-1, not f(x) = x^(5/2)-1.
>>
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I don't understand the criteria to search for in a counterexample.
>>
When using the residue theorem, if the curve passes through some residues, do I count these in?
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>>12584685
I understand the rest of the image, just tell me what's the Omega.
>I don't understand the criteria
Like $a \vee (b \wedge c) = (a \vee b) \wedge (a \vee c)$.
Possibly some infinite analogue.
>>
>>12584706
Frame of opens over $\mathbb{R}$, basically topology over $\mathbb{R}$, with $\bigwedge S := \text{Int}(\bigcap S)$ and disjunction as normal union.
>>
>>12583394
best way to learn is to teach, but it's hard to find an audience
and so, we teach ourselves
>>
>>12584731
Oh, alright.
Try out $[(0,1) \cup (1, 2)] \vee \left[ \bigwedge _{a \in (1, 2)} (0, a) ] \right]$
>>
Does dark matter cause gravitational lensing?
>>
Splitting rent between 5 people + $50 where one person isn't paying rent, only their share of the$50

$2800 +$50 = $2850$2850 / 5 = $570$570 * 4 = $2280 or$2800 / 5 = $560$560 * 4 = $2240$2240 + $50 =$2290

Where does the extra $10 mysteriously disappear to in the first method? >> how to prove pic related for every f that is continuous in [0;1] ? >> >>12584760 Yes. It is one of the observations that indicates the existence of dark matter. >> >>12584767 It hasn't disappeared. You have just performed two different operations of addition and multiplication on different starting values so obviously you get different results. Also if$2800 is the rent then both methods are wrong since you stated the rent is split between 4 people since 1 isn't paying.
>>
>>12584770
oh I thought it was just inconsistent velocities, nice
>>
>>12584754
Seems to work unless I'm a big retard, thanks
>>
>>12584782
1 person is omitted from the rent, and is just paying the $10 extra per month. >> >>12584767 what the fuck is the point of the$50. $50/5 = 10 is where your mysterious$10 is coming from, retard.
>>
>>12584798
exactly. so it should be $2800 / 4 >> Does "momentum" flux couple through space similar to how magnetic flux does? Like, if two massive objects were speeding past each other, would they repel like wires with opposing currents? >> >>12584791 There are something like 5 or 6 different independent observations and measurements that suggest the existence of dark matter. The best alternative is MOND and that can explain 1 or at best 2 of those. So if dark matter doesn't exist then whatever the correct explanation is must be really fucking weird. >> >>12584806 We are not covering that person's rent, she paid her year's worth already. >>12584802 So which method produces the correct answer? Adding the$50 into the rent before splitting it or adding it to the rent after the person whose share is omitted is calculated?
>>
>>12584809
No because mass/momentum is always attractive unlike electromagnetism.
>>
>>12584824
So the fact the other person has paid their rent already is completely irrelevant and you had no reason to mention it.

So $560 is everyone's share of the rent and$10 is everyone's share of the surcharges.
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>>12584691
I don't think you can integrate in that case
>>
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So what's the big idea here. Is it not obvious that function is less than that same function multiplied by a constant?
>>
>>12584769
substitution inside the integrals?
>>
>>12584837
attractive or not, does momentum have any effects through space (ignoring the effects of gravity)?
Or is gravity necessarily a product of momentum?
>>
>>12584923
it's not the same function
>>
>>12584985
oh fuck i'm big stuid
>>
>>12584974
Well a faster moving mass would have more momentum and hence more energy. So in total that would have a higher effective mass/energy warping space-time. But in the end it's all just gravity.
>>
>>12584769
Alway rember thet $\sin(x) = \cos(\pi/2 -x)$
>>
>>12584769
$\cos(x)=\sin(x+\pi/2)$
$z=x+\pi/2,z \in [\pi/2,\pi]$
$\int_0^{\pi/2}f(\cos(x))dx=\int_{\pi/2}^{\pi}f(\sin(z))dz$
$\sin(\pi/2+y)=\sin(\pi/2-y),y\in[0,\pi/2]$
$\int_{\pi/2}^{\pi}f(\sin(z))dz=\int_0^{\pi/2}f(\sin(x))dx$
>>
I'm stuck with this, I'm supposed to use residues
[eqn]
\int_{0}^{+ \infty} \dfrac{dz}{z^{3} + 1}
[/eqn]
it's supposed to give me $\frac{2 \pi}{3 \sqrt{3}}$.
I've tried a curve that's a third of a circle, so I get two additional integrals (the curved and straight part of the arc) that I can estimate to 0, and I'm only left with the residue at $z = e^{\pi i/3}$ times $2 \pi i$, I'm not sure where I'm getting it wrong, could someone help me?
>>
Why does linear programming use all this fluffy language and terminology when all it is is basic algebra?
>>
>>12585171
brainlets coping by trying to sound as convoluted as possible. some subfields are riddled with this bullshit.
>>
>>12585110
I'd try left and right semicircles
>>
>>12585382
Wait I am talking nonsense.
Just take the semicircle lying on top of [0, R] and let R go to infinity.
>>
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What do you call these?
Points?
In a graph with 5 different plots in the same figure, can I say "Each line is made up of 40 points"?
>>
>>12585911
I would say datapoints assuming that these are actually points corresponding to data you have, where the lines between the points are simply connecting them
>>
>>12585952
yes that's the case, thanks
>>
Is data science fun?
>>
Given an uncertainty on the y values, how can i calculate the uncertainty of the x value that maps to the maximum value of y? i’m trying to find the uncertainty of my measured value for the phaseshift between two sine waves and have the uncertainty of the voltage measurements
>>
>>12586074
for me- no
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>>12586195
Why?
>>
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This isn't true, right? A matrix can have just a left, or right inverse. 1.1.20 just goes over block multiplication, so I'm not sure what the author is referring to.
>>
>>12570353
I'm messing around with some products, and I feel like there should be a connection with the gamma function, which I've done some reading about online but am otherwise not that familiar with. Is there any way to relate
$\prod_{n=0}^{m} (2n+1-z)$
to the gamma function? (z is some complex number with modulus less than or equal to 1, if that helps.)
>>
>>12586242
At least over a field, a square matrix is just a linear map between vector spaces of same dimension, so injectivity is equivqlent to surjectivity.
>>
>>12586261
*same finite dimension
>>
>>12586242
That's a group-theoretic result.
You have that $AB = A$ implies $B=I$, hence we can look at $A^{-1} = A^{-1}BA^{-1} = A^{-1}(BA^{-1}) = (A^{-1}B)A^{-1}$.
>>
>>12586270
>You have that AB=A implies B=I,
Forgot to mention, but this is assuming $A$ is invertible.
>>
>>12586270
Matrices only form a group under addition unless you restrict yourself to invertible ones, but that makes the argument circular. You need to show that AB=I or BA=I shows thst A is invertible.
>>
>>12586074
I like statistics and machine learning
>>
I'm lonely, someone add me on discord.
oka-tan#8719
>>
>>12586370
This is not the purpose of /sqt/.
>>>/soc/
>>
>>12586242
AB = I necessarily means that B is injective and A is surjective. therefore both A and B are isomorphisms by rank nullity
>>
>>12586387
>this isn't the purpose of this containment thread
>>
>>12586387
i’d imagine he’s looking for someone who would be in this thread so what could would posting on another board do him?
>>
>>12586529
It would help him not break the rules.
>>
What can you do with piss? I have a lot of it stored in bottles, currently.
>>
>>12570353
What are the rules for sudoku again?
>>
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>one more essay question
>300 world limit
>ran out of time
>submitted 2 vague sentences
>>
>>12587087
if you left it for the last second it probably wasn't high on your list anyways
>>
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Can any psychology anons explain what my dream meant.
>In the some small town in the deep south of Georgia USA.
>At a country restaurant, the food is delicious so I order seconds.
>I get up to go do something and when I return the path to my table is blocked off.
>I Am trying to get around it without being awkward, all of a sudden this really cute girl I know is watching me.
>A sperg out and start (figuratively) spilling my spaghetti everywhere.
>I get around the obstacle, now this little shit who couldn't be older than 15 is in my chair eating my Chicken.
>I VIOLENTLY SHOVE HIM TO THE GROUND!
>All of a sudden mt Brother arrives and starts lmao'ing histarically at my extreme actions against some teenage chicken thief.
>And before I could eat my chicken in peace I notice I don't have any silverware.
>The restaurant ran out of silverware.
>I eat my chicken with my hands.
>Cute girl is staring at me again as I eat the chicken with my hands like some sort of sentinalese Islander savage.
>Get so annoyed that I storm out of the restaurant with my brother.
>On the way out some nigger tries to rob us I proceed to stab him a billion times in the stomach until he falls over dead.
>My brother is driving my dads old suburban.
>As we are going down the road a boeing 737 flies over with it's right engine on fire and crashes in a nearby lake.
>Instead of taking the Highway home my brother insisted we take some rickety wooden bridge through a swamp that was connected to said lake.
>I am freaked out and put of a life preserver because I can't swim.
>Of course the bridge gives way
>The front half of the suburban is hanging of the bridge and the back half is in the water.
>Out of nowhere a beautiful spirit girl comes floating through the sky and caresses my brother.
>Than it suddenly bites him in the neck and the dream ends.
>>
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Will a gun fired in the vacuum of space have a greater muzzle velocity than in atmosphere?
I imagine with no air in front of the projectile it would have less resistance while being accelerated down the barrel, but would this only have a negligible impact?
>>
>>12587192
how would the gunpowder ignite?
>>
>>12587228
Self oxidizing powder.
>>
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>>12587228
>>
>>12587192
You could think it in a way that in the atmosphere the "projectile" consists of the bullet but also the air in the barrel since it also needs to be pushed away. Bullets weigh about a gram and air in the barrel about a milligram so the bullet would fly out at about 999m/s instead of 1000m/s.
>>
>>12586191
Sounds like you could use some sorts of confidence intervals.
>>
Courant or Spivak for Calculus?
>>
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How do I prove Pic related
>>
>>12587448
Specifically how do I prove that H is a set/subset of G
>>
>>12587448
>>12587450
I've tried every tool in my belt to crack this one. I would appreciate it very much if one of you fine gentlemen could help
>>
>>12570998
>13 pages into lang "Basic" mathematics
>It's been 3 years since I started
>I have gotten farther than most but still not yet there
>I have become adept at manipulations of the algebraic variety
>I can feel the transfer of knowledge
>I have asended to another plane of existance
>It is there I see WHY minus 1 times minus 1 (the fools say negative, but I know that minus in unambigious langauge) equals 1
>I can express so in the language of the universe
>I have learned the language of the universe and
>I AM MINUS 1 TIMES MINUS 1 WITH THE UNIVERSE
>>
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Newton's cradle consists of five equal-sized steel balls that hang in a stand (see figure). The balls can be pulled out to the side and released, whereupon they collide elastically with the other balls. If two of the balls are pulled to the side and released, two balls are fired on the other side as the figure shows. The momentum would be preserved even if only one balls was fired on the other side but at double the speed (compared to the two balls). Why does it never happens in the real world, how could I show this through calculations?
>>
>>12587547
Both momentum and energy are conserved.
m1*v1 = m2*v2
(1/2)*m1*v1^2 = (1/2)*m2*v2^2
=> m2=m1, v2=v1
>>
>>12587547
Kinetic energy =/= momentum. A single ball going at twice the speed of the initial two balls would have more energy than two balls at the same speed.
>>
>>12587550
oh, now I see. I love you :*
>>
>>12587448
bump
>>
>>12586618
>>
How do you guys *start* studying? I can study for a long period of time with ease but I have a hard time starting. I'm just never in the mood to sit and read for several hours. How do you set up/prepare or motivate yourself to study?
>>
>>12587448
that's a definition
>>
>>12587448
nigga, there's nothing to prove, the author is just giving names to things
>>
>>12587791
I study in theorem/exercises/problems bursts
I prove a theorem then do something else then I come back to prove the next theorem repeat. Then I do the exercises. I'll do exercises that are related/could be related. A good book will have simply stated exercises that don't look related but have multiple solutions one of which uses an exercise you just solved (Spivak Calculus is the classic example) Then do something else.
If the book has real research level problems I'll try them for 10 of these sessions resetting the count if I make progress.
>>
>>12587792
>>12587843
I know I am trying to show
>>12587450
>>
>>12587845
are you asking how would you go about proving that H is a subset of G in general, or are you asking how to ""solve the exercise"" that you've posted?
>>
>>12587845
Ok, so you say that you are trying to show that $H \subseteq G$.
What are the assumptions about G and H?
>>
>>12587921
I don't know All I know Is that (H,+), (G,+) form groups and that H is in G. So how should I show that H and G are sets, so I can show that H is a subset.
>>
Bros, to prove that differentiable at a point implies continuous at a point without using limits theorems, is this sufficient?

$\varepsilon>0, \exists \delta > 0 : |y-x|<\delta \Rightarrow |\frac{f(y)-f(x)}{y-x}-f'(x)|<\varepsilon$

$|\frac{f(y)-f(x)}{y-x}|<|f'(x)|+\varepsilon$

$|f(y)-f(x)|<(|f'(x)|+\varepsilon)|y-x|<(|f'(x)|+\varepsilon) \delta$

$\textrm{set }\delta=\varepsilon/(|f'(x)+\varepsilon|$
>>
>>12587972
*$\delta=\varepsilon/(|f'(x)|+\varepsilon)$
>>
>>12587934
What am I missing here? You already have an answer? Groups are sets with certain properties. You said you already know that H is in G so you're done.
>>
>>12587989
H is in G if H is a set*
>>
>>12587972
>>12587975
Kinda hard to parse through tbqh.
>>
>>12570353
Why when I post my question here does it look like it's going to post but then my post doesn't appear when I reload the page?
>>
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>>12570353
>>12588003
Guessing picture was too big.

How do I read this graph from a sleep study?

It has time on the Y axis and no X axis? Usually I'm used to having time on the X axis.
>>
>>12587934
> and that H is in G
> show that H is a subset
nigga what?

You want to so that if G is a group, then the elements of G form a set?
Everything in math is a set.
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>>12588144
>Everything in math is a set.
I can see that a corollary of this would be H is a set but this seems impossible to prove.
Though maybe I was wrong I think I need to prove that it has an element then I could conclude that is it an inhabited set.
That makes more sense.
Ya it has to be inhabited to be a group. So I need to show H =/= {}.
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>stack piles and piles of trivial results until something miraculously pops out
Why is half of mathematics nowadays like this? Why did we do for Grothendieck to cast us into this hell?
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>>12587791
you don't
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How do you stop yourself from overcomplicating questions. For example the pic related. It's required that a million photos have to be taken in the time it takes for the rock to fall. But the random intervals make this question practically unsolvable. One set of random intervals can be zero for the first 99% of the falling rock and then all million in the last 1%. Make the shit difficult for myself like this makes it really frustrating to study. I'm scared that if I go with "the spirit of the question" I might end up simplifying the question too much and removing important details out of it.
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>>12588413
I don't see the issue. You've determined the correct major issue with the question's formulation (the fact that it talks about a specific realization of the experiment, rather than how it doesn't tell you the distribution) and you know how to interpret it correctly (compute $h/2$).
You didn't do anything wrong.
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Alright, I think should be obvious but I'd like someone to check I'm not doing anything sacrilegious here.

Let $R$ be a commutative unitary ring. Take an $R$-module $M$ and an ideal $I \subseteq ann_R(M)$ (the annihilator of $M$). Then $M$ can be viewed as an $R/I$-module by defining the scalar product as $(r+I) \cdot m = rm$. This thing is well defined because $I$ kills $M$.

Now, I say that the lattice of submodules of $M$ as an $R$-module is the same as an $R/I$-module, and that a function $f:M \rightarrow N$ between two modules such that $I \subseteq ann_R(M) \cap ann_R(N)$, is $R$-linear iff it's $R/I$-linear (with the structure defined above, obviously). Am I right?
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>>12587306
Spivak but he uses no lube.
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>>12588413
>How do you stop yourself from overcomplicating questions.
solve for 1
solve for 2
see why solving for 2 is harder
find a method that does not make 2 any harder
solve for n
solve for 1 million
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>>12587192
Yes it would be faster but not my much. Air resistance is not important for muzzle velocity but the air counterpressure. And this is tiny compared to the gas pressure so the difference is tiny.
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What is meant by the set aZ where Z is the integer sign? For context the question is asking to prove if L=lcm(a,b) aZintersectbZ=LZ but idk what is meant by these sets
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>>12588584
i assume it means integer multiples tell me if im wrong
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>>12588584
Do you mean $a\mathbb{Z}$? It's all the multiples of $a$.
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>>12588653
ya okay thanks thought so
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>>12588741
In general, aG means {ag | g in G}
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>>12587661
Dude, you're helpless.
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>>12587448
>>12587661
THERE IS NOTHING TO PROVE
IT'S A FUCKING DEFINITION

Let me rephrase it:
A subgroup H of G IS DEFINED AS a subset of G that also forms a group (under the operation of G).
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Quick notation question, what does the superscript V mean in this integral for mole balances? Does it mean to integrate over the entire volume? trying to figure out the limits of integration one would use on this. The book is Elements of Chemical Reaction Engineering 5th edition.
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>>12589306
>Does it mean to integrate over the entire volume
Yes.
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>>12589365
Thanks. So the limits of integration would basically be from 0 to V where V is the entire volume of the reactor?
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>>12587448
is this bait?
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>>12588515
>I say that the lattice of submodules of M as an R-module is the same as an R/I-module
Sure.
>and that a function f:MN between two modules such that I⊆annR(M)∩annR(N), is R-linear iff it's R/I-linear
Sure.
Think you can prove this one quickly by looking at the $M \rightarrow M \otimes R/I$ functor.
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>>12589368
> So the limits of integration would basically be from 0 to V
The term "limits" isn't really meaningful unless you have a volume defined in terms of equations in some coordinate system. It just means integrate over the volume.

Note that a volume integral would normally be shown as a triple integral, [eqn]\iiint^V ... dV[/eqn]. So if you were actually calculating a definite integral for e.g. a unit sphere, you'd have
[eqn]\int_{-1}^1 \int_{-\sqrt {1-z^2}}^{\sqrt {1-z^2}}\int_{-\sqrt {1-z^2-y^2}}^{\sqrt {1-z^2-y^2}}r_j(x,y,z)\,dx\,dy\,dz[/eqn]
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>>12589916
how many hours a day do you spend doing maths 2hu anon? I always see you in these threads
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>>12566254

This might not be relevant anymore, but I'm gonna sketch the solution anyways.

Firstly, I'm gonna assume the area moment of inertia is known for both sections of the beam, labeled $I_1$ and $I_2$. I'll define the length of the first section as $L_1$ and the length of the whole beam as $L_2$ Next I'll assume you only care about the upwards bending of the beam (labeled $w_1$ and $w_2$), not its lengthwise compression by the force (which is small in comparison). If you actually wanted to take that into account, the problem would be a lot more complicated.

You have realized that you can simply decompose the excentric force into an axial force (which you didn't picture) and a torque. The torque needs to be at the end of the beam, shifting forces along their line of action is generally only possible for rigid objects. At this point we just have a beam with 2 sections and torque at the free end (if you cared about the tension you would of course still have to add the impact of the force, but as I stated the compression of the beam is probably negligible when just looking at deformation). You can solve this with your method of choice, either with the differential equations of the beam and then integrating:

[eqn]
w_1^\mathrm{IV}(x) = 0, w_1(L_1) = w_2(L_1), w_1(0) = w'_1(0) = 0
[/eqn] [eqn]
w_2^\mathrm{IV}(x) = 0, EI*w''_2(L_2) = Fd, w'''_2(L_2) = 0
[/eqn]

Or alternatively you can just use a table and view the left section as a cantilever beam with Fd at its right end (since the torque needs to be transmitted through the connection). View the right section the same and just add the deformation of the left secion at $L_1$ to it as a constant.

Hope this made any sense, it's been ages since I did any elastic mechanics.
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Why do masks and social distancing keep away the flu but not the coronavirus? What are the differences between them that explain this?
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if the set of reals is uncountably infinite, then does the universal set have the same cardinality? even though it clearly has more elements by virtue of containing the complex numbers.
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>>12590405
R and C have the same cardinality.
The power class PR of R or C is "bigger" than R and the universal class indeed is, yet, bigger than PR.
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How likely is it to get into grad school for physics without an undergrad degree?
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>>12590453
Not possible
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can someone please explain me why "3 cubed times 192" is the constant?
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>>12590518
this was the pic, sorry
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Literally what. How is this wrong.
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>>12590566
you probably fucked the syntax up
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>>12589985
Recently I'm just degenerating, so zero hours plus the time I spend answering math questions here.
Thanks for asking, I've been needing to feel embarassed for a while now.
>>12590566
Write the solution in fucking integers damn it, what the fuck.
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>>12590530
Yo hablo español pero esto es un sitio web inglès-hablante. Hay que traducir tu pregunta, y solamente para que los anons podrian comprenderla
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>>12589955
I was originally thinking that it should be a triple integral, but it seems that they are not being used in the text. Whatever, thanks for the help.
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Can a virus possibly evolve into effectively becoming a single cell organism? I figure that maybe tho mutations that go towards that direction might be counter-productive and that's why it doesn't happen
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>>12590566
Maybe you have to use an asterisk for multiplication?

If that's not the case, try using the vector (-1, -3, 2) instead of its half
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>>12590530
"Find 'm' in F(x), if the main coefficient is equal to the independent term"
That's the translation
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given the middle left example, how is $\{1\} \union \{ 2 \}[\math] retained under the finite intersection property? >> >>12590530 >>12590518 That looks wrong. >> >>12590587 I hope to one day reach your level of autism anon, godspeed. Are you a grad student or just a freelancer? >> >>12587972 Ok bros I found out this proof is quite legitimate, but the last delta should be [math]\hat{delta}=min(\delta,\varepsilon/(|f'(x)|+\varepsilon)$
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Why is the set of a^2 mod p and the set of -(b^2) mod p not intersecting? p is prime, a and b < p.
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Suppose that f is analytic on the complex unit circle, how do I show that
[eqn]
\sup_{|x| \leq 1} |f(x)| \leq \sup_{|x|,|y|\leq 1} |f(x) - f(y)|
[/eqn]
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