/sqt/ /qtddtot/ - stupid questions thread

[Anonymous No.14958813]

Previously >>14946053

>what is /sqt/ for?
Questions regarding maths and science. Also homework.
>where do I go for advice?
>>>/sci/scg or >>>/adv/
>where do I go for other questions and requests?
>>>/wsr/ >>>/g/sqt >>>/diy/sqt etc.
>how do I post math symbols (Latex)?
rentry.org/sci-latex-v1
>a plain google search didn't return anything, is there anything else I should try before asking the question here?
scholar.google.com
>where can I look up if the question has already been asked here?
warosu.org/sci
eientei.xyz/sci
>how do I optimize an image losslessly?
trimage.org
pnggauntlet.com
>how do I find the source of an image?
https://images.google.com/
https://tineye.com/
https://saucenao.com/
https://iqdb.org/

>where can I get:
>books?
libgen.rs
z-lib.org
stitz-zeager.com
openstax.org
activecalculus.org
>articles?
sci-hub.st
>book recs?
sites.google.com/site/scienceandmathguide
4chan-science.fandom.com/wiki//sci/_Wiki
math.ucr.edu/home/baez/physics/Administrivia/booklist.html
>charts?
imgur.com/a/pHfMGwE
imgur.com/a/ZZDVNk1
>tables, properties and material selection?
www.engineeringtoolbox.com
www.matweb.com

Tips for asking questions here:
>attach an image (animal images are ideal, you can grab them from >>>/an/. Alternatively use anime from safebooru.donmai.us)
>avoid replying to yourself
>ask anonymously
>recheck the Latex before posting
>ignore shitpost replies
>avoid getting into arguments
>do not tell us where is it you came from
>do not mention how [other place] didn't answer your question so you're reposting it here
>if you need to ask for clarification fifteen times in a row, try to make the sequence easy to read through
>I'm not reading your handwriting
>I'm not flipping that sideways picture
>I'm not google translating your spanish
>don't ask to ask
>don't ask for a hint if you want a solution
>xyproblem.info

[Anonymous No.14958837]

Unanswered questions:

Maths questions:
>>14946064
>>14949063
>>14951757 [Usually it's the indefinite integral.]
>>14953124
>>14953161
>>14955647
>>14955676
>>14955776 [Right.]
>>14957690
>>14957721 [Incomprehensible tbqh.]
>>14957932 [I'd try to help this guy but he's talking about numerical stability while inverting matrices over finite fields and that's completely outside of my understanding.]

Physics questions:
>>14946237
>>14953827
>>14953910

Chemistry questions:
>>14957472

/g/ questions:
>>14949171

Stupid questions:
>>14946717
>>14946807
>>14947578
>>14949237
>>14949667
>>14951032
>>14951454
>>14953887

[Anonymous No.14958844]

Let [math] T = \{ \frac{1}{2^n} \mid n \in \mathbb{N} \}[/math].
Is [math]f(x) = \begin{cases}
x & \text{if $x \not\in T$}\\
2x & \text{if $x \in T$}
\end{cases} [/math] a bijection from [math](0,1)[/math] to [math](0,1][/math]?
How do you visualize the function?

[Anonymous No.14958868]

>>14958844
Yeah think of it as playing hilbert's hotel with the powers of 2.

[Anonymous No.14958873]

It is actually true that you seem to use more anime pictures than other academic boards. In g I usually see less, at least.

[Anonymous No.14958877]

Should I drop out of math and try doing something easier? I am not good at solving problems at all

[Anonymous No.14958883]

>>14958837
I was almost going to make a new thread but you beat me to it, anyway here are two stupid questions you missed:
>>14949374
>>14946277

>>14958873
>In g I usually see less, at least.
What?? have you been to /g/? almost half the catalog has anime pics at any moment, even their sticky has an anime girl. /sci/ is actually pretty modest when it comes to animeposting.

[Anonymous No.14958890]

>>14958813
Riemann sums are always infinite. They give the indefinite integral in terms of a whatever variable(s)

To find a definite integral, you plug the endpoint into the sum and subtract out the same sum with the starting point substituted

Then you can group terms and usually simplify it

[Anonymous No.14958894]

>>14958883
>even their sticky has an anime girl
Remilia in the sticky never ever ever.

[Anonymous No.14958896]

Anime pictures are posted by trannies.

[Anonymous No.14958904]

>>14958883
Well, I guess that's right.
I meant more like math.
Sci is a curious place as a whole, but this thread other than using many anime girls is nice.

[Anonymous No.14958911]

>14946237
Feynman is always a good jumping off point for nearly everything. Take a look at Chapter 26 forward.

https://www.feynmanlectures.caltech.edu/I_toc.html

I know it's not a video, but he's preternaturally good at explaining things without dumbing them down

[Anonymous No.14958914]

>>14958911
>>14946237

[Anonymous No.14958919]

>>14958904
>other than using many anime girls
Shut up and get out of my thread.

[Anonymous No.14958933]

>>14953161
Try https://www.youtube.com/watch?v=j5cj_4Mk9_M&list=PLZzHxk_TPOStgPtqRZ6KzmkUQBQ8TSWVX&index=8
>>14946807
Looks like tapeworms to me, google "tapeworms in a jar" and you'll get similar pictures.
>>14953887
Yes.
>>14949667
Maidistan, obviously.
>>14958896
I post anime but i'm not a tranny, therefore it is not true that for all x such that if x is an anime poster then x is also a tranny.
>>14955647
Eh, these conditions are simply to make sure you don't have division by zero when simplifying the expression.
[eqn] \left(\frac{2b}{a}\right) \bigg/ \left(\frac{b^{3}-2ab^{2}}{4a^{3}-2a^{2}b}\right)\\=\left(\frac{2b}{a}\right) \bigg/ \left(\frac{b^{2}(b-2a)}{2a^{2}(2a-b)}\right)\\=\left(\frac{2b}{a}\right) \bigg/ \left(\frac{-b^{2}}{2a^{2}}\right)\\=\left(\frac{2b}{a}\right)\left(\frac{-2a^{2}}{b^{2}}\right)\\=-4\frac{a}{b} [/eqn]

[Anonymous No.14958949]

>>14957472
HCl doesn't react with chlorine, and that's not what the tabs actually contain. It has a complex chemical that donated chlorine easily, and the acidic conditions are liberating it.

Moistutr hydrolyzes it too (obviously or they wouldn't work)

I would put dry baking soda on it to both neutralize it and dry it out, but you have to make sure it's well ventilated first and foremost. Chlorine gas will kill you

[Anonymous No.14958981]

>>14958877
yes

[Anonymous No.14959009]

I have a test in 2 hours and I only know how to use le'hospital rule for basic bitch problems

I don't know anything about arc tan,arc cos, etc
I don/t know anything about Having multiple variables in the problem and I'm only vaguely familir with how to deal with trig functions in general. Please help

[Anonymous No.14959013]

>>14959009

[Anonymous No.14959022]

>>14959013

[Anonymous No.14959160]

Just here to say shout out to all the /sci/ anime posters tirelessly answering our stupid questions around the clock. I'm sure you've gotten countless numbers of us through uni!

[Anonymous No.14959227]

>>14959013
>>14959013
>>14959022
Feeding you a spoonful
>I don't know anything about arc tan,arc cos, etc
https://en.wikipedia.org/wiki/Differentiation_of_trigonometric_functions

>(a)
[eqn] \lim_{x\rightarrow0}\frac{x}{\tan^{-1}3x}=\lim_{x\rightarrow0}\frac{\frac{d}{dx}\left(x\right)}{\frac{d}{dx}\left(\tan^{-1}3x\right)}=\lim_{x\rightarrow0}\frac{1}{\frac{3}{\tan^{2}(\tan^{-1}(3x))+1}}=\lim_{x\rightarrow0}\frac{1}{\frac{3}{9x^{2}+1}}=\lim_{x\rightarrow0}\frac{9x^{2}+1}{3}=\frac{1}{3} [/eqn]

>(b)
Literally the same example from wikipedia but multiplied by 3, so the answer should be 3/2
https://en.wikipedia.org/wiki/L%27H%C3%B4pital%27s_rule#Other_indeterminate_forms

>(c)
[eqn] \lim_{x\rightarrow0}\frac{\cos mx-\cos nx}{x^{2}}=\lim_{x\rightarrow0}\frac{-m\sin mx+n\sin nx}{2x}=\lim_{x\rightarrow0}\frac{-m^{2}\cos mx+n^{2}\cos nx}{2}=\frac{-m^{2}+n^{2}}{2} [/eqn]

>(d)
[eqn] \text{Let }L=\lim_{x\rightarrow\infty}\left(1+\frac{a}{x}\right)^{bx}\\\ln L=\ln\left[\lim_{x\rightarrow\infty}\left(1+\frac{a}{x}\right)^{bx}\right]=\lim_{x\rightarrow\infty}\ln\left[\left(1+\frac{a}{x}\right)^{bx}\right]=\lim_{x\rightarrow\infty}bx\ln\left(1+\frac{a}{x}\right)=\lim_{x\rightarrow\infty}b\frac{\ln\left(1+\frac{a}{x}\right)}{x^{-1}}=\lim_{x\rightarrow\infty}b\frac{-\left(1+\frac{a}{x}\right)^{-1}ax^{-2}}{-x^{-2}}=\lim_{x\rightarrow\infty}b\left(1+\frac{a}{x}\right)^{-1}a=ab\\\Rightarrow\lim_{x\rightarrow\infty}\left(1+\frac{a}{x}\right)^{bx}=L=e^{\ln L}=e^{ab} [/eqn]

[Anonymous No.14959251]

>>14959227
>d
[math]\displaystyle \lim_{x \to \infty} \left( 1 + \dfrac{a}{x} \right) ^{bx} = \lim_{x \to \infty} \left( \left( 1 + \dfrac{a}{x} \right)^x \right) ^b =\left( \lim_{x \to \infty} \left( 1 + \dfrac{a}{x} \right)^x \right) ^b = e^{ab}[/math]
Because [math]f(x) = x^b[/math] is continuous.

[Anonymous No.14959374]

Can I get a bit of help?
Let [math]f:R\rightarrow S[/math] be a homomorphism of rings. Let M be a right S-module and N a left S-module, clearly M and N can also be considered as the respective R-modules through f. I have to show that f induces a well-defined [math]\mathbb{Z}[/math]-epimorphism from [math]M\otimes_R N[/math] onto [math]M\otimes_S N[/math].
Basic idea I have: there is a unique [math]\mathbb{Z}[/math]-morphism g such that the diagram in the picture commutes. It seems reasonable that g is defined by [math]m\otimes_R n\mapsto m\otimes_S n[/math] and that if [math]m\otimes_S n\in M\otimes_S N[/math], the corresponding element
[math]m\otimes_R n[/math] is in [math]M\otimes_R N[/math], motivating that g is epi.
I don't really know how to prove the things I am expecting though, and I am doubting my expectations a little, because I could just as easily flip the g arrow and make the same "argument" to show there is an epi in the reverse direction, which I don't think is true in general.

[Anonymous No.14959420]

>>14959374
Use the universal property of tensor products for bilinear maps

[Anonymous No.14959625]

>>14959227
Hey I just took the test and he didn't any of those

He just had the basic hopital questions

I do have two questions though

is the derivative of sin(7x) different than sin7x

and
can someone do this for me

I did it on the test and I think I got it right but I finished the test first in the class which makes me think I got it wrong

Did I really just need to dinf the critical points then local min,max and then take the critical point and plug it in to get the y value that is the turning point
and then take the derivative again f'' and then do basically the same thing with the number ling and plugging in values close to x to find the concavity it all seemed too easy

[Anonymous No.14959725]

I'm working out of Spivak's Calculus right now and I've kinda hit a brick wall with one of the logical steps I've been using to help solve one of the problems. That is that the square root of a nonnegative number maps to simply the positive square root and we ignore the negative square root. For the exercises I'm working through, should I assume that he means I am allowed to assume that [math]0 \leq x \implies 0 \leq \sqrt{x}[/math]? It's throwing me for a loop simply because math teachers have beaten it in my head that [math]\sqrt{x^2} = x[/math] or [math] \sqrt{x}=-x[/math]

[Anonymous No.14959747]

>>14959725
The only thing that is true is that
[math] \sqrt{x^{2}} = |x| [/math]

Therefore,
[math] x \geq 0 \rightarrow \sqrt{x^{2}} = x [/math]
[math] x < 0 \rightarrow \sqrt{x^{2}} = -x [/math]

[Anonymous No.14960231]

>>14949063
This will not answer your post directly. I just hope it might give you some ideas.
Anyway, there's a category equivalence between affine schemes and commutative rings. More generally, if [math]Y[/math] is an affine scheme, then for any scheme [math]X[/math], there's an injection
[math]\text{Hom}(X, Y)\rightarrow\text{Hom}(\Gamma(Y), \Gamma(X))[/math] .
As a consequence, every scheme is naturally a [math]\mathbb{Z}[/math]-scheme but if I remember well, the map above isn't an equivalence.
When I took a class on alggeo I was also wondering about this functor for non-commutative rings: can you extend the [math]\text{Spec}[/math] functor to non-commutative rings? The answer is essentially no: https://arxiv.org/pdf/1101.2239.pdf

[Anonymous No.14960285]

>>14959374
I wanted to practice some TeX in case you haven't figured it out with the help of the other anon.
https://a.uguu.se/CmYMKVXS.pdf

[Anonymous No.14960328]

>>14960285
You can post PDFs on 4chan. It bypasses the cp filter.

[Anonymous No.14960400]

I have an exam this late evening (6pm), how do I make sure I'm in my best conditions by then? I think I'm not going to study anything today, just blandly read the textbook, and then have a good lunch

[Anonymous No.14960485]

>>14960285
okay thanks, but now what is stopping us from using the same argument for the commutative diagram in pic related to obtain an epi [math]M\otimes_S N \rightarrow M\otimes_R N[/math]?

[Anonymous No.14960489]

>>14959625
Sin 7x is the same thing as sin(7x), just like ab is the same as a(b), obv times in the latter case. Things like that should always have the most obvious interpretation, or it should be written better

The derivative is 7 cos 7x by the chain rule

[Anonymous No.14960497]

>>14959625
I have no idea what you're trying to say in the second half

If you take the first derivative and solve for where it equals 0, though pointsnor are all potential local minima or maxima (or just saddle points)

If you set the second derivative equal to 0, you get the "critical points," where concavity potentially changes. The 2nd derivative of some point that doesn't equal zero tells you if it's "concave up" or "concave down," which isn't terribly descriptive, you just have to remember what those look like

[Anonymous No.14960498]

>>14958877
No, get better at it

[Anonymous No.14960507]

>>14959625

If the first derivative is the slope, the 2nd derivative tells you how it's changing, so if it's positive then it's getting steeper and steeper like the side of a right side up bowl.

It's not always that intuitive with parabolic or substituted functions where the change isn't along the y axis in a neat way

[Anonymous No.14960612]

>>14960483
>Are axioms just a thing you make up?
Yes, axioms are statements which we assert without proving. You can't prove an axiom, because that would require other axioms, and to prove those other axioms would require more axioms, can you see how this could get out of hand?

You can't really prove an axiom because you can't prove something from nothing, you need some starting statement.
For example, you need Y to prove X, but to prove Y you need Z, and to prove Z you need W, etc. at some point in this logical chain you must have a statement which you can't prove, otherwise you run the risk of infinite regression (see picrel for what infinite regression looks like) or circular reasoning (example of circular reasoning: "X is true because Y is true and Y is true because X is true").

>Also "Axiom Schema" is a hard concept but I think I will understand it by reading more.
Axiom Schema is a basically many axioms put together, its actually infinitely many axioms, one for each property P.

[Anonymous No.14960678]

>>14960612
>You can't prove an axiom, because that would require other axioms, and to prove those other axioms would require more axioms, can you see how this could get out of hand?
Thank you for telling me. This problem with recursion is interesting. It also seems like axiom could be malformed in a way that makes problems or paradoxes. Is there an easy way to tell if axiom is nonsense?

>This axiom is false

Seems like nonsense but it might be nonsense because my comprehension is low currently.

I am going to keep reading this book until it completes. I do not have a lot of read time today because I have to do a lot of boring tasks unrelated to books or computers, but should have a big amount on the weekend.

[Anonymous No.14960718]

>>14960612
>>14960678
>You can't prove an axiom, because that would require other axioms, and to prove those other axioms would require more axioms, can you see how this could get out of hand?
Not completely correct. Real Analysis was all about minimising axioms in Calculus. For decades, completeness of the reals was an axiom, but now it is a theorem of a more fundamental and smaller system of axioms.
There are also theorems that are equivalent to an axiom. For example, well ordering principle of the naturals is equivalent to induction. Either one can be treated as an axiom, and the other will follow as a theorem.
>This axiom is false
A single axiom cannot be false, but a system of axioms can contradict each other and hence, be inconsistent. ZFC which is the current system of axioms we follow for most math, is unprovable to be consistent, using only its own axioms.

[Anonymous No.14960748]

>>14960718
>is unprovable to be consistent
Thank you for telling me fren. What happens if axioms are inconsistent or contradict?

[Anonymous No.14960749]

what's the general solution to nonhomogeneous second order differential equation, ie
Az'' + Bz' + Cz = constant > 0
and no this unironically isn't homework

[Anonymous No.14960755]

>>14960718
>but now it is a theorem of a more fundamental and smaller system of axioms.
My point was that if you tried to prove every axiom then you would end up in infinite regression or circular reasoning.
>>14960678
>It also seems like axiom could be malformed in a way that makes problems or paradoxes
Yes, a system of axioms can lead to contradictions, such a system would be called an inconsistent system. Example of such a system would be "Axiom 1: X is true, Axiom 2: X is false".
In an inconsistent system every statement is provable by the principle of explosion, so every statement is true in an inconsistent system.
https://en.wikipedia.org/wiki/Principle_of_explosion
>Is there an easy way to tell if axiom is nonsense?
Gödel proved that a system cannot prove its own consistency.
That means if you have a collection of axioms then you can't prove from those axioms that they make sense, a system of axioms cannot prove its own consistency. However, a larger system of axioms can prove the consistency of a smaller one, for example, ZFC can prove the consistency of Peano arithmetic but Peano arithmetic cannot prove its own consistency.

Generally speaking, most axioms are made with intuition, axioms are supposed to make intuitive sense so that we can use them to prove less intuitive statements as theorems.

[Anonymous No.14960780]

>>14960748
>What happens if axioms are inconsistent or contradict?
That's what happens. They contradict each other. So it's useless. What's the point of proving any theorem in a system, when it is entirely possible there may be a proof that disproves it, in the same system?

[Anonymous No.14960783]

I really have to do something about my memory.
Anyone tried anything from this list?
Would they make any difference in clearing the fog and make me remember easier formulas and solving problems?
https://www.hollandandbarrett.com/shop/vitamins-supplements/condition/brain-memory-support/

[Anonymous No.14960787]

Why is it that if A is a commutative ring with 1, f in A that
A[X]/(1-fX) = 0 it follows that f is nilpotent?

The direction that if f is nilpotent the qutienring is the zero ring is easy, but this way around seems hard.

[Anonymous No.14960798]

>>14960780
>They contradict each other. So it's useless.
It's even worse than that, if a single contradiction exists in a system then every statement (along with its negation) is trivially true by the principle of explosion. There is no point in proving or disproving anything because everything is both true and false.

[Anonymous No.14960812]

>>14960718
Some things don't need to be proven

[Anonymous No.14960817]

>>14960489
fuck I did the chain rule on one but not the other
>>14960497
>>14960507
I think I got it right then but fuck I'm nervous there were only three(6) questions on the test

[Anonymous No.14960818]

>>14960787
Since [math]A[X] / (1 - fX) = 0[/math] you can find some [math]p = \sum_{k = 0}^n a_k X^k[/math] such that [math]f = p (1 - fX) = \sum_{k = 0}^n a_k X^k (1 - fX)[/math]
Rewrite that and compare graded components on both sides.

[Anonymous No.14960819]

>get blind drunk in college slut bar
Reject females, stumble home to pass out
>puking hung over up next morning
Irresistible urge to beat off repeatedly

Is there a scientific explanation for this phenomenon?

[Anonymous No.14960821]

>>14960749
You lads are really bad at googling this stuff.
https://www2.math.upenn.edu/~moose/240S2013/slides8-05.pdf

[Anonymous No.14960822]

>>14960749
https://www.wolframalpha.com/input?i=az%27%27+%2B+bz%27+%2B+cz+%3D+d

[Anonymous No.14960848]

>>14958813
I try every day to make one idea about cooling off the planet. Yesterday the idea was use C02 to make soda. I decide put the idea here instead of make a thread.

>space gun and moon dumpster
We use machines to get C02 out of the water or out of the air. Whichever is more efficient. Then we compact it into a munition and fire it out of a giant space gun.

Gun's purpose is to fire projectiles that hit the moon. This would let us test space shooting and also get rid of carbon dioxide by putting it on the moon. If a munition misses that doesn't matter because it just goes away forever in space.

Moon is a big unimportant dumpster. All it has to do is float around and make tides. It doesn't matter if we shoot the moon with our space gun and the technologies developed can later be adapted to deliver things to other planets via shooting them from a space gun. Also we could put hydrogen bombs in the space gun in case we need to show bad aliens what hydrogen bombs are for.

>alternate idea: space vent
Machine isn't connected to a gun. It is connected to a big vent that dumps C02 in space. Vent is a big tube going from earth to space. Machines have to be able to push C02 hard enough to make it go to space.

Space vents could also be attached to machines that make a lot of C02 so they can just vent to space directly.

[Anonymous No.14960859]

How can you statistically increase your chances to win the Powerball Lottery? Random number generator a good idea? Anything I come up with would be a pattern I’d assume

[Anonymous No.14960963]

Why isn't Compton effect possible with visible light? I mean, I understand that apparently photons having a wavelength over ~400nm aren't energetic enought to scatter the free electron, but I would like to mathematically show it.
I tried using energy and momentum conservation, so I have that:
[eqn]\frac{hc}{\lambda_i}+m_e c^2=\frac{hc}{\lambda_f}+\sqrt{(m_e c)^2+c^4 {( \frac{h}{\lambda_i} - \frac{h}{\lambda_f} )}^2}
[/eqn]
I would like to show that right side from the equation is greater than the left side when [math]\lambda_i>380\ nm[/math], but I don't really know how to follow from here. I tried using [math]\lambda_i - \lambda_f = \lambda_c (1-\cos(\theta))[/math], but I didn't arrive at any result.

[Anonymous No.14960996]

>>14960963
What are the constants in the equation?

[Anonymous No.14961000]

>>14960848
Just take an asteroid off another planet and make however many moons we need, if we get enough of them we can just block howver much sun we want

[Anonymous No.14961009]

What is the simplest factorial for an elliptic curve?

[Anonymous No.14961026]

>>14960963
> Why isn't Compton effect possible with visible light?
You can't apply that formula to regimes it does not apply to. Compton scattering requires that the energy of the photon be much higher than the electron binding energy of the atom. So for example the binding energy of hydrogen is 13.6eV which equates to a wavelength of ~1 nanometers and hence much shorter than visible light (this is in the x-ray range)

[Anonymous No.14961027]

>>14960996
h=planck constant
m_e=mass of an electron
c=velocity of light
lambda_c=compton's lambda

[Anonymous No.14961063]

Need some help with Set theory.

1) Prove the set of strictly increasing functions is equinumerous with the powerset of the natural numbers.

2) Prove the set of strictly decreasing functions is equinumerous with the powerset of the natural numbers.

I'm not too sure how to go about proving these. There has to exist a bijection, but I can't think of one.

[Anonymous No.14961080]

>>14960678
Which Jech are you using? If it is picrel, it is not for you.

[Anonymous No.14961096]

>>14961063
>strictly increasing functions
from where to where?

[Anonymous No.14961098]

>>14961063
Functions of what? i'll assume your functions are from N to N.

I have a general intuitive idea of how this should be done but i don't know how to put it in formal terms.
Basically you are trying to find a bijective function which maps subsets of N onto strictly increasing functions.
To make matters simpler its easier to represent an increasing function from N to N as a sequence of natural numbers, the simplest such function would then be <0, 1, 2, 3, 4, ...>, this sequence should be mapped to the empty set
For every subset of N you construct an increasing function by making gaps in the sequence, for example the subset {1} would be mapped to <0, 2, 3, 4, 5, ...>, the subset {3, 5} would be mapped to <0, 4, 10, 11, 12, ...>, i think it's better if you draw a number line and see that the size of the gaps in the sequence corresponds to numbers in the subset of N.

I'll try to think of a way to formalize this.

[Anonymous No.14961101]

>>14961063
Strictly increasing [math]f: \mathbb{R} \to \mathbb{R}[/math]?
You can force out a proof using https://math.stackexchange.com/questions/84870/how-to-show-that-a-set-of-discontinuous-points-of-an-increasing-function-is-at-m and the fact that continuous functions are entirely determined by their restriction to [math]\mathbb{Q}[/math], I think.

Brain is failing to come up with anything better, unfortunately.

[Anonymous No.14961113]

>>14961101
The set of functions from R to R have a higher cardinality than |R| = |P(N)| so it's not possible to find a bijection, i'm pretty sure he meant functions from N to N or some other countable set.

[Anonymous No.14961124]

>>14961113
>The set of functions from R to R have a higher cardinality than |R| = |P(N)| so it's not possible to find a bijection
Not all reals to reals functions are strictly increasing so your argument doesn't mean anything.
>i'm pretty sure he meant functions from N to N or some other countable set.
He cannot possibly have meant naturals to naturals because there are no strictly decreasing naturals to naturals functions.

[Anonymous No.14961152]

>>14961096
>>14961098
>>14961101
for strictly increasing:
Functions with domain N and range N such that f(n) < f(m) for 0 <= n < m

[Anonymous No.14961175]

>>14961152
>the spaces are different on 1 and 2 but he doesn't mention the space for either
You faggots are ABSURDLY dimwitted sometimes.

Map any strictly increasing function to its image (the subset of the naturals.)

[Anonymous No.14961195]

>>14961175
Wait, this is for monotonic increasing functions.
Map [math]f(n) \to f(n) - n[/math] to go from strictly increasing to monotonic increasing and then take the image.

[Anonymous No.14961201]

what is a "proof-theoretic ordinal"?

[Anonymous No.14961208]

>>14961195
I sort of understand what you're saying but am a little confused. So I define a function g(n) such that g(n) = f(n) - n. I can understand why this creates a bijection, but I have trouble proving it. Also why do you have to do f(n) - n?

[Anonymous No.14961219]

>>14961152
No such function exists.

[Anonymous No.14961232]

>>14961175
This will produce an injection but not a surjection, the finite subsets of N are unreachable this way.

>>14961195
This is good but it suffers a slight problem, and that is the empty set is still unreachable because the image will always be non-empty, so it's technically still not a bijection but very close to being one.

I think i found an injection from the powerset of N to the set of all strictly increasing functions:
[eqn] \text{Let $S\subseteq\mathbb{N}$, Then consider $A : S \mapsto f$ Where $f$ is a strictly increasing bijection from $\mathbb{N}$ to $\mathbb{N}\backslash2S$, where $2S=\{2x\mid x\in S\}$ Then $A$ is an injection because it can be proven that there exists only one such $f$ for each $S$.} [/eqn]
I'm not sure if i can actually prove the existence and uniqueness for f. I will try and see.

If both of these are injections then you can use the Cantor-Shroder-Bernstein theorem to prove the existence of a bijection.

[Anonymous No.14961329]

I have a very dumb problem.

There is a person making an interesting Computer Language and invited me to make contributions and use their board (not on 4chan) and never get banned for maids.

This person is very nice to me and I want to contribute. However, this person might be Russian (judging by where domain was registered) and I don't want the US government to get angry at me or cause me problems.

I do not care who is foreign, or about foreign wars. I deal with foreign people when they come here and they all obey laws and are nice but otherwise I don't think in a global way. I think about what is happening on my street not what is happening on a different continent I will never go to.

This style of local thinking suits me. I don't feel like I owe the world a strong opinion about a foreign war. I didn't care about Saudi Arabia fighting Yemen. I don't care about political problems in Sri Lanka. I don't care about Israel doing mean things to Palestine. That is the other side of the planet and not my concern. I will never go to these places, so to me they might as well be fictional. I just don't want to get in trouble for playing with my computer and talking on the internet.

>question
I don't know how laws work because I never had to care about laws before. Can helping with a Computer Language get me in trouble if the person I help is a Russian?

>>14961101
I really like this maid.

America has a lot of secret internet police and posting on 4Chan is like posting on the CIA's front door. So here I am knocking on the door. Please tell me will I get in trouble if I help with Eremias?

>>14961080
Book is called Introduction to Set Theory.

[Anonymous No.14961344]

>>14958813
Zlib is down OP
see >>14961221 and spread the word

[Anonymous No.14961349]

>>14961026
>You can't apply that formula to regimes it does not apply to.
Why? Is just the conservation of energy and momentum. I mean, if I would like to show that the photoelectric effect doesn't work for a free electron I would be able to use this conservation to end up with an absurd.

[Anonymous No.14961360]

What do I need to study to understand this proof?

[Anonymous No.14961366]

>>14961360
Logic

[Anonymous No.14961385]

>>14961329
>I don't know how laws work because I never had to care about laws before. Can helping with a Computer Language get me in trouble if the person I help is a Russian?
Yes. Helping Russian people with anything is a federal offense. Since we don't have geoflags on /sci/, even answering questions in /sqt/ is a legal gamble

[Anonymous No.14961401]

There's a test with 12 questions, each with 4 choices, a correct one is 1 point and a wrong or blank one is 0 point. The minimum to pass is 7. What's the likelihood that you get at least 7 if you're sure about 4 answers and for the other you're 1/3 sure that you got it right?

[Anonymous No.14961411]

>>14961401
binomial distribution

[Anonymous No.14961421]

>>14961411
man the test I'm talking about was an actual test that I just took about linear algebra and it went so bad I'm literally calculating the rough chances I get the minimum to pass can't you do the math for me

[Anonymous No.14961427]

>>14961385
What if I just make my own fork? He is making Python much nicer and I think that is an interesting task because the worst part of any Python program is the Python code itself. Python grammar is poorly designed because of a manifesto somebody wrote. "Pythonic" might as well just be a polite way to say "awful on purpose".

Python feels like a practical joke that accidentally took off.

[Anonymous No.14961462]

She was in my dream
Except instead of being low risk taking she was the opposite
She went in reverse on her car over a clift and i jumped out. She then proceeded to swing from vines and make her way down safely then kicked a soccerball into a goal. Basically called me a pussy. Ans challenged me to do the same. And all i did was grab birds out of the air and crush them in my hands
Amygdala increases fear therefore less risk taking
Less risk taking is associated with things like autism due to how it impacts the amygdala
I think the dream represents something deep about the source of my behavior

[Anonymous No.14961484]

>>14961401
>>14961421
If you're 100% certain about 4 of them then you only need 3 more, the chance that you get at least 3 questions right from the 8 remaining (assuming a probability of 1/3 for getting a question right) is
[eqn] \sum_{k=3}^{8}\binom{8}{k} \left( \frac{1}{3} \right)^k \left( \frac{2}{3} \right)^{8-k} \approx 0.5318 = 53.18\% [/eqn]

Good luck!

[Anonymous No.14961490]

>>14961349
> It is just the conservation of energy and momentum
Yes it is *but only* if there is enough energy to knock the electron out of its shell. At the cut-off of lower energies the electron is stuck because of quantum mechanics so the photon will simply experience an elastic collision and no scattering will occur; and hence the formula doesn't apply.

[Anonymous No.14961491]

Will /sqt/ watch our match with /vr/ today?
>>14961488

[Anonymous No.14961505]

Given [math] B=\bigl(\begin{smallmatrix}
1 & 2 \\
3 & 4
\end{smallmatrix}\bigr) [/math], and the application L defined as: L(A)=BA ([math]L: Mat\mathbb{R}(2\times 2)\rightarrow Mat\mathbb{R}(2\times 2)[/math])

is L both linear and invertible?

[Anonymous No.14961513]

whatever happened to the deferoxamine guy?

[Anonymous No.14961517]

>>14961505
Yes.

[Anonymous No.14961519]

>>14961491
Why would I watch a 4chan-themed digital game of football?

[Anonymous No.14961522]

I think the simplest way to describe autistic behavior vs psychopathic would be high vs low risk taking behavior
I think women are already programmed to be attracted to high risk taking behavior. Which is why they see me and my appearance and assume i would do that
My amygdala needs to get fucked
Low risk taking behavior is k selection and why my life is more sustainable long term

/sqt/ what do you think about this

Subconciously ive always been someone with low risk taking behavior trying to display someone who has high risk taking. I.e dont break rules that much and dont do things i deem as stupid. My mother is highly moral highly k selected and always cemented this into my mind through examples and her opinions
But i associate with people who do high risk taking shit and i pretend to be that way
So if i wanna be a psychopath i cant just diddle in the mud i need to take risks
That starts with d serine
And maybe ill take ssris
Maybe not always actually
I think i was socialized into low risk taking to ant extent
Fuckin christ my mother truly fucked my life

[Anonymous No.14961526]

>>14961484
thanks :)
i actually like linear algebra (first year uni just to be clear, i dont know if its also taught in hs in the US) and I felt like i knew the concepts but I got really bad anxiety during the test + apparently i didnt really know the concepts like i thought i did.

is there general consensus on what's the best and most complete LinAlg book? I picked up "linear algebra done right" from the library and skimmed through it but it felt like it was too oversimplified, too concise (at the expense of clarity) and didn't give enough practical examples. I dont know how that book is viewed here on sci.

[Anonymous No.14961528]

>>14961519
Those are some good remis

[Anonymous No.14961553]

Why are Americans like that? https://www.youtube.com/watch?v=u2j578jTBCY

[Anonymous No.14961592]

>>14960818
I hate coming up with "concrete" constructions, reminding me of functional analysis.
How can I use this equivalence
A[X]/(1-fX) = 0 iff f nilpotent
to shot that the intersection of all prime ideals is subset of the nilradical?
I would like to avoid localization or going the zorn's lemma route, but have no idea how the equivalence itself helps there.

[Anonymous No.14961593]

>>14961427
That does sound interesting, unfortunately it is currently illegal to collaborate with Russians on tech projects, or even to fork existing projects from them. Hopefully the supreme court will overturn this soon

[Anonymous No.14961646]

>>14961593
>it is currently illegal to collaborate with Russians on tech projects, or even to fork existing projects from them
Is this real or are you trolling? I'm not an american but this sounds very retarded.

[Anonymous No.14961798]

Who can come up with some more info on this guy: https://en.wikipedia.org/wiki/Thomas_Weddle

I wanna learn about Thomas Weddle

[Anonymous No.14961813]

I was thinking more about axiom. In software there is an idea called unit test. If axiom can be written as a unit test, and such a test can run all test cases for the axiom, then was some kind of proof by exhaustion reached for the axiom?

>>14961593
Thank you for telling me. I don't want to get caused problems. I will disregard Eremias until I am sure it can't give me problems.

[Anonymous No.14961989]

>>14961427
> Python grammar is poorly designed
I have no idea what gave you that idea. As far as main-stream coding languages go Python is one of the best designed. Compare it to something like PHP and the difference is crystal clear.

[Anonymous No.14961997]

>>14961813
> If axiom can be written as a unit test, and such a test can run all test cases for the axiom, then was some kind of proof by exhaustion reached for the axiom?
That's all drivel and nonsense. A unit test is just code. You can't prove an axiom with code. In fact you can't prove an axiom by its very definition.

[Anonymous No.14962032]

do you have to do epsilon delta proofs for the continuity of functions past the first semester? What are the most complicated functions you have to proof/disproof continuity of using this method

[Anonymous No.14962051]

>>14961989
PHP is awful, but Python made bad decisions on purpose, like having significant whitespace. PHP is at least awful on accident and doesn't try to call bad design "PHPic".

>>14961997
>You can't prove an axiom with code.
Why not? In the Jech book it has something called Axiom of Existence which says that there exists an empty set. If I make a code implementation of Set, and I make an empty one, and a unit test shows it to be empty, then didn't I just prove the axiom by making the thing it says exists, actually exist and conform to the description?

[Anonymous No.14962072]

>>14962051
> but Python made bad decisions on purpose
that's just your opinion, not a fact. it hasn't done anything to dent the popularity or usefulness of Python.

> then didn't I just prove the axiom
no. all you've done is create a test for some code. it hasn't proven anything fundamental.

[Anonymous No.14962092]

>>14962072
>that's just your opinion, not a fact. it hasn't done anything to dent the popularity or usefulness of Python.
Python isn't popular because of it's awful grammar. Python is popular because it gives you access to a big amount of packages containing science programs written in better languages than Python.

All the usefulness comes from the packages, not the awful grammar. A good Python program is a Python program that spends as much of it's time as possible in packages which were probably written in C.

Python is more like bash in this respect than an actual language. This is why Eremias looked nice to me. You can still use the packages but better grammar design decisions were made.

>no. all you've done is create a test for some code. it hasn't proven anything fundamental.
And what is that code? An implementation of the math idea with a test demonstrating that the implementation works. The axiom stops being an abstract drfinition and starts being a thing you can concrete interact with on a computer.

I think implementing something is a good demonstration that it exists.

[Anonymous No.14962115]

>>14961592
>How can I use this equivalence A[X]/(1-fX) = 0 iff f nilpotent to shot that the intersection of all prime ideals is subset of the nilradical?
No idea. Presumably you show that if [math]A[X] / (1 - fX) \neq 0[/math] then there's a prime ideal that doesn't contain [math]f[/math]. That seems to me to be the correct direction for the construction.
>I would like to avoid localization or going the zorn's lemma route
In my experience, if one proof requires choice all of them do.
>>14962032
You usually use the properties, i.e. being closed under sums and stuff.
>>14961989
In spite of the $ all of the place and the general lack of quality of the standard library I personally prefer PHP to Python.

[Anonymous No.14962343]

After life probability with our current knowledge is 50%
Same goes to prediction if that life is either good, bad or neutral. Let's assume that neutral is included as good outcome.
That means that i got 33,3% chance of harem issekai when i die right?

[Anonymous No.14962518]

>>14961813
>>14962051
Making an implementation of the axioms is called making a model. For example, you can model rational numbers as pairs of integers and then prove axioms about rational numbers using axioms about integers. Proving a set of axioms has a model is useful because it means your axioms aren't inconsistent garbage (provided the axioms you use to build the model aren't inconsistent garbage themselves).

Testing all possible cases can be a valid proof, but many theorems have infinitely many cases. To prove such theorems, you need a type checker, not unit tests.

[Anonymous No.14962547]

>>14961593
Are you all actually for real? Just use opsec and take your life into your own hands damnit!

[Anonymous No.14962549]

Is this the right place to ask a research question about quadratic forms and hyperbolic spaces?
>>14961491
Way too early for me nowadays, I always liked /sci/ though.

[Anonymous No.14962606]

What is the significance of this if A1 and A2 are non-empty?
[math] \{A_{1},A_{2}\} - \{\emptyset\} [/math]

[Anonymous No.14962681]

Why the fuck is Einstein notation a thing? Are physicists real?

[Anonymous No.14962755]

>>14962681
>Why the fuck is Einstein notation a thing?
It's shorter
>Are physicists real?
No

[Anonymous No.14962757]

>>14962681
I hated it at first but it's actually good

[Anonymous No.14962839]

>>14962681
>Why the fuck is Einstein notation a thing?
Einstein notation turns expressions that don't make sense (because stuff like [math]a^{\mu}b_{\mu}[/math] doesn't actually have a behavior under coordinate transformations) into expressions that make sense.
It's only goofy if some mathematician tries to sell you the version where you sum over any two repeated indexes instead of lower and upper.

[Anonymous No.14962841]

>>14962681
Try writing out the all the equations involved in GR in-full, including their summations and ask yourself that again.

[Anonymous No.14962949]

>>14962841

[Anonymous No.14963011]

How can I count the size of the similarity class (of matrices in particular)? By dividing the order of the group by the order of centralizer of representative of this class or are there any other possibilities?
Group, for example, is GL(2, k), where k is a field.

[Anonymous No.14963016]

>>14962549
Well...give it a shot. What's the question?

[Anonymous No.14963157]

Is there any method of quickly calculating the square of large polynomials? E.g. [math](3n^4 + 2n^3 + n^2 + 1)^2[/math]. The way I do it right now is to make a table but it still takes me like several minutes to square one such polynomial/

[Anonymous No.14963241]

Why did the number 69 become a sex number?

[Anonymous No.14963242]

>>14962606
If neither are empty then
[math] \{ A_1 , A_2 \} - \{ \emptyset \} = \{ A_1 , A_2 \} [/math]

[Anonymous No.14963290]

>>14963157
If you expand the square of a general polynomial you get the following:
[eqn] \left(c_{0}+c_{1}x+c_{2}x^{2}+\dotsb+c_{n}x^{n}\right)^{2}\\=\left(c_{0}c_{0}\right)+\left(c_{0}c_{1}+c_{1}c_{0}\right)x+\left(c_{0}c_{2}+c_{1}c_{1}+c_{2}c_{0}\right)x^{2}+\dotsb+\left(\sum_{i+j=k}c_{i}c_{j}\right)x^{k}+\dotsb+\left(c_{n}c_{n}\right)x^{2n}\\=\sum_{k=0}^{2n}\left(\sum_{i+j=k}c_{i}c_{j}\right)x^{k} [/eqn]

The second sum might be confusing a bit, it mean that you should take the sum of all coefficient whose degrees sum to k. The example below illustrates this:
For your polynomial you should determine each coefficient separately

[math] c_{0}=(1\cdot1)=1\\c_{1}=(1\cdot1)+(1\cdot1)=2\\c_{2}=(1\cdot2)+(1\cdot1)+(2\cdot1)=5\\c_{3}=(1\cdot3)+(1\cdot2)+(2\cdot1)+(3\cdot1)=10\\c_{4}=(1\cdot3)+(2\cdot2)+(3\cdot1)=10\\c_{5}=(2\cdot3)+(3\cdot2)=12\\c_{6}=(3\cdot3)=9 [/math]

So

[math] \left(1+x+2x^{2}+3x^{3}\right)^{2}=1+2x+5x^{2}+10x^{3}+10x^{4}+12x^{5}+9x^{6} [/math]

[Anonymous No.14963301]

>>14963290
>>14963157
I misread your example, there should be a 0 coefficient there, redoing the calculations:

[math] \left(1+x+2x^{2}+3x^{4}\right)^{2}=\left(1+x+2x^{2}+0x^{3}+3x^{4}\right)^{2} [/math]

[math] c_{0}=(1\cdot1)=1\\c_{1}=(1\cdot1)+(1\cdot1)=2\\c_{2}=(1\cdot2)+(1\cdot1)+(2\cdot1)=5\\c_{3}=(1\cdot0)+(1\cdot2)+(2\cdot1)+(0\cdot1)=4\\c_{4}=(1\cdot3)+(1\cdot0)+(2\cdot2)+(0\cdot1)+(3\cdot1)=10\\c_{5}=(1\cdot3)+(2\cdot0)+(0\cdot2)+(3\cdot1)=6\\c_{6}=(2\cdot3)+(0\cdot0)+(3\cdot2)=12\\c_{7}=(0\cdot3)+(3\cdot0)=0\\c_{8}=(3\cdot3)=9 [/math]

So [math] \left(1+x+2x^{2}+3x^{4}\right)^{2}=1+2x+5x^{2}+4x^{3}+10x^{4}+6x^{5}+12x^{6}+9x^{8} [/math]

[Anonymous No.14963304]

>>14958949
I don't carry baking soda in my truck, but I do have soda ash. Should I just chuck my cart in the pool if I ever have a serious reaction between the acid and chlorine? I know chlorine gas is no joke

[Anonymous No.14963342]

>>14958813
How does the circulatory system of an ant work? Because I saw that it's not a conventional one like mammals and fish have.

[Anonymous No.14963347]

>>14961421
by the way i did pass but with the minimum possible grade (7/12). i dont know if i should be happy (53% of the class got a 6 or less and didnt pass) or not.
this test accounts for 40% of the final grade, the other 60% is determined by another test that I'll take in a few months; my options are to accept this 7/12 and take the second test in a few months or i could not accept it and take a bigger test which will account for 100% of my grade instead. What would you do?

[Anonymous No.14963405]

>>14960821
this covers if the RHS is a function but not just a flat constant
Im not smart
>>14960822
the DE is equal to a constant, not its variable

[Anonymous No.14963416]

>>14963405
let's try that again
https://www.wolframalpha.com/input?i=a%28d%5E2z%29%2F%28dx%5E2%29+%2B+bdz%2Fdx+%2B+cz+%3D+d

[Anonymous No.14963495]

>>14963342
Arthropods (which include insects) have what's known as an open circulation.

All animal cells need oxygen and nutrients, insect cells are no exception.
However, instead of blood being delivered through arteries and returned through veins, all the internal organs (and indeed all cells) of an arthropod are bathed by a fluid known as the hemolymph, the hemolymph is analogous to blood in mammals, it carries nutrients and waste products, insects also have a heart that facilitates convection and movement of the hemolymph so that waste products don't accumulate at a single site and new nutrients are delivered to cells, movement of the muscular system also facilitate movement of the hemolymph.

The circulation is called open because the ends of the vessels are open, in contrast to mammalian circulation which has not openings or holes in the arteries or veins.

Another note is that unlike mammals, the respiratory and circulatory system are separated in insects. The hemolymph does not carry oxygen, instead the respiratory system delivers oxygen directly to tissues and cells (contrast this to mammals where oxygen is delivered by the respiratory system to the circulatory system which then delivers it to tissues)

[Anonymous No.14963575]

What's a good first machine learning/data science book? I know python, currently polishing math skills.

Want to do something hand-on and practical to see if I even care about this topic as much as I was hyped about it half a year ago.

[Anonymous No.14963583]

Is it normal to take a long time to solve questions like these? These questions took me 2 days to solve, but the solutions are very short and simple.

[Anonymous No.14963626]

how would I graph an equation like this:
0 <= x <= n
x * (n - x)

[Anonymous No.14963695]

>>14963157
You can do fast polynomial multiplication with the FFT.
Because, yannow, polynomial multiplication is just convolution.

[Anonymous No.14963722]

>>14963242
ty anon. why would they add it if they explicitly state none are empty, is it just to trick you? also what if one or both were empty?

[Anonymous No.14963725]

>>14963695
vewy good wemi

[Anonymous No.14963755]

>>14963722
[eqn] \text{If $A_1$ is empty, then:$ \\ \{ A_1, A_2 \} - \{ \emptyset \} = \{ \emptyset , A_2 \} - \{ \emptyset \} = \{ A_2 \} \\ $If $A_2$ is empty, then:$ \\ \{ A_1, A_2 \} - \{ \emptyset \} = \{ A_1, \emptyset \} - \{ \emptyset \} = \{ A_1 \} \\ $If both $A_1$ and $A_2$ are empty, then:$ \\ \{ A_1, A_2 \} - \{ \emptyset \} = \{ \emptyset , \emptyset \} - \{ \emptyset \} = \{ \emptyset \} - \{ \emptyset \} = \emptyset \\ $} [/eqn]

[Anonymous No.14963758]

>>14958813
what the fuck is a singularity point? I have everything done besides 7A

[Anonymous No.14963781]

>>14963758
discontinuities of the function

[Anonymous No.14963785]

>>14963781
you know what it would be then? no idea what to do

[Anonymous No.14963798]

>>14963785
[math]f[/math] is not continuous in [math]x=1[/math] and [math]x=-1[/math] since there's a division by zero, those are your singularity points
[math]x=-1[/math] is an infinite discontinuity because there's a vertical asymptote at this point of the graph
[math]x=1[/math] is a removable discontinuity because the limit on both sides is the same ([math]3/2[/math])
read the wikipedia article if you're not familiar with it (https://en.wikipedia.org/wiki/Singularity_(mathematics))

[Anonymous No.14963837]

>>14963798
thank you fren

[Anonymous No.14963855]

>>14963755
ty anon, i'm having a lot of trouble knowing whether something is a member or subset of other sets.

like if x is a set, what this set even is
[math]\{x\} \cup x [/math] and whether x is a member or subset of it

[Anonymous No.14963879]

please help a retard on this one

Let $X$ be a normed space and let $B$ be closed unit ball in $X$. We have map $T_0: B \rightarrow B$ which satisfies Lipschitz condition with some constant $k > 1$. We extend this map to $T_1: 2B \rightarrow B$, where $2B = \{x: \|x\| \leq 2 \}$, in the following way: for $x \in B$ we put $T_1x = T_0x$; for $x \in 2B \ B$ we let $T_1x = (2-\|x\|)T_0(Px)$, where $P$ denotes radial projection. I want to show that $T_1$ satisfies lipschitz condition with constant $2k + 1$ but im stuck.

[Anonymous No.14963892]

>>14963879

Let [math]X[/math] be a normed space and let [math]B[/math] be closed unit ball in [math]X[/math]. We have map [math]T_0: B \rightarrow B[/math] which satisfies Lipschitz condition with some constant [math]k > 1[/math]. We extend this map to [math]T_1: 2B \rightarrow B[/math], where [math]2B = \{x: \|x\| \leq 2 \}[/math], in the following way: for [math]x \in B[/math] we put [math]T_1x = T_0x[/math]; for [math]x \in 2B \ B[/math] we let [math]T_1x = (2-\|x\|)T_0(Px)[/math], where [math]P[/math] denotes radial projection. I want to show that [math]T_1[/math] satisfies lipschitz condition with constant [math]2k + 1[/math] but im stuck.

[Anonymous No.14963896]

Let G be a group of order 55. Let a,b in G be non-identity elements of different orders. Show that a and b generate G

[Anonymous No.14963897]

>>14963855
[math] \{ x \} \cup x [/math] Is basically the set containing the elements of x plus x itself

Example: Let [math] x = \{A,B,C\} [/math] then [math] \{ x \} \cup x = \{ x \} \cup \{A,B,C\} = \{A,B,C, x \} = \{A,B,C, \{A,B,C\} \} [/math]

Another example: Let [math] x = \emptyset [/math] then [math] \{ x \} \cup x = \{ \emptyset \} \cup \emptyset = \{ \emptyset \} [/math]

[math] \{ x \} \cup x [/math] Is commonly used to define the natural numbers in set theory (von Neumann definition), see
>https://en.wikipedia.org/wiki/Set-theoretic_definition_of_natural_numbers
for details

[Anonymous No.14963907]

>>14963897
>>14963855
>and whether x is a member or subset of it
[math] x [/math] is both a member and a subset of [math] \{ x \} \cup x [/math]
That is, [math] x \in \{ x \} \cup x [/math] and [math] x \subseteq \{ x \} \cup x [/math]
Looking at the examples i made above might help you see why that is the case.

[Anonymous No.14963915]

>>14963897
>>14963907
tyvm anon

going by your example, does that mean something like {x} - {{x}} is just {x} because {x} is not in x?

[Anonymous No.14963932]

>>14963915
>does that mean something like {x} - {{x}} is just {x} because {x} is not in x?
Yes, assuming x is a well-founded set (that is, x does not contain itself or [math] x \neq {x} [/math]) which is the case in ZFC which has the axiom of foundation
https://en.wikipedia.org/wiki/Axiom_of_regularity

[Anonymous No.14963934]

Is the set of all automorphisms of Z16 isomorphic to Z8?

[Anonymous No.14963936]

>>14963896
https://math.stackexchange.com/a/1502364

[Anonymous No.14963937]

>>14963932
I forgot to escape the curly braces
>[math] x \neq {x} [/math]
I meant to write [math] x \neq \{x\} [/math]

[Anonymous No.14963947]

I'm having trouble proving that if x in a union of A and B, then x is in the union of collection of sets {A,B}

i think i can prove the other way where you start with the collection and prove its in AUB but i dont know how to turn AUB into the collection by starting with suppose x is in AUB.

[math]x \in A \cup B \Rightarrow x \in \bigcup_{X \in \{A,B\}} X [/math] I know i probably have to use [math] (\exists X)(X \in \{A,B\} \wedge x \in X) [/math] but i dont know how to get this from supposing [math]x \in A \cup B [/math].

I was thinking about a proof by contradiction or indirect proof but then both of those would screw up the collection of sets

[Anonymous No.14963948]

>>14963932
>>14963937
tyvm anon i really appreciate your help

[Anonymous No.14963950]

>>14963934
https://math.stackexchange.com/q/3013033
prove that the automorphisms are all of this form and then compute their orders in the automorphism group
result is Z4xZ2

[Anonymous No.14963959]

>>14963947
>>14963947
can i say do it this way?

Suppose [math] x \in A. [/math] Then by definition of {A}, [math]A \in \{A\}[/math]. So then [math](\exists X)(x \in X \wedge X \in \{A\})[/math].

[Anonymous No.14963974]

s-so whats the essence of mathematics? sets? categories? interaction nets?

[Anonymous No.14964025]

>>14963974
Successions
1 = succ(0)
2 = succ(1) = succ(succ(0))
3 = succ(2) = succ(succ(1)) = succ(succ(succ(0)))
All operations can be defined as successive iterations of successions.
It's too bad the name for the inverse of the succession function isn't blow() or spitOut().

[Anonymous No.14964031]

>>14964025
sounds like constructivism. what about relationships between objects that may or may not exist?

[Anonymous No.14964080]

How do I find good datasets?
Kaggle is shit.
For example, I want to find a dataset with the race, sex, and height of many randomly selected individuals so that I can answer the question of "At what height is the sex distribution 1:1 for Whites?"

[Anonymous No.14964201]

>>14964080
That's actually one of the hardest parts of data science / machine learning, and why enterprises pay so much for good data.

[Anonymous No.14964251]

>>14960859
>How can you statistically increase your chances to win the Powerball Lottery? Random number generator a good idea? Anything I come up with would be a pattern I’d assume
Anyone?

[Anonymous No.14964255]

>>14964251
It's impossible as long as the balls are chosen randomly. The only thing you can do is pick numbers that are selected by people infrequently so if you do win the chances are higher you'll be the only winner.

[Anonymous No.14964337]

>>14964251
just think you have the same chance of winning if you pick 1 2 3 4 5 as you do some mystical random combination

and yet i bet NO ONE ever seriously puts down 1 2 3 4 5 (or however many numbers are needed) and thinks they will win

[Anonymous No.14964362]

>>14959725
>>14959747
Alright good catch, but >>14959747 isn't explaining what is going on.

Starting from 3rd grade all the way until even precalculus, some math teachers will meme that [math]\sqrt{x^2}= \pm x[/math] because [math]xx=x^2[/math] and [math](-x)(-x)=x^2[/math]. However when you start getting into serious maths, when you start treating the square root like a function from the nonnegative reals to the nonnegative reals, so you only get one output. Traditionally we just implicitly state it and expect any decent student to see what we are doing and copy us without asking questions. So, starting in analysis, we take the nonnegative of the outputs of the square root function, which makes many of the inequality proofs in your book work.

[Anonymous No.14964387]

>>14963947
>I'm having trouble proving that if x in a union of A and B, then x is in the union of collection of sets {A,B}
the union of A and B and the union of the collection {A,B} are the same thing by definition

[Anonymous No.14964405]

>>14958813
How do i show that [math]A \cup B = \bigcup{\left\lbrace A, B \right\rbrace}[/math] using the binary intersection and the big intersection definitions? It seems to be some first-order logic trick if i don't want to simply resort to semantics

[Anonymous No.14964433]

>>14964387
>>14964405
i think my question is similar to this too. i dont think i can just say it's by definition, i think i need to show it like this anon is also asking

[Anonymous No.14964457]

>>14964405
binary union* and big union* definitions

[Anonymous No.14964472]

>>14964450
i think so. i think my problem is because the set is {A, B} not just {A}. and my second problem is i have to start from the side where x is in AUB.

When it was just {A} and i started from the bigU side, i could say suppose x is an element of bigU, and then by the definition of bigU, there must be a set Y in bigU such that x is an element of Y, and then since it is only {A}, Y = A, and then i could say therefore x is an element of A.

I dont know how to reverse this if i have to start from x being in A and show x must be in bigU because i dont know how to suppose a set Y in bigU when i only have x being in A to work with.

then the other problem is once bigU = {A,B} i cant just say suppose Y is in bigU, now Y can be either A or B. and likewise starting with AUB, i still have the problem of not knowing how to derive bigU's definition when all i have is AUB.

i'm not sure about the formua you wrote because the definition of bigU that i have is [math]\ \bigcup_{X \in C}X = \{x | (\exists X)(X \in C \wedge x \in X \} [/math]

[Anonymous No.14964476]

>>14964472
sorry when C = {A} or {A,B}. and bigU = A or bigU = AUB, i mixed up the collection C and bigU.

[Anonymous No.14964589]

Can any of you guys help me understand this random ass assumption my book does?
That is not one of the saturation conditions as far as I know.

[Anonymous No.14964613]

>>14964251
If you think about how the payouts work, then you should pick wtv combo is least likely for someone else to pick, since the top prize is split between everyone who picked the same numbers

1, 2, 3, 4.. seems stupid, but you know a lot of dipshits prob did the same thing as a joke. You'd want to eliminate possible birth date components, maybe combos of sequential numbers. You'd really need a data set of every number recently played to make accurate assumptions, but you have to employ some psychology.

You're not trying to avoid matching with anyone, just as many people as possible

[Anonymous No.14964618]

>>14964613
It's reverse Family Feud

[Anonymous No.14964634]

>>14958813
Is it normal to take a long time to solve questions like these? These questions took me 2 days to solve, but the solutions are very short and simple.

[Anonymous No.14964673]

>>14961519
>Why would I watch a 4chan-themed digital game of football?
Its fun

[Anonymous No.14964711]

>>14963495
thank you anon!

[Anonymous No.14964876]

if I find that a series converges absolutely (Σ|an|, where an is the given succession, converges), then Σan converges. Can I say anything about Σan if Σ|an| diverges?

[Anonymous No.14964894]

I have a question regarding https://en.wikipedia.org/wiki/Vacuum_ejector

I understand Bernoulli's principle in that increasing fluid speed reduces pressure, and to keep the same volumetric flow rate through a restriction you have to increase the fluid's speed reducing the pressure in exchange. Which results in a vacuum being created.

I'd like to know how to calculate the amount of air and the rate that it will be sucked in through port D in pic related since I can't seem to find any formulas for that online.

[Anonymous No.14964912]

>>14964876
Kind of.
Either [math]\sum a_n[/math] also diverges or you have the Riemann rearrangement theorem.
>>14964634
It's normal to struggle and take longer when you're starting out and getting used to proving things.

[Anonymous No.14964927]

>>14964912
>It's normal to struggle and take longer when you're starting out and getting used to proving things.
I am not new to proofs, I am new to Linear Algebra.

[Anonymous No.14964957]

>>14964876
The convergence of Σ|an| implies the convergence of Σan
Therefore by contraposition, the divergence of Σan implies the divergence of Σ|an|
However the convergence of Σan may or may not imply the convergence of Σ|an|
If Σan is convergent but Σ|an| is divergent then the series is called conditionally convergent.

[Anonymous No.14965019]

Why is the lexicographic product necessary to define an isomorphism? Why wouldn't just any ordinary relation on [math]B[/math] suffice?

[Anonymous No.14965110]

Not sure how to do this one

[Anonymous No.14965202]

>>14965110
[eqn]
x(t) = r(\theta(t)) \cos(\theta(t)) \\
y(t) = r(\theta(t)) \sin(\theta(t)) \\

\theta(t) = \frac{2 \pi}{3} t
[/eqn]
Just plug this shit in.

[Anonymous No.14965323]

>>14964927
Doing an intro to proofs class doesn't make you not new to proofs.
>>14965019
>Why is the lexicographic product necessary to define an isomorphism?
It's not, the book just placed both definitions next to each other.

[Anonymous No.14965357]

Let f Z_60 -> Z_60 be an isomoprhism. Assume f(7)=23. Whats f(13)?

[Anonymous No.14965381]

>>14965323
>Doing an intro to proofs class doesn't make you not new to proofs.
I have solved entirety of Analysis by Abbott, and Number Theory by Long, stupid anime poster.

[Anonymous No.14965384]

>>14965357
>>14963950
you just have to find a such that 7a = 23 then f(13) = 13a

[Anonymous No.14965417]

>>14965381
Okay, since we've finished rejecting the other possible reasons you could be struggling with basic linear algebra we'll have to resign ourselves to the fact that you're just stupid.

[Anonymous No.14965476]

Let q be prime, b an element of the finite field F_q, and f the polynomial f(x) = x^q + b^q. How to decompose f as a product of irreducibles? I realize that f(-b) = 0, but how to proceed?

[Anonymous No.14965484]

pls help i have calc1 exam tomorrow

i got stuck on an exercise and the solution of the textbook says that [math]\frac{1}{n^{\alpha }}\left ( \frac{1}{n^2sin\frac{1}{n}} -n(sin\frac{1}{n})^2)\right )\sim \frac{1}{2n^{\alpha +3}}[/math]

note that I haven't covered Taylor series and out of all the Landau notation the teacher has only covered what [math]\sim [/math] is. So I can only do this with the "known" asymptotic relationship (for example sin(epsilon) where epsilon goes to zero is asymptotic to epsilon)

what I would do is use this thing that I just wrote but that would give me (1/n^alfa) times zero. Googling around i think i sorta understood that I can't use asymptotics in cases like this where I have something minus something because of things related to taylor series or other stuff I haven't done yet.

I just can't understand if there's a way to get to the result on the book using only the tools that I have, ive been trying for the last hour

[Anonymous No.14965489]

>>14958877
No, it's hard for everyone

[Anonymous No.14965512]

>>14965417
Ok.

[Anonymous No.14965544]

>>14964405
What are the definitions you have to work with?

[Anonymous No.14965560]

>>14965489
Shut the fuck up worthless tranny

[Anonymous No.14965577]

>>14958877
People mindlessly saying "get good" are not that helpful. First, you need to figure out what your problem is. You can just be taught wrong, just be unlucky zone out or miss critical definitions and so on. What helps everybody I've ever taught: Review from your earliest point of failure. If you cannot do certain fraction manipulations, go back to fractions. Khan academy is good for this.

Example on khan academy, you can do whole unit tests. Do those, figure out what you forgot or just never learned, and do that to progress.

[Anonymous No.14965585]

>>14965560
So who fingered you as a kid was it your dad or your uncle?

[Anonymous No.14965693]

>>14964405
>>14964433
>>14964387
Look at this, maybe it could help:
The union of a pair is the union of its members. Proposition 5.7 of [TakeutiZaring] p. 16.
https://us.metamath.org/mpeuni/unipr.html

[Anonymous No.14965703]

>>14964255
You would have done well with that this time. It seems people frequently pick only low numbers. So if you pick larger numbers you have a better chance of being the only winner.
Anyone know why people tend to pick smaller numbers?

[Anonymous No.14965722]

>>14965476
(x+b)^q = x^q + b^q

A linear factor is trivially irreducible.

[Anonymous No.14965723]

>>14965703
They pick numbers that a personal: so birth dates, ago of their kids, "lucky" numbers etc. Those all tend to be smaller than the range offered by lotteries.

[Anonymous No.14965724]

Let's say that [math]x \in(E, \lVert \rVert)[/math] an [math]R[/math]-normed vector space.

Is it correct to say that [math]x.o(1)=o(\lVert x \rVert)[/math] because [math]\frac{x.o(1)}{\lVert x \rVert}\leq x.o(1)[/math] and [math]\lim\limits_{\lVert x \rVert \to 0 } x.o(1) = 0[/math]? Is it that simple?

[Anonymous No.14965773]

>>14958813
Anyone able to help me with this one?

[Anonymous No.14965786]

>>14965773
Why is your answer positive? Friction doesn't increase kinectic energy, usually.

[Anonymous No.14965810]

>>14965786
Honestly? I don't know. I genuinely have been confused in my physics class because I just got out of the military, and I haven't done algebra since like 2016. I'm not sure how I'd go about solving these problems.

[Anonymous No.14965841]

>>14965773
you have to multiply the 50 N by 11 m, same as part A

[Anonymous No.14965859]

I have decided to see a psychiatrist for my depression. What books can I read to get an idea of what to expect? I have little respect for the profession and I am wary of getting kiked like Kanye.

[Anonymous No.14965872]

>>14965484
I think you have to substitute the second order asymptotic expansion [math]\sin x = x - \frac{x^3}{6} [/math] and then it works out

[Anonymous No.14965881]

>>14963892
My bad, almost forgot to answer your question.
Let [math]X = \mathbb{R}[/math]. Define [math]T_0 (u) = 100[/math]. It's Lipschitz continuos with constant, say, [math]2[/math].
Then [math]\|T_1 (2) - T_1 (0) \| = \| 0 - 100 \| = 100 \not \leq (2k + 1) \| 2 - 0 \| = 10[/math]
>>14965724
Stop fuckabouting with incomprehensible Landau symbols and ask your question properly.

[Anonymous No.14965882]

>>14965841
Absolutely radical. Thank you man. Now I just need to find out the last question.

[Anonymous No.14965907]

>>14964589
> [math] V_D > V_G [/math]
that is definitely sufficient for saturation. consider the point in the channel right next to the drain. if [math] V_D = V_G [/math] then theres no field that sends the semiconductor into inversion and creates the conductive layer.

[Anonymous No.14965917]

>>14965693
tyvm anon this is really cool

is this an automated proof solver or just a collection of proofs with steps? either way i've been looking for something like this for a while.

i've seen proof checkers for logic but usually they can only prove by contradiction so not as useful

[Anonymous No.14965932]

>>14965323
So the relation symbols used are arbitrary, thank you.

[Anonymous No.14966114]

I'm studying the Fourier Transform's properties right now and something doesn't make sense. I'm probably way overthinking this.

The shifting and scaling properties don't sit right with me. Let's say we have some function and its transform, [math]g(t) \Leftrightarrow G(f)[/math].
We then have the properties
[math]g(t-t_0) \Leftrightarrow e^{-j2\pi ft_0}G(f)[/math]
and
[math]g(at) \Leftrightarrow \frac{1}{|a|}G(\frac{f}{a})[/math]

Alright, this is all well and good when we know we have some definite [math]g(t)[/math], which serves in effect as some "reference" function for any time scaled/shifted version of it.
If I go out to the lab and take the FT of some random signal with an oscilloscope, it has no notion of the signal having been time scaled or time shifted. It just sees a signal. The signal would just be its own [math]g(t)[/math]. But, if the time scaling/shifting properties are valid (and they have to be), this implies I can derive an equation for that transform that would inherently have shifting and scaling terms within it, even though there's nothing for the physical signal to be relative to.
The time shifting/scaling properties seems to imply that there is some "canonical/absolute" [math]g(t)[/math], even though a signal in the real world would just be relative to itself.

what the fuck

[Anonymous No.14966121]

Why do tards believe in entropy? It literally doesn't exist.

[Anonymous No.14966122]

How to construct a 4x4 matrix to describe [math]S^2[/math] of a two particle system each with spin [math]1/2[/math]?

[Anonymous No.14966168]

>>14965881
>Stop fuckabouting with incomprehensible Landau symbols and ask your question properly.
Is [math]x.o(1)=o(\lVert x \rVert)[/math]?

[Anonymous No.14966171]

>>14965859
>see a psychiatrist
Don't. Instead, give purpose to your life. Fight for a better world or something. That is the best cure for depression. Drink lots of water, eat lots of healthy plant based food, exercise, sleep well. Fuck psychiatrists.

[Anonymous No.14966202]

>>14966122
https://physics.stackexchange.com/questions/342123/total-spin-of-two-spin-1-2-particles

[Anonymous No.14966448]

>>14966121
there are more grains of sand than there are atoms in the universe dude

i think its safe to say you dont know what your talking about

[Anonymous No.14966462]

>>14966448
Prove it retard. Yeah maybe there are enough universes with sandy planets for that to hold true but you don't know that.

[Anonymous No.14966471]

What's the inverse z transform of this? Is it:
(X[n-0] + X[n-1] + X[n-2] + X[n-3])/4

[Anonymous No.14966629]

>>14966448
>>14966462
is this a meme?

[Anonymous No.14967110]

>>14958813
When I was growing up it seemed that string theory was considered old hat. Or something that physicists explored and then dumped. This was when I was a teen in the 2000's. Now it seems like string theory has had a resurgence. That universe acts on the basis of different vibrations of strings. When did this happen? Thanks.

[Anonymous No.14967208]

>>14966629
Yes, also read the damn OP
>>ignore shitpost replies
>>avoid getting into arguments

[Anonymous No.14967283]

>>14966471
Technically it's h[n] = (δ[n]+δ[n-1]+δ[n-2]+δ[n-3])/4

H(z)X(z) = Z{(x[n]+x[n-1]+x[n-2]+x[n-3])/4} where X(z) = Z{x[n]}, i.e. the discrete convolution of h[n] and x[n].

Z^(-1){H(z)} is the impulse response, Z^(-1){H(z)X(z)} is the response to the signal X(z)=Z{x[n]}.

[Anonymous No.14967284]

>>14967110
String theory has never been considered old hat. It's always been at the bleeding-edge of theoretical ideas. It has gone through phases of popularity though. The time you speak about, the early 2000's, was the start of the biggest surge in popularity when Witten unified a lot of conflicting theories and proved they were all parts of a single higher dimensional theory: M-Theory . That was when it was shown string theory could explain all the known particles and their interactions, and so led to lots of physicists working on it. In recent years it has led to the development of the AdS/CFT correspondence (holographic principle) which has applications in other areas of physics such as blackhole research.

However all modern string theories rely on something called supersymmetry (SUSY) and so far there is zero experimental evidence that exists. One of the main reasons the LHC was built was to detect these SUSY particles but it has seen zero. While supersymmetry is not completely dead as an theory many now think it is not a description of reality no matter how nice the mathematics was. This currently leaves (super)string-theory in a precarious state.

[Anonymous No.14967289]

>>14966114
For the shifting, note the occurrence of "f" in the scale factor. G is a function in R->C, G(f) is a (complex) number, the complex amplitude of the e^j2πft component. So each and every component in the signal (whatever it may be) gets multiplied (i.e. rotated) by an amount proportional to its frequency (|e^jx|=1 for all real x, so the amplitude doesn't change).

For the scaling, note that multiplication or division by a is applied to the parameter.

In each case, you aren't simply transforming the value of the function, but the function itself.

[Anonymous No.14967428]

How would I go about transforming the points on the plane described by the normal vector n passing through a specific point?

I think normally planes don't have orientation right? So you describe points on them as vectors relative to the normal vector + pass-through point, but in this case my plane has a fixed size and an orientation, so not really sure how I'd do that...

[Anonymous No.14967433]

>>14967428
woops, forgot image. the planes corners are labeled as if it had a normal vector {0,0,1} (0,0,0), and I want to go fro that position to where it is located in the image, but I want to update the corners to their new real position

[rpyth No.14967488]

>>14961329
This is sad.

[Anonymous No.14967498]

>>14967433
That's just a translation. Since the norm is a unit vector each corner point would transform as p' = p + a * n, where a is some scaling value.

[Anonymous No.14967665]

>>14965917
>is this an automated proof solver or just a collection of proofs with steps?
The latter, they've been written by people. Check the homepage to know more.

[Anonymous No.14967701]

>>14961385
I am becoming increasingly worried about this. If you are a secret internet police I propose the following.

>what I request
1. I get a small building with a variety of computers.
2. I live in this building and conditions are made possible that I never have to physically leave or go outside. Everything is delivered to the building or already contained in it.
3. There is a space online where I can go to talk to people about computers and math and not get banned for maids or worry about getting in trouble by accident of helping make Russian technology. Site should be as similar to 4chan as possible because it is the only website I find useful.
4. I think vampire maid from touhou might be foreign. If she is from a country which is friendly to America or neutral to it, you must offer her to go to any school in America she wants for free. You must also get her a citizenship if she wants to stay and make similar offers to any family member she asks about.
5. There should be like a handler or something and I give that person my research. The handler has to be a maid.
6. Tohru has to go in the /g/ sticky.

>what I offer
1. I can make very cheap research.
2. I can help apply the research.
3. You don't have to pay me. If this arrangement happens I have no use-case for money.
4. Research goes directly to handler instead of CC0.

>what I refuse to do
1. Make anything for a Terminator.
2. Make or improve weapons.
3. Make anything related to mind control.

>instead of doom I'll make flowers bloom for everyone around to see

[Anonymous No.14967709]

>>14967488
I apologize, but there is nothing I can do. I don't want to get in trouble with the government. They can make a lot of problems for me and I would not be able to withstand them. I don't want an FBI person knocking on my door asking why I made technology for Russia.

Neither you nor I caused Cold War 2. We are in agreement it is sad, but that does not change unfortunate realities about politics or laws.

If Cold War 2 stops, I would be happy to contribute, but the last one took most of a century and if this one takes that long it will exceed my remaining lifespan.

For now I must politely decline to contribute.

[Anonymous No.14967740]

is there any way to simplify erf(a) + erf(b)?
what about erf(a) + c*erf(b)?

[Anonymous No.14967753]

>>14967740
for reference Im trying to solve this for t

[Anonymous No.14967822]

>>14967740
sum of erf doesn't have a closed form
you have to solve it numerically

[Anonymous No.14967837]

How do i prove using the definitions, that if there are two unique minimal elements, there can not be a smallest element?

I figure maybe a proof by contradiction, so you are assuming there are two minimal elements and a smallest one. But i cant figure out how their definitions lead to this. Should i not use a proof by contradiction?

[Anonymous No.14967848]

>>14967837
>two unique minimal elements
Let [math]x[/math] and [math]y[/math] be two minimal elements, since [math]x \neq y[/math] then either [math]x < y[/math] or [math]x > y[/math] by the law of trichotomy. If [math]x < y[/math] then [math]y[/math] is not a minimal element (a contradiction) and if [math]x > y[/math] then [math]x[/math] is not a minimal element (also a contradiction), so both possibilities lead to a contradiction and the proof by contradiction is complete.

[Anonymous No.14967852]

>>14967822
I tried that already ;-;
the left hand side is 0.3 but the plot doesnt hit 0.3 until like 63 hours which is very very unreasonable for this problem. I checked the equation I put in my code over and over and I cant see where I made a mistake

[Anonymous No.14967889]

>>14965773
>>14965882
Two ways of doing part c:
conservation of energy, considering parts a and b
calculate the portion of work done against just the frictional force, similar to part a

[Anonymous No.14967892]

>>14967837
What type of order relation do you have? That statement is not true for general preorders. For instance you could consider the order where [math]x \prec y[/math] for all elements on a two-elementric set. Then both elements are both smallest and minimal elements.
>>14967848
You only have that trichotomy if the order relation is a strict total order. There are many other types of order relations.

[Anonymous No.14968030]

>>14967892
>>14967848
sorry its for a partially ordered set, the relation is [math]\preceq [/math]

[Anonymous No.14968046]

>>14967740
>>14967753
>>14967822
>>14967852
I found the issue.
That + should be a -
I LOVE when professor's give me incorrect notes. I should just stick to reading the text

[Anonymous No.14968603]

>>14958813

How can I scale the batch size of my neural network larger than 42? It does a Cholesky Decomposition, which I think has to be square, right?
It outputs 42 predictions so I give it a batch of 42.
Is there any other way?
Can I scale up in increments of 42? 84x84 and 420x420 and so on?
With the inputs and the actions get crossed like this?

[Anonymous No.14968724]

>>14968603
Batch size relates to the number of inputs, not the outputs. All you need to increase it is more memory.

[Anonymous No.14968732]

Is the Hubble Constant caused by blackholes located all around the universe sucking spacetime into them? Has anyone run the numbers on this? Where can I read more about this or how it's a wrong way to look at the Hubble Constant?

[Anonymous No.14968811]

>>14968732
You can't run the numbers on something that doesn't happen. But lets say it did, however the Hubble Constant describes the rate the universe is expanding and not how everything is being sucked into blackholes.

[Anonymous No.14968848]

>>14958813
How to find time dependent expectation values

[Anonymous No.14969000]

how is the graviton supposed to work? if massive objects eject these particles wouldn't that imply that you push things further away and not towards you when these particles crash into other massive things?

[Anonymous No.14969009]

>>14969000
In the same way photons mediate electromagnetism, or gluons mediate the strong force.

[Anonymous No.14969033]

>>14968811
Thanks for your answer. I'm looking to see if anyone else has worked on this idea? I might be asking an absurd question.

[Anonymous No.14969093]

>>14958813
Is there anything worthwhile studying or doing professionally in STEM? I’ve only ever been interested in sci-fi shit that wasn’t remotely real when I was a kid, and highschool/college killed any love I would’ve had for science for good. Before then I wanted to make robots and I was told as a little kid “robots aren’t real, you’ll never be a robot” by some really shitty adults.
Nowadays Boston dynamic is a thing, so is machine learning, and it’s only a matter of time before the two are one. But I have no educational or professional background in stem so I can’t really get in on that anymore.
I’m thinking about changing up my career and going back to school but I feel that existence is pretty hopeless and bleak and that nothing I can do will matter so it’s hard to know what to actually go into. But stem makes money right, and I’ll be useful right, not just a useless eater? If I can hack it of course.

[Anonymous No.14969106]

>>14969033
It's an absurd question.

[Anonymous No.14969136]

What does induction have to do with the concept of a least element?

[Anonymous No.14969168]

>>14969136
You can prove they are equivalent statements.

[Anonymous No.14969299]

Is this definition illegal?
[math] x \in \bar{\emptyset} \Leftrightarrow x \in U \wedge x \notin \emptyset[/math]

because

[math] a \in \bar{A} \Leftrightarrow a \notin A [/math]

Isnt it a circular definition because of this?

[Anonymous No.14969554]

>>14969093
> going back to school
You only need that for the paperwork. There are so many free educational resources available. For anything remotely related to "engineering" you're going to need to learn programming and mathematics, and most of that is useful for other stuff. Also, a Comp Sci degree is an incredibly inefficient way of learning programming; most CS graduates can barely program.

Now, most decent STEM jobs will require a degree, but if you can learn the basics by yourself it will a) give you an idea of whether you can "hack it" and b) give you an alternative route (some programming jobs won't require a degree if you can prove that you can actually program) that doesn't involve spending enough money to buy a house.

Also: avoid "robotics" or "mechatronics" courses. Robotics is a multi-disciplinary field: control systems engineering, electronic engineering, mechanical engineering, programming, machine learning (AI). Commercial robotics development is done by a team of people, each of whom specialised in one of those fields. If you try to learn all of them, you won't learn any of them to the required level.

[Anonymous No.14969566]

>>14969009
but what absorbs them? what's supposed to happen when you absorb or emit them?

[Anonymous No.14969874]

dumb question:
>Problem set asks for specific thing
>Come up with general solution that works on all items on the problem set

Should I still go through the problem set like I should have from the start or is just coming up with a general solution for the entire thing good enough from a pedagogical pov?

[Anonymous No.14969882]

>>14969874
If it's a problem set from a book and you used stuff from future sections, then it's bad. Very common in Linear Algebra, where people use determinants and row operations to solve questions related to basis and inverses. Actually, I am solving a Linear Algebra book, and it presents specific cases of more general theorems and algorithms as exercises much earlier.

[Anonymous No.14969885]

>>14968848
Depends what kind of problem you have. Discrete, continous, what kind of equation governs your outcome?
In general you do a weighted sum over all future possibilities and calculate the average.

[Anonymous No.14969888]

>>14969554
>Also: avoid "robotics" or "mechatronics" courses. Robotics is a multi-disciplinary field: control systems engineering, electronic engineering, mechanical engineering, programming, machine learning (AI). Commercial robotics development is done by a team of people, each of whom specialised in one of those fields. If you try to learn all of them, you won't learn any of them to the required level.
Can confirm this. All those fancy new courses like "robotics", "renewable energy engineering" and so just exist to attract inexperienced freshmen and don't prepare you for actual jobs.
Learn something properly, specialize in a direction you like but thats actually needed. Like, I'm a control engineer, I'm completely unfirable because they'd take years to replace me.

[Anonymous No.14969889]

test

[Anonymous No.14969893]

What's the precedence in predicate logic? Conjunction or implication?

P(x)∧F(y)¬I(x,y)

like in something like this, is it "if (P and F) then not I", or "P and (if F then not I)"?

[Anonymous No.14969898]

>>14969893
The implication is after the F(y)

P(x)∧F(y)->¬I(x,y)

[Anonymous No.14969935]

doing the first one of these and I arrived at [math]x \sin m \sin n[/math], but I don't know if I'm supposed to do some other step here to get [math]\sin mx \sin nx[/math] or if I messed up along the way

please give me a hint

[Anonymous No.14969954]

>>14969935
I think you messed up, x*sin(n)*sin(m) is linear function while the required solution is not

[Anonymous No.14969958]

>>14969935
>>14969954
Also i just noticed, the x is inside the cosine on the right hand side, you might have misread the queastion.

So it should be read as cos((m-n)*x) not cos(m-n)*x

[Anonymous No.14969972]

>>14969958
I think that's it, gonna check when I get to a flat surface to write on. I hate this way of notating the [math]\sin \cos \tan[/math] without using brackets, it's not so clean in my opinion

[Anonymous No.14969981]

>>14969893
Relations always take precedence after operations. Write it down in LaTeX and the spacing makes it obvious.

[Anonymous No.14970185]

does this mean the cartesian product is the set of all choice functions?

[Anonymous No.14970191]

If I randomly rank the four chaos gods, what is the probability that I order them correctly?

[Anonymous No.14970206]

No idea if this counts as homework help, but this is the cloest thread.
>need to crack a game for class.
>try looking for uncracked dos games, since A) they have copy protection to break that doesn't require internet and B) want an excuse to use dosbox
>found no uncracked games except for https://www.toughdev.com/content/2012/01/the-good-old-days-cracking-16-bit-dos-games/
>seems like a good resource on the games, and a guide on what to do
Issue is, am I allowed to copy what was done to crack? I said I would crack it myself to my professor, not look up a guide on it. And if I tell my professor that I found a guide on it, I doubt he would let me use it.

[Anonymous No.14970209]

>>14970206
Fuck I forgot the most important part: my class has nothing to do with cracking games, I just said I would like to do it. Professor doesn't even know what DRM is. This isn't a class on how to crack, it's a internet security class

[Anonymous No.14970227]

>>14970185
Yes.
>>14970206
>>>/g/sqt

[Anonymous No.14970254]

>>14970227
>>>>/g/sqt
This is more about if I can just follow a guide rather than crack a game

[Anonymous No.14970260]

>>14970209
If it's just for fun then why is it an issue to just do whatever you think suits you best? Try cracking it and if you get stuck, look it up in the guide.

[Anonymous No.14970358]

What is the definition of exponentiation?
I know you can explain the basic properties of exponentiation like [math]a^0=1[/math] through the definition of repeated multiplication but what is the "rigorous" definition?
Is a list of all the properties like [math]a^n\cdot a^n=a^{n+m}[/math] sufficient as a definition?

[Anonymous No.14970379]

>>14970358
A list of properties does not really make the definition. Those properties you refer to are consequences of the definition, and can be proven by using the definition. If you think of just integers right now then you may as well just consider it a notation, a convenient way of expressing repeated multiplication. But this does not explain what fractional, or even complex exponentiation is defined as. There are various ways to extend the definition to those cases but you don't need to worry about repeated multiplication.

[Anonymous No.14970489]

I want to solve some coupled pde's numerically how do I approach that? Do you just use a standard library like pypde or try to work by hand until you have something of a linear system of equations?
Also can FFT be used to solve coupled pde or is that for only good for simple pde problems?

[Anonymous No.14970537]

So we all know the whole thing of "if you shoot a 1000mph bullet from the back of a train going 1000mph, to you the bullet appears to be moving away from you at 1000mph, but to an outside observer the bullet would merely hang in place and drop to the ground, because of relative velocities.

If the bullet was SLOWER than the train, say, 700mph, it would still appear to be moving away from you at 700mph, but to an outside observer would the bullet appear be moving 300mph backwards until it hits the ground?

[Anonymous No.14970609]

Working with the poincare group generators in their differential form, trying to show the conmutator of rotation with translation. Problem is, I'm getting the negative of what the result should be. Anyone know where I can find the property written out step by step so I can figure out what I've done wrong?

[Anonymous No.14970660]

>>14970206
I'd find some old shareware stuff where you'd enter a code to unlock the full game. Open it up in something like ollydbg. Look for the text from the unlock dialog in the executable (it's often just included as plain text) and use that to set a breakpoint... from there, see if you can follow the assembly code to where the "OK" button is clicked, and puzzle out the math behind the code confirmation.

Something like this can be done with a debugger and maybe a hex editor for looking at the game's config files for a serial number particular to your installation, etc.

It's basically just exploring until you find the relevant section of code and sussing out what it does. More sophisticated DRM won't allow you to explore the code until you've applied some tool built for that specific variant and version.

[Anonymous No.14970851]

>>14970537
>to an outside observer the bullet would merely hang in place and drop to the ground
No it wouldn't, what the fuck gave you that idea? Newtonian mechanics would apply, so v_ground = v_train + v_bullet

[Anonymous No.14970858]

>>14970537
>but to an outside observer would the bullet appear be moving 300mph backwards until it hits the ground?
Yes.

[Anonymous No.14970910]

>>14970851
The velocity of the bullet is negative if you're shooting it off the back of the train.
v_train + v_bullet = 0

[Anonymous No.14970965]

my DSP professor assigned us problems on finding the inverse Z transform of some functions based on the method of contour integration and residues.
He didn't actually teach us this method, and left us to figure it out for ourselves. I've got most of it figured out, but I'm a bit confused on something that really shouldn't stump me at this level.

Given that
[math]\sum_i (z-z_i)X(z)z^{n-1}|_{z=z_i}[/math]
am I supposed to also substitute the pole into the z in [math]z^{n-1}[/math]?

[Anonymous No.14971043]

>>14970358
For positive integer n, a^n is defined as repeated multiplication of a n times. The regular properties follow from this definition. When you want to perform the operation with n=0, negative integer n, fractional n, complex n, etc you need to extend the definition.

[Anonymous No.14971088]

>>14958813
Why are we - consumers - not isolating everything with homemade starlite (PVA glue and corn starch)?
Is carbon foam only good isolation against direct flames?

[Anonymous No.14971094]

>>14970858
Thanks anon. I was pretty certain it would work that way, but it just sounded wrong and I wasn't sure if I was being retarded or not.

[Anonymous No.14971126]

verilog question, sorry if I come across as a retard
trying to implement a clock divider, if I wanted to use the slowClock as the clock input for a 10Hz counter, would I need twice the clockspeed to have a high clock every 0.1 seconds?

As is wouldn't it be
0 cycle : 0 seconds : Low
1 cycle : 0.1 seconds : High
2 cycle : 0.2 seconds : Low
3 cycle : 0.3 seconds : High
etc
which is only counting ever 0.2 seconds for a posedge counter

[Anonymous No.14971145]

>>14970358
For integers, exponentiation is defined as repeated multiplication.
For fractions, roots.
For reals:
[math] |b|^r = \sup \{ |b|^q : q \in \mathbb Q \land |b|^q \leq |b|^r \} [/math]
For complex:
[math] |b|^z = \exp(z \ln b) [/math]

[Anonymous No.14971160]

>>14970358
>>14970379
>>14971043
Sorry, but this doesn't really help.
Don't the field axioms give a rigorous definition of multiplication and addition by their properties like distributivity? Are you telling me we can't do the same thing but with exponentiation?
And what I meant was that the definition of repeated multiplication as [eqn]a^n=\prod_{k=1}^{n}a[/eqn] can be used to deduce the usual properties like [math]\frac{a^n}{a^m}=a^{n-m}[/math] (via the intuition cancel out like terms in numerator and denominator) which in turn implies [math]1=\frac{a^n}{a^n}=a^{n-n}=a^0[/math].
Fractional powers can be explained by [math]y^{\frac{2}{3}}=x[/math] for [math]x[/math] and [math]y[/math] such that [math]yy=xxx[/math] (we are still using repeated exponentiation).
What is the definition of exponentiation of real and imaginary numbers? come on dude. Give it to me.
>you need to extend the definition.
How do you do that "rigorously"?

[Anonymous No.14971164]

How can I get a stronger intuition for complex numbers?
I'm fine when there's a complex unit in, say, an exponential. I have a vague notion that this corresponds to a rotation or oscillation. However, this intuition is contingent on the complex unit being inside of the exponential.

Once the complex unit is outside of the exponential, all hell breaks loose and I have absolutely no idea how to interpret it.
For example:
[math]\frac{1}{2}(e^{j\omega_0t}+e^{-j\omega_0t})[/math]
cool that complex unit is in an exponential and I know that means something akin to rotation. Sure enough, this is [math]cos(\omega_0t)[/math]
[math]\frac{1}{2j}(e^{j\omega_0t}-e^{-j\omega_0t}[/math]
[math]\frac{1}{2j}[/math] what the fuck

[Anonymous No.14971181]

>>14971164
You keep using the word rotation when in fact i in the exponential is describing a wave (oscillation). By itself a complex number describes a rotation.

[Anonymous No.14971185]

>>14971145
Thanks for answering my questions here >>14971160, bro.
Could you explain, if even just briefly, why the real exponentiation is defined that way?
Exponentiation of the logarithm is basic and pretty intuitive. Is it really helpful for finding complex properties of exponentiation? and if all reals are also complex, why not just use that definition always?

[Anonymous No.14971302]

>>14971185
I made a mistake.
[math] |b|^r = \sup \{ |b|^q : q \in \mathbb Q \land q \leq r \}
[/math]
Now read the definition and see how the supremum is the limit of exponentiation as rational exponents approach the real exponent.

(Picrel from Rudin)

[Anonymous No.14971304]

>>14971185
>>14971302
If [math] |b| < 1 [/math], then it would be [math] \inf [/math].
You can derive properties of exponentiation pretty easily from complex definition. The complex definition is an extension of real definition, so you need to have exponentiation defined for reals first.

[Anonymous No.14971326]

Can someone recommend 10th or 11th grade level math book?

[Anonymous No.14971813]

>>14971145
That definition for reals is circular.

I'm personally used to using your complex definition for the reals as well.
Exponents are defined by the power series and logarithms by the integral.

[Anonymous No.14971839]

>>14958813
test

[Anonymous No.14971866]

>>14971813
>That definition for reals is circular.
[math] |b| \geq 1 \mathrel : |b|^r = \sup \{ |b|^q : q \in \mathbb Q \land q \leq r \} \\
|b| < 1 \mathrel : |b|^r = 1/(1/|b|)^r [/math]

[Anonymous No.14971868]

>>14971813
>>14971813
>That definition for reals is circular.
[math]
|b| \geq 1 \mathrel : |b|^r = \sup \{ |b|^q : q \in \mathbb Q \land q \leq r \} \\ 0 < |b| < 1 \mathrel : |b|^r = 1/(1/|b|)^r
[/math]

[Anonymous No.14971942]

>>14971164
i = e^(iπ/2). Multiplication by i is a 90° rotation. 1/i=-i so division by i is a -90° rotation.

e^ix = cos x + i sin x
e^-ix = cos (-x) + i sin(-x) = cos x - i sin x
e^ix - e^-ix = 2i sin x
(e^ix - e^-ix)/2i = sin x

[Anonymous No.14972656]

Is there a better way to calculate n given this starting information?
>p1, p2, v1

The way I'm doing it is as follows
>compute L as the distance between p1 and p2
:= sqrt((p2x-p1x)^2 + (p2y-p1y)^2 + (p2z-p1z)^2)
>create the vector v2 but subtracting p1 from p2
:= {p2x - p1x, p2y - p1y, p2z - p1z}
>calculate the angle, theta, between the 2 vectors with arccos of L and the dot product
:= arccos((p1x*p2x + p1y*p2y + p1z*p2z) / L)
>calculate n as hypotenuse * sin(theta)
:= L * sin(theta)

I feel like maybe I'm introducing extra steps, mainly with the points to vector conversion, and then I feel like I should be able to reduce the arccos to get theta and the subsequent sin on theta into a single operation?

[Anonymous No.14972657]

Is there a better way to calculate n given this starting information?
>p1, p2, v1

The way I'm doing it is as follows
>compute L as the distance between p1 and p2
:= sqrt((p2x-p1x)^2 + (p2y-p1y)^2 + (p2z-p1z)^2)
>create the vector v2 but subtracting p1 from p2
:= {p2x - p1x, p2y - p1y, p2z - p1z}
>calculate the angle, theta, between the 2 vectors with arccos of L and the dot product
:= arccos((p1x*p2x + p1y*p2y + p1z*p2z) / L)
>calculate n as hypotenuse * sin(theta)
:= L * sin(theta)

I feel like maybe I'm introducing extra steps, mainly with the points to vector conversion, and then I feel like I should be able to reduce the arccos to get theta and the subsequent sin on theta into a single operation?

[Anonymous No.14972685]

I need to prove that for a general topological space, sequential compactness implies limit point compactness. How do I do this? My initial instinct was to take an infinite set A and assume it has no limit point then to derive a contradiction by finding a sequence with no convergent subsequence, but I don't know how to actually do that

[Anonymous No.14972717]

>>14972685
Deadass?
You have an infinite subset [math]S[/math] of your [math]X[/math]. You want to show that it has a limit point. Choose an injection [math]a: \mathbb{N} \to S[/math]. Some subsequence of [math]a_n[/math] has a limit which is a limit point of [math]S[/math].

[Anonymous No.14972750]

>>14972717
Thanks. I'm having trouble seeing why the limit is a limit point if S, but I'll spend some time trying to prove that instesd.

[Anonymous No.14972910]

How is a Pareto Front different than the optimization of a multivariate function?

[Anonymous No.14972925]

>>14972910
it's not
computer "scientists" like to steal concepts from dynamical systems and extant engineering and mathematical fields, add "...on a computer", and call it a novel idea

[Anonymous No.14972943]

>>14972910
The Pareto front is useful when you don't know exactly what is it you're maximizing.
>>14972925
Pareto fronts come from economics.

[Anonymous No.14972990]

>>14972943
>The Pareto front is useful when you don't know exactly what is it you're maximizing.
What the fuck are you talking about?

>>14972910
Pareto frontier is the locus of points that maximises the function. It is derived by maximisation.

[Anonymous No.14973023]

Has anyone any idea of answering this question?

[Anonymous No.14973097]

>>14970965
As it's written, you substitute z_i for every z, so the terms become all zero. That's probably wrong, could you tell us what integral this sum of residues is supposed to come from?

[Anonymous No.14973162]

>>14973097
The inverse Z transform

[Anonymous No.14973218]

Retard here. How much glycine is in trimethylglycine by mass? Is there a way to quickly determine this in wolframalpha so I can do it next time?
Thanks

[Anonymous No.14973229]

>>14973218
Sorry, a better question would be specifically how much glycine is in 648mg trimethylglycine hydrochloride salt (betaine HCl) by mass?

[Anonymous No.14973372]

Suppose [math]x_1, x_2, x_3...[/math] is a Cesaro convergent sequence of reals, say [math]\lim_{n \to \infty} \frac{1}{n} \sum_{i=1}^{n} x_i = L[/math]. Can we then say that [math]\lim_F \frac{1}{|F|} \sum_{i \in F} x_i = L[/math], where [math]F[/math] ranges over the directed set of finite subsets of [math]\mathbb{N}[/math]?

[Anonymous No.14973399]

>>14958813
The "animals detecting food in your backpack from a mile away" part is bullshit, but is the "titty juice to stabilize blood sugar" straight fuckin bullshit as well?

[Anonymous No.14973415]

Well, there is sugar in milk... Question is does it "just werks"?

[Anonymous No.14973564]

>>14972990
>What the fuck are you talking about?
Assume a business can produce items [math]A[/math] and [math]B[/math], where the markets for [math]A[/math] and [math]B[/math] both work under perfect competition.
If you don't know what the actual market prices of [math]A[/math] and [math]B[/math] are, you don't know what are the optimal amounts of each to produce. However, you do know that it's some solution that isn't strictly dominated by another solution in the set of possible outputs it can achieve with its resources.
You don't know the optimal solution, but you do know it's in the Pareto front.
>Pareto frontier is the locus of points that maximises the function.
No it isn't. Reread the definition.

[Anonymous No.14973581]

I need your help, /sqt/
How to solve this? It sounds trivial but I'm getting
filtered real hard by it.
Determine f(x), if [math]f(\frac{x}{x+1})=x^2[/math]

[Anonymous No.14973582]

>>14973564
You should reread your own definition dumb anime poster shut the fuck up

[Anonymous No.14973585]

>>14973581
[eqn]
y = \frac{x}{x+1} \implies x = \frac{y}{y-1} \\
f(y) = \frac{y^2}{(y-1)^2}[/eqn]

[Anonymous No.14973617]

>>14973585
Thank you, bro! I was able to repeat the process and arrive at the results, just to confirm, if [math]f(y) = \frac{y^2}{(y-1)^2}[/math] we can simply change the variable and conculude that
[math]fx) = \frac{x^2}{(x-1)^2}[/math], right?

[Anonymous No.14973640]

>>14973582
Okay man, have fun being wrong.
>>14973617
Yeah.

[Anonymous No.14973666]

>>14973640
I know you can't comprehend this but the picture of my post is actually relevant to my post unlike yours. And I literally wrote that thing, so shut the fuck up.
The PPF is literally the efficiency locus which is the locus of points that constraint maximises the function but plotted in the output plane instead of the input. There's a bijection, they're the same thing.

[Anonymous No.14973676]

I can't make the new thread, not rangebanned but weird error.
>>14973666
>The PPF is literally the efficiency locus which is the locus of points that constraint maximises the function but plotted in the output plane instead of the input.
The PPF is the locus of point in the constraint that aren't dominated by any other points, where we say that [math]x \in \mathbb{R}^n[/math] dominates [math]y \in \mathbb{R}^n[/math] iff [math]y_i \leq x_i[/math] for all [math]i[/math] and [math]y_i < x_i[/math] for some [math]i[/math].

[Anonymous No.14973855]

>>14973676
I made new thread

>>14973844
>>14973844
>>14973844
>>14973844