/sqt/ - Stupid Question Thread: Qubit Edition

>>8804566
quantum computing would mean all posting is faster. This obviously means that there will be a huge increase in useless shitposts, but it also means the super rare quality post becomes common.

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>Will we be able to shitpost faster on quantum computers?

We can mine tripfaggotry faster as far as i know...

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>>8804591
underrated

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y witen is saad??? :(

>>8804623
because his theory is bullshit

In Gauss-Legendre quadrature, you can increase the order of the approximation by playing with the weights Wi and the function evaluations Xi, so you can accurately integrate functions up to order 2n - 1. But how can you actually find the Xi separately from solving a system of non-linears?

If some optimal Xi exist, wouldn't finding them essentially reduce the order of the quadrature method back down to n - 1? You only have the weights to play with if you know the best values for all of the Xi terms.

>>8804566
>Will we be able to shitpost faster on quantum computers?
Unless your shitposting relies on solving a problem in BQP or something, probs not.

>>8805264
>inb4 future captcha require solving problems in BQP

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How would you find the voltage between the two red points on either side? The top battery is 4V and bottom is 1V.

Can quantum computing fasten the development of AIs?

>>8805341
better than clicking on google street view images all day long

>>8805508
no

I have this equation for finding the n-th member of a sequence.
[eqn]A_n=3^n+2^{n+1}[/eqn]

How do I find the recursive equation of the sequence, ie something like this?
[eqn]A_n=A_{n-1}[/eqn]

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>>8805522
>An=An−1

>>8805525
I just need to find the recursive formula that uses the previous member of the sequence to compute the next one. My english is not that good, so included it as an general image what I'm searching for.

idk is this what you want?

A_n
= 3^n+2^(n+1)
= 3(3^(n-1))+2(2^(n))
= 3^(n-1)+3^(n-1)+3^(n-1)+2^n+2^n
= 3^(n-1)+2A_(n-1)

>>8805530
god fucking damnit im retarded

thanks

>>8805508
AI will be as 'smart' as the algorithm written for it. Anyone unironically believing in AI learning is uneducated. If robots destroy humanity it'll be because some amoral fag designed them to.

>>8805505
Kirchoff cutting the circuit in that points. The upper side must have the same current of the lower side. Sorry for bad english

>>8805505

Voltage equations, (Kirchhoff law). Find for both Ua and Ub, then Uab = Ua - Ub.

>>8805581

The currents aren't equally divided because the resistors are different in each branch. Iin = I1 + I2, Iin = Iout.

Whats a good tutorial for learning LaTeX? For all manner of purposes, not just posting here like the one on the /sci/ wiki.

>>8805610
just start writing stuff and when you need something you don't know look it up.

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gents, how do I laplace transform this thing

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>>8805610
>>8805754
This. You can start from a simple file you found somewhere, and just replace stuff in it. Also a good editor helps at first.


You can also switch to XeLatex as soon as you'll need to type utf8 chars (the only difference is that it requires other packages to specify encoding and language). It also supports pstrick better, for example to draw graphs of functions.

>>8805779
https://www.khanacademy.org/math/differential-equations/laplace-transform/properties-of-laplace-transform/v/laplace-transform-of-the-unit-step-function

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>>8804566
What is the best way to think abstractly

>>8805849

think of it like computer parts

you start with the logic circuits
bunch of logic circuits together make a component
bunch of components make a bigger component
this component interacts with other components

>>8805849
This image always confused me. How does the number of holes influence electrical conductance? Is it because there are more paths for electricity to take?

Will quantum computing help me suck my own dick?

>>8805885
Resistors in parrallel add inversely maybe? That's my brainlet take on it

>>8805921
Yeah, sorry that's what I was trying to get at when I was talking about more paths lol. That's how I remember that resistors add inversely in parallel. It's like using 5 straws to drink water instead of 1.

>>8805849
Look for the essence of what the abstraction is trying to capture, don't get hung up on the language or notation.

Strive for the most minimalist explanations possible. Ask yourself "Does this piece of information need to be here?"

Always look for the simplest explanation, don't get lost in the technical jargon. Try to state your assumptions and conclusions in plain English.

>>8805885
iam beginner in general topology , sorry i cant help u anon

>>8805852
its means everting is component of component?

>>8805951
>Strive for the most minimalist explanations possible. Ask yourself "Does this piece of information need to be here?"
>Always look for the simplest explanation, don't get lost in the technical jargon

Useful tips

>>8805522
nigger have you even tried, it took me literally 30 seconds

[math]A_n=3^n+2^{n+1}, A_{n-1}=3^{n-1}+2^n[/math]
[eqn]A_n=3\cdot 3^{n-1}+2\cdot 2^n=3(A_{n-1}-2^n)+2(A_{n-1}-3^{n-1})=5A_{n-1}-3\cdot 2^n-2\cdot 3^{n-1}[/eqn]

What are some math problems that are made up of individual tasks that come together at the end?

I'm trying to find a problem to program parallelism with, to increase efficiency of. The more unique and interesting the better.

So I saw this shitpost >>8804520 and it's bugging me because it's making too much sense when it shouldn't. Can anyone explain to a guy who isn't into math why it's bullshit?

>>8806017
I'm at the other end, I dont get it at all. I don't see the relation between the roots and the dimensions

>>8805885
look at the picture of resistors in parallel here:
https://en.wikipedia.org/wiki/Resistor

you can see that in this circuit, there's a direct relation between the number of resistors and the number of holes (n-1 holes for n resistors).

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>>8804566
if someone surgically removed all of their digestive organs, how long would they live before complete systemic failure?

>>8805979
no whitey

>>8806161
You can survive for at least a month without eating. Take out the liver or the reins, I don't think you'll be well for more than a day.

>>8804566
so i've been solving some thermodynamics exercises on the side, and now my brain shut down

how do i go on about finding the entropy change for water at 110c, if im given, enthalpies of vaporization, and heat capacities for the gas and liquid phases?

im not asking for a solution, mind you, just the right equation to use, or a kick in the right direction

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https://gyazo.com/540adcf472626f9a957ac59e33f6f73a

What's the issue with this Mathematica code lads? Why won't it solve my equation?

I'm doing khanacademy, should I precalculus or trigonometry first?

>>8806381
tri

Hey guys, is the following true: Let [math]a<c<b<d[/math] and let [math]f[/math] be a convex function of [math][a,b][/math] and [math][c,d][/math], does it imply that [math]f[/math] is convex on [math][a,d][/math]?

>>8804566
studying for a stats exam, I understand all the equations and how to explain values and shit.

I just don't understand the difference between Bonferroni's procedure and Scheffe's test. I met with prof today and she said they were essentially the same thing, and judging by the problems given in the study guide, it seems like they ARE the same thing.

from the study guide:
>The method used to make planned comparisons that involves dividing the total significance level by the number of comparisons to be made is the Bonferroni Procedure.

Except I did literally that in the question before, which had us conduct a Scheffe's test, so what's the difference between the two?

>>8806402
no. of course not.

>>8806442
really? why?
Not the poster just asking.

>>8806452
define a function that is convex in [a,b] and [c,d] and concave in [b,c]

>>8806534
[b,c] is the empty set...

>>8805522
> A_n = A_n-1

Are you trying to stack overflow me on this one, son?

>>8805993
anyone?

This is probably a real stupid question, but can someone explain to me what a professor actually is? I know it's a person with a PhD who also has the academic grade of Professor and teaches at universities while doing research, and is often the head of a department (but not necessarily).

But the reason i'm asking is: in the anime Detective Conan, there is a guy called professor Agasa, and i just realized that he never taught any classes in the 800 episodes of the show. And he's too young to be retired. he mentioned being in his early 50s in some episode.

If [math]f[/math] is an odd function, how do i prove [math]f(x)=f(|x|)[/math]? i get it intuitively but dont know how to prove it

>>8806648
shit i meant even

>>8805885
Greater surface area for electron flow

>>8806648
I might be crazy, but isn't that literally the definition of an even function? How do you want to prove something that you define?

>>8806161
why is 'vagina' bolded

>>8806648
I guess one way to do it is using Fourier analysis. Show that the function is made up of a linear combination of only cosine functions and then use the fact that cosine is even. But then you'd have to prove that cosine is even, which is kind of a definition as >>8806676 said.

>>8806648
If x>=0, then f(|x|)=f(x) because x=|x|
if x<0, then x=-|x|, and f(x)=f(-|x|)=f(|x|) because f is odd.

>>8806723
I mean even, and you meant even too

>>8806534

I'm the >>8806402 poster, I don't think that you got the question right. I have two overlapping intervals [math][a,b][/math] and [math][c,d][/math] and [math]f[/math] is defined on the whole [math][a,d][/math]. Assuming that I know that [math]f[/math] is convex on [math][a,b][/math] and [math][c,d][/math] does it imply that [math]f[/math] is convex on the whole interval [math][a,d][/math]?

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I'm buying a new battery for my laptop, and I did some quick math last night to see which is a better value, an 8800mAh or 4400mAh batter. Can someone tell me if my equations make any sense? You'll see where I go with it.
So, first I calculated the [math]\frac{mAh}{\$}[/math] for each battery. This lets me know which battery has a better cost effectiveness of each battery. The larger, 8800mAh battery has [math]\frac{101.2mAh}{\$}[/math] and the 4400mAh battery has [math]\frac{88.1mAh}{\$}[/math]. So, the larger battery is 15% more cost effective. This is a nice thing to know, but it still doesn't tell me if I should bother with the larger battery or not as 15% isn't very significant in my eyes (except that a 15% cost effectiveness difference, along with twice the capacity is significant). So, I next calculated that the larger battery costs 74% more than the smaller battery.
The reason I make this post is because of the next equation, I'm wondering if it yields any useful information, or if I'm just playing around too much. My aim is to use the Cost Ratio (how much each battery costs, relative to each other) and the Cost Effectiveness of each battery, yielding something like an 'Effective Value' for each battery. The smaller battery is given a cost ratio of 1, since the larger battery is defined by dividing its cost by the smaller batterys cost.
[eqn]\frac{\frac{101.2mAh/\$ }{1.74}= 58.16}{\frac{88.1mAh/\$ }{1}= 88.1}= \frac{58.16}{88.1}= 0.66[/eqn]
So, the larger battery has an effective value of 0.66, meaning the smaller battery is a better option. Is my math and logic sound, /sci/?

>>8806755
>meaning the smaller battery is a better option.
I think it's only the better option if you plan to buy more than 1 battery. Look at the denominators of your final equation (1.74 and 1). The unit is effectively "number of small batteries costwise". So it's saying you can get almost 2 small batteries for the price of 1 large battery. So what you calculated as .66 is the ratio between the small and large batteries' mAh per dollar per # of small batteries. I'm not sure what these units mean and if maximizing it is any use to you, but that's just something to consider.

>>8806711
for emphasis
why else

>>8806432
anyone?

>difference between Bonferroni's procedure and Sheffe's test

>>8806788
Thanks for that insight, that helps me think about this better. I'm not trying to maximize any value, there's no variables, I'm just trying to see which battery has a better value.
Essentially, I should've began with this: 74% more for twice as much capacity. So, obviously from this we see that for less than the price of two small batteries I get the capacity of two small batteries. Thanks anon, my original equations were sleep-deprived pillow thoughts.

>>8805849

Don't think of it as abstraction, think of it as minimalism. A good way to get started is to think in extremes, think about the boundary of a concept. How much can you remove from a definition without losing the meaning of the concept? After how much removing does the thing become indistinguishable from anything else?

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What do you think of the scientific field of Psychology?

With all else held constant, why does increasing the radius of a pulley increase its angular acceleration?

>>8804623
Because he sounds like faggot with helium in his lungs

Is there any kind of complete CompSci course online?
I mean, no missing CSXXX

>>8806648
A function is even if f(x) = f(-x).

If x > 0, f(x) = f(/x/) since x = /x/.

If x < 0, f(-x) = f(/x/) since -x = /x/. But f(-x) = f(x) by definition. Therefore f(x) = f(/x/).

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what am I doing wrong here. Never use excel and keep getting error for this formula. Just trying to take average of cells in B only including numbers that are greater than 300 and less than 1600.

studying probability

if my random sample size of my population is equal to the size of the sample space, i essentially get the distribution of the sample space right?

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>>8805074
>>8806857
REEEEEEEEEE
WITEN HAS AWAKEN

What is sci's opinion on introduction to mathematical proofs courses?

They're required at my university and surprisingly people don't know this shit. The people going into teaching are the ones that usually don't know it beforehand (it's a third year class).

The important naive set theory and proof techniques can be covered in a week long seminar or something equivalent to be honest.

>>8807017
probably the most important math class you'll take. not for the content of what you learn, but because it teaches you how to think. if you can't do proofs on that class then you'll struggle in algebra, analysis or any other proof class

how do I prove that

[eqn](\forall \epsilon \in \mathbb{R})(\forall \delta \in \mathbb{R}) ( \epsilon < \delta \Rightarrow \delta > \epsilon ) [/eqn]

>>8807017
probably the least important math class you'll take. mathematical maturity cannot be taught nor can anyone other than yourself supply you with lucidity. It is a waste of time course and something that we in the business call "brainlet life support"

>>8807031
trivial

>>8807031

i think use contradiction, then contradiction will arise immediately because you will get something like A and not A are true.

ATTENTIONAL STATISTICIANS

WHAT THE FUCK IS DIFFERENCE BETWEEN SAMPLE MEAN AND MEAN, OR VARIABILITY WITH STANDARD DEVIATION

>>8807031
Change > for <.

>>8807046
the average IQ among all people is 100. Alice and Bob have IQs of 110 and 95, respectively. Mean=100, sample mean=102.5.

>>8807031
Usually a < b is the only thing defined, and b > a is shorthand for the same thing. You also usually have trichotomy, which says for all a and for all b, exactly one holds: a < b, b < a, or a = b.

So with this in mind, it's going to depend on what axioms you have and what definitions you were given.

>>8806845
it doesnt

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>>8807017
>its a third year course

Are there cool things you can do with sets?

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>>8804566
hello.
how the fuck does a secondary spermatocyte with one n chromsome produce two cells with n chromosomes?
Does this diagram mean that primary spermatocyte has 4n, then secondary spermatocyte 2n and the spermatids and spermatozoa n?

>>8807046
Read ur friggin book

>>8807247
nope. literally nothing.

>>8805539
Wouldn't quantum computing make deep learning more efficient?

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Suppose I had the following:

Random variable $$Y = X_1 + X_2 + ... + X_n$$, where $$X_i$$ are independent and identically distributed.

I know that $$E[Y] = n * E[X]$$.

What is $$Var(Y)$$?


$$Var(Y) = Var(X_1 + X_2 + ... + X_n) = Var(n * X_i) = n^2 * Var(X_i) $$?

Or because the $$X_i$$ are independent, can I just claim that $$Var(Y) = Var(X_1) + Var(X_2) + ... + Var(X_n) = n * Var(X_i)?$$

>>8807365
yeah variance of independent rvs is the sum of the variances

>>8807325
difference between homologous chromosomes and sister chromatids and understanding what n is referring to.

primary spermatocyte will have 2n=46. each pair of homologous chromosomes is formed of 2 sister chromatids. technically you will have 92 total chromosomes but n represents chromosomes in a single set

meiosis I gives 2 secondary spermatocyte by separating the homologous chromosome pairs (but each pair is still composed of 2 sister chromatids). this is considered n=23 because once again n refers to chromosome sets and not sister chromatids and each secondary spermatocyte has half the chromosome set.

During meiosis II the sister chromatids are separated giving rise to 2 cells that are also considered n=23.

I don't know if that explanation is fully correct or even understandable because I just skimmed through my old bio book. But just review the terms for chromosomes and what n means and draw out an example of meitosis and meiosis with a small set of like 3 chromosomes

>>8806738
ok, so then yes.

One easy way to interpret convex functions is to say that it's functions such that [math] f'' > 0 [/math] (when you can calculate the second derivative).

So if f'' > 0 on [a;b] and f'' > 0 on [c;d], then clearly f'' > 0 on [a;d].

Got a stat question. One of my teachers told me to get the eta-squared or η2 from a Kruskal-Wallis test and I got a negative value. What does this mean? A negative correlation?

How hard is it for a computer science major to get into computational science?

>>8807243
You can take it your first year if you took calculus in high school (here anyways). Its only prerequisite is linear algebra.

Does anyone know about david bohm and the pilot wave theory ? what does it change in respect to the copenhager interpretation?

link related couldnt read the full story though

https://www.newscientist.com/article/mg23431200-200-realitys-comeback-the-hidden-network-that-controls-what-we-see/?cmpid=SOC|NSNS|2017-Echobox&utm_campaign=Echobox&utm_medium=Social&utm_source=Facebook#link_time=1491403994

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I can't wrap my head around these. Where do I start? Fucking radians and shit.

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I had a physics test today, and I got stuck on this question:

>Michaela likes to go to an amusement park with water slides. The height of her favorite water slide is 8.2 metres. What is the max velocity she would achieve going on this slide, given that the force of friction is excluded and doesn't have any effect on the process?

I'm pretty sure it has something to do with gravity "g = 9,82", and that her mass is irrelevant(?) because the force of friction is 0. I might just be stupid or missing something since the rest of the test was a lot easier than this question.

I'd appreciate any help guys.

>>8807869
translate the height energy potential into kinetic energy

>>8807835
1. is just applying the inverse of sin on both sides.

2. are just the solutions to cos(x)= 0 and (x-6/x)=0

>>8807869
[math] E_g = E_k [/math]
[math] mgh=0.5mV^2 [/math]
[math] \sqrt{2gh}=V [/math]
[math] \sqrt{2\cdot9.8\cdot8.2}=12.67ms^{-1} [/math]

>>8804566
Best all rounder book for topolgy

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>>8807990
Thanks man!

>>8807869
the answer that your professor was looking for was >>8807990
but you could also solve it with [math]x=v_it+\frac{a_0}{2}t^2[/math]
[eqn]8.2=0t+4.9t^2 \\ t=\sqrt{\frac{8.2}{4.9}} \\ v_f=9.8\sqrt{\frac{8.2}{4.9}}[/eqn]

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anyone recognize this molecule? what is it?
I'm guessing some kind of an illegal substance...

>>8807986
actually, those are wrong answers man.

>>8808124
Tryptophan?

>>8808155
doesn't look like it.

btw, that's a tattoo on some dumb bitch's leg. can't be something interesting.. must be some kind of a drug to get you high...

>>8804566
What Pre-Calculus and Calculus books should I get if I want to get into math as a hobby and as a way to forget about pathology?

>>8808161
Didn't notice the nitrogen, it's been a while since I touched biochem/ochem.

Yeah, given that its a tattoo, it probably is something edgy. A drug would be the obvious assumption, maybe something to do with a type of medication, or something to do with some sort of illness she has.

>>8808155
>>8808124
Looks like DMT

>>8808196
>DMT
WINRAR! Thanks anon. Def DMT. kek.

>>8808161
It's DMT. The God molecule. Looks like your "dumb bitch" is more profound than you think.

https://en.wikipedia.org/wiki/N,N-Dimethyltryptamine

>>8808246
>The God molecule
>more profound than you think
you're an idiot. post less.

I've got an inductor between two resistors. When getting the total resistance, do I just ignore the resistor after the inductor since it doesn't affect it in any way?

So the Jacobian for the change of variables [math]f: x,y \to u,v[/math] [eqn] J = \left|\begin{array}{cc}
\frac{\partial u}{ \partial x} & \frac{\partial u}{ \partial y} \\
\frac{\partial v}{ \partial x} & \frac{\partial v}{ \partial y}
\end{array} \right|[/eqn]
where [math]f(z) = u + i v[/math] is analytic. I'm supposed to show [math] J = |\frac{\mathrm{d} f}{\mathrm{d} z}|^2[/math] but as far as I can see
[eqn]
J = \frac{\partial u}{ \partial x} \frac{\partial v}{ \partial y} - \frac{\partial u}{ \partial y} \frac{\partial v}{ \partial x} = \left( \frac{\partial u}{ \partial x} \right)^2 + \left( \frac{\partial u}{ \partial y} \right)^2 = 0
[/eqn]
Where I have applied the Cauchy-Riemann equations for [math] v_y [/math] and [math] v_x [/math].
Since for any analytic function [math]f(z) = uj + i v[/math], u and v seperately obey Laplace's equation.

Where am I going wrong, if indeed I am going wrong?

>>8806755
Also take into account that the larger battery has less chance of completing a full drain cycle thereby further increasing it's life. Practically speaking

>>8808324
Why is the last part zero?

>>8808376
Oh shit I'm retarded.
I was thinking of [math] \frac{\partial^2 u}{ \partial x^2} + \frac{\partial^2 u}{ \partial y^2} =0 [/math] which is clearly not the same thing as what I wrote.

1)Take n number of things out of which p are identical to one another and other q are identical to one another.
Total number of arrangement of n number of things among themselves without repitition is
nPn = n!
2)But total number of unique arrangement is
nPn / (p! * q!)

>How do i conceptually and logically infer 2 from 1?
Please explain.
Don't give example to prove this.
Best is to give pure mathematical path of infering 2 from 1.

I want to buy a hand-held thermometer to measure air temperature wherever I go, would this one be a good choice for my purpose?

http://www.omega.com/pptst/TPD36_TPD37.html

>>8808011
munkres

>>8808324
If [math]z=x+iy[/math] and [math]f(z)=f(x,y)=u(x,y)+iv(x,y)[/math], and [math]\frac{\partial z}{\partial x}=1, \frac{\partial z}{\partial y}=i[/math], and [math]\frac{\partial k}{\partial t}=1/\frac{\partial t}{\partial k}[/math]. Now: [eqn]\frac{df}{dz}=\frac{\partial f}{\partial x}\frac{\partial x}{\partial z}+\frac{\partial f}{\partial y}\frac{\partial y}{\partial z}=(u_x+iv_x)\cdot 1 + (u_y+iv_y)\cdot\frac{1}{i}[/eqn]
[eqn]=2u_x-2iu_y\Rightarrow \left|\frac{df}{dz}\right|^2=4u_x^2+4u_y^2[/eqn]
which is off by a factor of 2 (4)
:thinkan:

>>8807501
Sure my friend, but there is a problem here, I don't assume the differentiability of the first derivative. Well I know that the result has to be true, I just don't know how to prove it.

Is there or has there ever been a project in physics to find connections between physical constants through dumb calculational force? I mean, take Faraday's constant, which turned out to be Avogrado's number times the elementary charge; or Stefan-Boltzmann's constant, which contains h, c, pi and k. Methinks it may be possible to find hidden connections such as these.

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OK, I'm stuck on step B. I believe that I'm adding one Cl to the benzene ring, but I'm not sure where. Once that's done I have a good idea about what to do for step C (another friedel-crafts alkylation)

>>8808669
I'm pretty sure you get a syn-addition of chlorine at two adjacent carbons on the benzene ring. As for where, I'm not sure, but the two chlorines are gunna be next to each other.

>>8808530
Yeah I already got it when I realised this >>8808387

you can verify pretty easily that
[math]\frac{\mathrm{d} f}{\mathrm{d} z} = \frac{\partial f}{ \partial x } = \frac{\partial u}{ \partial x } + i \frac{\partial v}{ \partial x } [/math]
hence
[math] \left | \frac{\partial f}{ \partial z} \right|^2 = \left( \frac{\partial u }{\partial x} \right)^2 + \left( \frac{\partial v }{\partial x} \right)^2 = \left( \frac{\partial u}{ \partial x} \right)^2 + \left( \frac{\partial u}{ \partial y} \right)^2 [/math]

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are black holes the merger of the 3rd and 4th dimensions?
would a 2 dimensional entity see something like a black hole as a 3 dimensional entity passed through/near 2d's space

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Can any of you nitwits identify the skeletal formula behind this Pepe?

>>8808729
tert-butyl lithium, thiophenol, and sterol that's been functionalized with a protected sugar derivative?

>>8808744
thanks pal

Is there any trouble with saying 0/0=the set of all numbers?

>>8805522
Geometric sequence sum, so its the homogeneous solution to a second order linear difference equation. Eigenvalues = 3 and 2.

An+2 - 5An+1 + 6An = 0

This is the most general recurrence relation for your sequence. You'd also need to state the two initial conditions, A0 = 3 and A1 = 7.

>>8808074
[math] x=v_it+\frac{a_0}{2}t^2 [/math]
[eqn] 8.2=0t+4.9t^2 \\ t=\sqrt{\frac{8.2}{4.9}} \\ v_f=9.8\sqrt{\frac{8.2}{4.9}} [/eqn]

>>8808850
Yes, because division by 0 is literally undefined.

>>8808885
why can't you just define it?
like why not define 0/0 = 3?

>>8808892
0/0 indeterminate forms of limits and stuff would all get fucked over if that were the case. It needs to remain undefined/indeterminate to have any utility

>>8808892
Because that is not how maths works?

>>8808892
>why can't you just define it?
you can

https://en.wikipedia.org/wiki/Wheel_theory

>>8808899
>that is not how maths works
I've been learning mathematics for a while and basically every area of maths I've studied has started off from axiomatic postulates and definitions, and proceeds to find the logical consequences of those postulates and definitions. You can define whatever you want as long as you proceed carefully and avoid logical contradictions.

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So I'm obviously thinking something completely retarded here, but does f = -1, g = 1 instantly contradict this question?

>>8808885
But algebraically, 0/0=x is just an equation with every possible number as a root.

>>8808913
Defining x/0 as anything that's not either inifinite or undefined would contradict a whole lot of other postulates and definitions that already exist though. You would have to find a way to logically redefine everything at that point.

>>8808916
go read what positive definite means

Can you use arrow notation with imaginary numbers? Like [math]2\uparrow\uparrow i[/math]

>>8808932
And there's where I'm being retarded. Ta anon

>>8808542
I tried doing a proof from the definition but I couldn't go anywhere.
I guess you could try a geometric proof, or stay with local properties, only just using the first derivative, which is a growing function (so this would be easy if you can use this, you can check wikipedia for the exact properties).

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Can someone tell me what happened between (3) and (4)? Is there an error? I know you're supposed to do the +1-1 trick to get the equation set for inverse Laplace transformation but I can't figure out what to add and subtract to get it like in (4).

>>8809101
(3) is wrong, since C=D=-1 the numerator should be s+1

Explain general relativity and string theory to me without a whole load of bullshit jargon

>>8808124
It's Dmt you fucking normie

>>8809120
> general relativity
mass warps space-time

> string theory
utter bullshit designed to sell pop-sci magazines

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Does anyone know what maths are important for data entry/data administration?

For example, I'm taking linear algebra rn. Is it useful for the job?

What if Earth had as many moons as Saturn?

>>8809175
We would have a calendar in 13 dimensions. There would have been a cast of mathematicians devoted to manage the calender and walk the population through it. Then people would get angry at mathematicians priviledge, and would burn everyone that uses math in more than one dimension.
That's about it.

>>8809198
I kek'd

I watched a video about the fat indian man of infinity and it made it seem like infinite operations other than sums(infinite exponents, infinite roots, infinite fractions, etc) are trivial to reduce. Are they really, or am I just lacking imagination?

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>>8804566

Hi /sci/, hopefully someone can help me out with this or point me in the right direction.

If given the following:

Weight: 165 lbs.
Height: 6'1"
BF%: ~14

Intake (per day)

Liters of water: 2
Grams of Carbs: X
Grams of Fat: Y
Grams of Protein: Z

Is there a method with which I can calculate how much I can increase my testosterone per 1 chin-up, assuming I do each chin up the exact same way?

I'm currently just taking note of things that are obvious signs of test increases:
-pits begin releasing that* odor
-skin getting a little more oily
-backne
-voice dropping a bit
-faster arousal, harder, lasting longer

These are all easily detectable but I want to know for sure what kind of limits there are per actual chin up. Do I stop getting an increase after 100? 1000? I'm going to keep doing this by trial-and-error anyway but I was curious if there was a more precise way of measuring test increase since I know it does increase a little during and after exercise.

Under what conditions on [math]f[/math] do we have [math]\sum_{i \,=\, 0}^n f\left(n\right) \,=\, \underset{n \,\to\, \infty}{\Theta}\left( \int_0^n f\left(x\right) \,\mathrm dx\right)[/math]?

>>8809173
you're mom's bum is a good data entry point

>>8804566
No because quantum computers are over-hyped.
Quantum computers do not have an infinite number of outcomes, only 2 (thus still binary). It's the same shit as a normal computer, but much smaller.

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Can any circuit fags help me out? This seems simple but I just don't have the fundamentals and i`m lost.

>The shunt regulator is used to short out the array to ground when the solar array output exceeds the requirements of the loads.
>The isolation diode prevents other arrays or the battery (which are connected in parallel, but not shown) from putting current through the array in the reverse direction

What does it mean by "short out array to ground"?

In algebra we use the quadratic formula over and over again before they prove it in calculus.
Why do we use the thing before we prove why it works?
It seems idiotic.

>>8808669
>>8808684
I fucked this up. It's anti-addition.

>>8809215
I don't really know what you're speaking about, but usually, a lot of the trouble in infinite operations is verifying if it converges, ie: showing that the limit does exist. In some cases, it might be easy to calculate a certain expression/limit/whatever, but you do that assuming that such an answer does exist. Real analysis is mostly about finding out when one can do such calculations, while calculus is about actually doing them with the assumption that there's a unique answer.

A good example to how dealing with infinity isn't too easy is the Riemann rearrangement theorem, which says that any conditionally convergent infinite series (ie: not absolutely convergent), can be rearranged to sum to any real value, and even can be shown to diverge.

>>8809574
an example of a conditionally convergent series is [eqn]\sum_{k=1}^\infty \frac{(-1)^k}{k}=\log 2[/eqn] but can be rearranged to diverge by making it look like the harmonic series [eqn]\sum_{k=1}^\infty \frac{1}{k}=\infty[/eqn]

>>8809564
ground is a capacitor with a theoretically infinite maximum chage that it cn store, and the name of this pretend capacitor is the ground beneath you, earth.

This circuit diagram seems to be a solar array diagram. The basic premise (from what i can infer) is that "[Shorting] out (the) array [into the] ground" is reffering to the rerouting of the electrical current into the ground, instead of into the load (which i assume is a capacitor bank with a high amount of ferads).

I learned this is grade 12 anon, i dont know how you did not know this (and also i am not al electrician so if you plan on carrying out this circuit consult and expert first).

tl;dr - "short out array to ground" means redirecting power into ground so that load is not over-encumbered.

>>8808246
>DMT molecule tattoo

Gutter trash. One night stand and nothing more.

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>>8809762
>2/10 would not bang

Is there an accepted model to use to describe water flowing out of a bottle w/ a particular nozzle? I imagine there would be some complications w/ the pressure in the bottle as well as a bottleneck occuring depending on the width of the nozzle.

>>8809784
but he just said he would bang you retard

>>8809566
You don't need calculus to prove it. Complete the square on the general form of a polynomial.

>>8806534
so... just a 4th degree polynomial....

>>8806602
Are you trying to find problems to hit with your GPU hammer?

>>8806629
So, first point - shit's not real so please don't gauge actual professor status based on TV.

Second, academic job titles vary depending upon the institution (there's no golden rule saying what make/does not make a "professor"). Typically the path to Professor status is limited by availability of funds in the department the professor belongs to (as tenure is typically guaranteed as a professor) as well as the individual's success and future potential. It's really akin to any job promotion where the dean will try to promote those most capable in order to retain them so they can contribute in the future for research funding, prestige, or other functional responsibilities the department has to maintain.

>>8806719
That's like fixing a clock with a sledgehammer. I'm a huge fan of Fourier, but I think it's just easier to explain that the person asking this question was just fucking re-phrasing the goddamn definition of an odd function, then asking "why."

>>8806845
With what you said,

"all else being constant" = angular velocity is constant.

angular acceleration = d()/dt of angular velocity, = 0

Now if you mean centrifugal acceleration, then yes the acceleration increases (a = v^2/R, if v increases, so does a).

>>8806952
This may be easier to accomplish by performing the logical operations of ">300" and "<1600" separately (i.e. making new columns that are either the value if they fall in the range specified, or a blank space, "") then averaging the result. I've only used averageif with only 1 conditional statement. I haven't tried two at the same time before.

>>8809873
Oh. I never tried it.
Okay. Well thanks anon.

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After viewing the images of children that had been killed in Syria, I have two questions. Why were their cheeks so flushed in some of the images? They looked in part like they had been in a sauna or on a brisk jog for sometime. Is that due to the acetylcholine overactivity of exposoure to sarin? What is that particular posture or pose called affected by people suffering damage to the brain, spinal cord, or nervous system? There are two variations. The only one I can visualize is the arms parallel side by side and the palms go out facing outward. There's another one too but I can't visualize it.

Thanks

This is by no means a covert post, and I have no interest in discussing anything else except maybe the realistic fear one might have of nerve agents in future warfare. If it's better to take this to /pol/ or /k/ let me know, but I think the /sci/ expertise will be lacking there...

>>8808291
Resistance calculation implies don't consider frequency dependence (treat the inductor as "0" resistance at DC). If they ask for the impedance, then you usually need to consider a certain frequency (usually specified by the question). The impedance of the inductor is j*2*pi*f*L (j = sqrt(-1), L = inductance, f = frequency).

>>8809215
It always seems impossible until it is done; then it is trivial.

>>8809561
woooo hooooo!!!!

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Say I have 2 things in line, and I pivot one by say 30 degrees, how do I find the length of the red arrow? Its for a personal project, and basically after I twist the object on the right I need to know the exact amount to move the object so that left most point of the object lines up with the right most point on the left object, sorry I suck at math.

I saw some video on YouTube explaining .9 repeating = 1 how would you prove this to be false or is it just a true statement?

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how do you get

$\hbar$^2/I


In case my latex does not work that is

(reduced planck constant)^2/(moment of Inertia)

>>8809995
h=(L/2)sin(theta), where h is the length of the red arrow, L is the black line length, and theta is the angle

>>8804566
Is there a name other than reals for the set of reals excluding interfere and rationals ?

>>8810018
>excluding interfere
>interfere
what?

>>8810018
irrational?

>>8810018
irrational numbers

>>8805505
What is superposition?

Can all quintics be solved with bring radicals? Or just some that you can't solve normally, but not all?

just trying my latex

[math]\epsilon[/math]

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>>8810191

[math]\sqrt[3]{e^{i \pi}}[/math]
[math] \sqrt[3]{e^{i \pi}}[/math]
[math] \sqrt[3]{e^{i \pi}} [/math]

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>>8809995

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>>8809566

How do we make it illegal for teachers, at all levels, to make students learn a theorem/identity without first proving it?

>>8810243
but that would be stupid, are you a freshman? there's plenty of times where it's useful to know a theorem but not yet need to go through the machinery of proving it

>>8810249
primary schoolers should be forced to study the foundations of mathematics

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>>8810258
agreed

I am really fucked anons

I have to give a presentation to my PI today updating on my project status

What are some bullshit excuses or technological mishaps that can get my ass out of this mess?

Please help anons

Electric field inside a conductor is zero? Is that true even if I put the conductor in electric field?

>>8810290
Anons please

>>8810409
Yes

>>8810290
dog ate homework

>>8810441
Like my computer crashed or some shit? Idk what to exactly say

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Can someone remind me how to get the alkene at the end? I am able to get the bottom structure but I'm blanking on what to do next

>>8810444
you crashed your car into your homework

>>8810469
Don't you have to use a thicc base to get that sweet sweet Hoffman elimination?

>>8809784
>Dating a girl who permanently inks a fucking dmt molecule on herself

Words can't describe how much of a beta bitch you are.

>>8810178
There exist quintics that can't be solved by radicals.

>>8810681
he asked about bring radicals

https://en.wikipedia.org/wiki/Bring_radical

>>8810258
This was tried in France. It failed miserably. It was called "maths modernes".

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>>8810785
bourbaki for grade school

Is learning to read/speak multiple languages helpful for someone majoring in math?
If so which one which ones?
I think I saw someone where that French, Russian, and German were recommended.

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I'm kind of confused about this question. It's asking me to write an equation of the function. The only information I'm given is that it is a sine function, with a zero of (Pi/4,0) and a max of (3Pi/4,2)

Trig is easily my worst subject. My best attempt is y = 2sin(4x) It gives me the correct zero, but I don't think the max adds up the the coordinate. It's making me angry because I just know the answer is probably something super simple I'm just not getting.


Taking a pre-calc course online was easily the worst decision I've made so far in college.

>>8810916
What do you mean by 'a sine function'? For example [math]1+\sin (-x)[/math] works, but is it allowed? Using other multiples of [math]x[\math] should do the trick, the 2 is right.

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>>8810941
I'm not completely sure. I think it may have glitched out/they messed up. Here is the exact wording.

I think, by what it says, there was supposed to be a graph picture to go along with it, but something went wrong/they forgot to add it.

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>>8810916
Pic related is what you want.

If you want to know how to do it, review transformations:
How do you expand a curve?
How do you shift a curve to the left or to the right? Up and down?

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>>8810916
Fuck, I misread it. This is how it looks:

Same thing. Transformations.

>>8810945
Without the graph we really cannot know. Scaling the argument doesn't work like I thought. Just try what >>8810957 did.

>>8810953
>>8810957
>>8810965

Thanks! That definitely gives me more to work with than I was given (see >>8810945
So, just from looking at your graph. I was right in assuming the first part is 2sin? Since the part before the cos or sin is the amp.

Also, I'm not incredibly good with knowing pi conversion off the top of my head, but the second notch after 2 would be 3pi/4 right? Or is it the green line? Still not sure how the space between would translate to pi.

>>8810965
>Scaling the argument doesn't work like I thought. Just try what >>8810957 did.

sin(x) has a max at 1. You want to make that max grow.

If you multiply the argument are you are doing is feeding the values of x "faster" so the max will still be at 1, but they will be more abundant.

But what happens if you scale the function outside of the argument? Like, say, 5sin(x)
Does that affect the max?

>>8810968
>I was right in assuming the first part is 2sin?
Yes, indeed you have to escale it by 2 (why?)

As for wha the graph is:
The green line is x= pi/4. That way you can see that it has a root there as requested.
The greenish brown line is x=3pi/4, to show that it has a max there as requested.

You are getting the idea now. You vertically modify a function by affecting it from the outside (like multiplying it by two). Now, how do you modify a function horizontally?

>>8810972
Well, from the original instructions it gave me, the max was said to be at y of 2.

For functions to shift horizontally, you have to add or subtract numbers from inside of it. I know it's the opposite the the -+. So, assuming it starts at 0,0 I would need to 2sin(x-3pi/2) to move it right?

>>8810981
*meant 3pi/4

Given this libreoffice command:

HYPGEOM.DIST(X; NSample; Successes; NPopulation; Cumulative)

>X is the number of results achieved in the random sample.

>NSample is the size of the random sample.

>Successes is the number of possible results in the total population.

>NPopulation is the size of the total population.

>Cumulative : 0 or False calculates the probability density function. Other values or True calculates the cumulative distribution function.

Consider: Two players have 10 cards each, face down. Player one flips a card over and gets a 6. What's the probability of player two flipping a card less than six.

Is this the right way to use the command:

=HYPGEOM.DIST(1,10,4,52,0)

It gives ~42.4%. It seems to make sense, since there are only four cards beneath six which could be lower and eight cards above it which are higher. Just need to be sure of this.

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>>8810983
Pic related is my function compared to yours.

Remember, you can always verify if your solution by graphing it or plugging in values and seeing if it has what you were asked for.

What would happen if a black hole absorbed a black hole?

>>8810998
I figured out the period is pi/2. So far, I'm getting to 2sin(4x) But I can't seem to get it over correctly.

I tried adding and subtracting in side the sin (4x - number) and outside but it changes both the period and everything else.

>>8811035
Answer is [math] 2sin(x - \frac{\pi}{4}) [/math]

>>8805849
What is this image trying to communicate?

>>8806711
To indicate emphasis

>>8811057
Thanks. I really think they messed up on their end and I was supposed to get a graph to go along with it.

>>8807046
Standard dev is the square root of *variance.

>>8807376
I second this, good explanation

>>8811067
You should be able to do this without a graph and if you need visual aid you at most need to graph sin(x) to be able to more easily see what happens when you shift it by pi/4 units.

>>8808183
Stewart's 7th

>>8810970
No nigga. Its max is at multiples of pi/2

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what the fuck is this garbage? what calculator do i need to get proper rounding?

>>8811084
I meant that 1 is the max.

>>8811085
it says "fix" in the lower one, that might have something to do with it

What if the electric field acting on a conductor is so large that electrons inside it are unable to cancel it?

I took college biology I & II out of interest and was disappointed because it didn't answer a question I had deep down.

So I know how a cell works and all that fun stuff, but what causes all of the cell parts to preform their functions? Like what causes the rna transcriptace to do its thing? Is it a complicated chemical reaction we have a formula for? Is it magic? Or am I asking the magic question of life we haven't answered yet?

>>8804566
Im on day three of no sleep after exams and I just couldnt stop studying I started looking into Alchemy. I don't believe there is full on TV magic but reading what I have for hundreds of years the top minds in the world believed they could find the elixir of eternal life am I losing it or is there something here

>>8811129
Easy. A long time ago God said:

BRRRRRRRRRRRRRRRRAAAAAAAAAAAAAPPPPPPPPPP

>>8811092
Oh. Then yes. 5sinx will scale that 1 up to a 5, then.

>>8811129
Bound RNA t-ase has a lower energy than RNA t-ase in solution does, so the enzyme in solution binds into the more stable state spontaneously

>>8811137
So life is a series of complex chemical reactions that just so happen by coincidence?

Is Real Analysis just a continuation of Calculus?

>>8805505

Measure the testpoints

>>8810794
kek

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how should i start part b) of this problem?

Why does this keep giving me a random number of 0?
Visual studios 15
| Dim X As Integer

Public Sub Window_Loaded(sender As Object, e As RoutedEventArgs)
Dim Ran As Random
Ran = New Random

X = Ran.Next(1, 11)
End Sub |

I'm depressed guys.
I think my friend has schizophrenia
https://www.instagram.com/brittan_younger_chance/
Listen to his findings
Cure to cancer

>>8811288
> posting self pictures on instagram
> relevant

wat ?

>>8811362
I am now talking Calc 3 and we are already beyond the part about constructive curves in the plane, space and n-space and I thought about this probem:

Given a continuous curve from R to R^n, what is the n-volume of the smallest box that contains the entire curve.

The simplest version would be a curve in two dimensions. What is the smallest rectangle that you can make around the curve.

My question is, is there any literature about this? This sounds like something that would have been solved a long time ago? I tried googling but all I get is "curve sketching" links.

>>8811391
What do you mean? You can project the curve onto each coordinate and take the product of those intervals.

how can i solve for v (or approximate if not solvable)
[math]\frac{dv}{dt}+av^2=\frac{u}{m}\frac{dm}{dt}-g[/math]

where a, u, g, and dm/dt are constants?

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>>8811402
Pic related. Squiggly thing is the curve and the box around it is a rectangle that surrounds the curve.

Is there a way to determine the smallest area such a rectangle can have depending only on the equation of the curve and that works for all curves?

>>8811409
(assuming this is for an interval of an equation) you can find the y-values of the global minimum and maximum, subtract them, and multiply by the interval length

>>8811421
Oh, you are right. This clearly becomes a problem of finding the global maximum. So I see the answer is no then.

>>8811405
i guess more generally i could have put this as
[math]\frac{dy}{dx}+ay^2=\frac{b}{t}-c[/math]

>>8811405
Is that the equation of motion for a rocket?

>>8811473
yes

>>8811484
Why is your velocity squared?

>>8811546
Whatever i see now that it's air resistance.
Well for starters note that mass is [math]m_0 - kt[/math] with k being the derivative of mass and [math]av^2[/math] should be [math]\frac{a}{m}v^2[/math].
Now as you can see you can't solve using separation of variables and you just give up.

>>8811546
thats for air drag. a actually = [math]\frac{C_dA}{2V}[/math]

Can someone explain me why the standard model is incompatible with general relativity?

>>8811577
It's not incompatible, it's incomplete, i.e. you can't explain gravity with quantum mechanics.

But it LITERALLY doesn't matter in any conceivable way. Even if we did somehow magically acquire the knowledge that completes the standard model, we wouldn't be able to do anything with it. The logic for this assertion is as follows:
Imagine it were possible for us to create a machine that utilizes some aspect of formerly mentioned magically acquired knowledge in order to function. If we were to build this machine(which we are assuming we are capable of doing), then whether or not this machine actually operates, acts as a test for our hypothetical theory of everything. We know that we can't test a theory of everything, therefore we actually can't build this machine, therefore even if we DID know the truth, we could do nothing with this knowledge.

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What do you need 1+1+1... = 0 for?

Math question, Linear System:
Given this system:
x+y-z=0
Mx+2y-3z=0
4x+y=0
Assuming that this system has infinite solutions, what's M?


I have been dying the entire night trying to solve this and I wasn't able to. The answer I got from fucking around with this system was that it is either impossible or it's -1, but this -1 was obtained through hours of meditation and fucking around and it's probably wrong.

>>8804566
how the fuck are we going to make a machine to read a quibit. the only closest thing to infinite data storage is in light induced spin crossover coupling of an iron coordination compound.

>>8804566
So hypothetically speaking, if a spaceship had an endless supply of fuel and was accelerating constantly at say a steady 1g, how long would it eventually be forced to slow down because of the speed of light or would it simply never reach the speed of light and be able to continue accelerating at that constant rate but gaining less speed over time?
I ask because I want to write a story and I figured the ship could use thrust to produce artificial gravity for the crew but over a very long time, and I don't know if this would work over long stretches of time (decades).

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>>8811610
In abstract algebra, you have fields. Fields, themselves, have characteristics, and the characteristic of a field is either:
>the minimal positive integer n such that the sum of n identity elements of the field's multiplication (denoted by 1) is the identity of its addition (denoted by 0)
>or if such a number n doesn't exist the characteristic is infinite

An example would be the (finite) ring [math]\mathbb{Z}_p[/math] of the congruence classes of a positive integer [math]p[/math]. If this integer is prime, then (this is known) the ring is a field. Moreover, its unit or the "1" is [math][1]_p[/math], and (if you are unfamiliar with these things, show that the remainder of the sum, resp. product, of two integers is the sum, resp. product, of their remainders) [math]\underbrace{[1]_p+\cdots [1]_p}_{n \text{times}} = [p]_p=[0]_p[/math], giving you an example of a field of a finite characteristic. This is what the Unabomber has in mind.

Since characteristics are algebraic invariants, they give us a simple way to see if two finite fields are isomorphic.

>>8811614
Pick M such that you have only have 1,2 linearly independent vector, those vectors will span a line, plane, and will provide infinitely many solutions.

>>8811656
>Since characteristics are algebraic invariants, they give us a simple way to see if two finite fields are isomorphic.
what do you mean by this? there are finite fields with the same characteristic that aren't isomorphic (F_p and F_{p^2})

>>8811672
Shit, I meant that they aren't. My bad.

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>>8804566
Hello everyone. ive done everything in my power but i cant seem to get the right answer. do you guys know what it is?

I can only calculate C, but the correct answer is apparently E

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What the fuck? That's my question

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Could someone explain to me a good way of telling if a Language is regular or not on sight? My professor said there will be some yes/no circle answers for the mid term and its not really easy for me to tell if something is regular or not on sight.... some things are counter intuitive for Languages as seen from past experiences...

Help please will love any useful info

>>8804566
if i have this operation

[math] \frac{d}{ds}[g(y)\frac{d}{ds}f(x,y)] [/math]
where
[math] ds = dx \sqrt{1+ \frac{dx}{dy}} [/math]
can i do this?
[math] \frac{1}{\sqrt{1+\frac{dx}{dy}}} \frac{d}{dx}[g(y)\frac{1}{\sqrt{1+\frac{dx}{dy}}}\frac{d}{dx}f(x,y)] [/math]

and if possible is there a proof for it

Why are basic arithmetic operations ambiguous when it comes to sets? Like, why does A + 5 not unanimously mean "add 5 to each element of A"?

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Retard question:

In a hypothetical situation where all of pic related ceased their existence and thus substracted from your system, what would be the closest approach to replace them/ survive without them, assuming that in this imaginary situation, cessation of all biological functions occurs only a week after such event?

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To all the analysts:
Is this even true? I went through the working out and found that delta<epsilon/(2c+1); how can delta<epsilon/c work?

>>8805508
>fasten
LOL

>>8812022
[eqn]\forall\varepsilon > 0 \exists\delta_{c,\varepsilon} > 0 \forall x\in\mathbb{R} (\lvert x-c\rvert < \delta_{c,\varepsilon} \implies \lvert x^2 - c^2\rvert < \varepsilon)[/eqn]
set x=0

>>8811865
because + is already reserved for the disjoint union, and that gets precedence because sets can contain other things besides numbers (and A+5 would invite confusion with the disjoint union of A with the set representing the von Neumann ordinal 5)

>>8811865
>why does A + 5 not unanimously mean "add 5 to each element of A"
Because no one can make up there fucking mind about notation.

>>8811838
nvm figured it out

in case anyone was curious invoke chain rule

[math] \frac{d}{ds} = \frac{d}{dx}\frac{dx}{ds} [/math]

if this is wrong let me know plz

>>8804566
how do i cope with the loneliness intrinsic to studying mathematics for long hours

>>8812246
doesn't it feel good to think the thoughts of many brilliant men before you? just imagine they're right there with you

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>>8811865
>Why are basic arithmetic operations ambiguous when it comes to sets?
they're not

>Like, why does A + 5 not unanimously mean "add 5 to each element of A"?
because 5 isn't a set, but if you write A + {5} then this is standard notation for sumset in arithmetic combinatorics
https://en.wikipedia.org/wiki/Arithmetic_combinatorics
https://en.wikipedia.org/wiki/Sumset

>>8812038
>because + is already reserved for the disjoint union
???

>>8812259
did you end up getting used to it ?

>>8812288
then I just thought my own brilliant thoughts because I'm a genius and I laughed in newton's face because he's too brainlet to understand inverse galois theory

>>8812309
are you interested in grothendieck-teichmuller theory

Got a soft question here: What is the rigorous way to explain "counting" arguments?

I am doing some introductory analytic number theory, which consists of properly count sums. And I just proved the following exercise:
[eqn] \sum_{d^2 |n}^{} \mu(d) = \mu^2(n) [/eqn]

And I did this by counting what the sum counts. The way I explained myself was this:

Suppose a number has s prime factors raised to the power of 2.
Then this function will count these primes, and combinations of these primes. And because of the nature of the mobius function, it will substract 1 for every single prime, then add 1 for every combination of 2 primes, then substract 1 for every combination of 3 primes and so on.

And as the mobius function of 1 is equal to 1, it will add 1 to the choice of "zero" primes.

What happens to other primes:
Prime factors raised to a power equal to any odd number won't be here because their square does not divide the number.

Then for primes with even powers, they will appear here. But notice that if p^4 divides n, then the function will count p^2 and the mobius function will value that at 0. If you have p^6 then the function will count p^3 and that will be turned to 0.
etc.

So the sum indeed only counts prime factors raised to the exact power of 2, and their combinations. This, through some n choose k identity equals 0. And then notice that if this number has prime factors with powers bigger than 2, the mobius function of that number is also equal to 0. 0^2 = 0.

In the case that the number has only prime factors raised to the power of 1, then this function will only count the number 1, so the sum will be equal to 1 and 1 is equal to [math]((-1)^k)^2 for all k[/math], where k is the number of prime factors the number has.

So this proves the theorem. What I care about is how to put it? Is it okay to simply describe what a sum counts and doesn't count? I haven't taken any combinatorics class before so I don't know what passes for rigorous in this business.

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>>8812323
I am grothendieck

>>8812343
>Prime factors raised to a power equal to any odd number won't be here because their square does not divide the number.
27 = 3^3 which is divisible by 3^2...

>>8812395
No, you need to understand the way the sum works. I meant the square root.

3^3 is not a square divisor because the square root of that is not even a number, so this sum will not count it.

Maybe I explained myself the wrong way.

>>8812403
Okay yeah, I think you expressed it wrong, because otherwise, it looks good.
So at this point, do you know anything about the mobius function or just the definition ? (to see how we can make a formal argument out of this)

>>8812354
give me your wizard powers

I have a solution of a certain salt + vodka.

How can I separate it so only the salt remains?

>>8812434
That would be extremely painful

>>8812458
You could use TIME

>>8812474
Open the container and wait for the vodka to evaporate?
But will it completely evaporate or something will be left behind?
How about setting the vodka on fire to make it quicker? My only concern would be damaging the salt...

>>8812486
How could I know ?

>>8812412
I know the first and second chapter of Apostol's Intro to Analytic Number Theory textbook

So I know the definition and a couple theorems about it.

>>8812532
Alright, let's do this. I thought it could be made easier with convolution by showing that the LHS is multiplicative but I don't see a short way to do it atm so we'll just make do with the definition.
The proposition is clearly true for n =1 so let [math] n = p_1^{a_1} \dots p_k^{a_k}[/math] an integer greater than 1.
Then[math]\sum_{d^2| n} \mu(d) = \sum_{d^2 |n, d \text{squarefree}} \mu(d)[/math] by definition of the Mobius function.
Assume that the p_i are ordered in such a way that [math]a_i > 1[/math] for [math]i \le j[/math] and [math]a_i = 1[/math] for [math]j < i \le k[/math] (set j = 0 if n is squarefree).
Now, the sum in the RHS of the above equality is over squarefree divisors of n whose prime factors are among the p_i for i <= j, hence we may write:
[math]\sum_{d^2| n} \mu(d) = \sum_{S \subset [\![1,j]\!]} \mu(\prod_{i \in S} p_i) = \sum_{S \subset [\![1,j]\!]} (-1)^{|S|}[/math]
Grouping these subsets by cardinal, we get:
[math]\sum_{d^2| n} \mu(d) = \sum_{i=0}^j {j \choose i} (-1)^i = 0^j[/math]. Hence, the sum is equal to 1 if j = 0 (ie. if n is squarefree) and 0 otherwise, which is exactly [math]\mu(n)^2[/math]

>>8812631
Looks pretty slick but you lost when you started summing over sets.

I understand what you mean at a surface level but I don't really get it.

>>8812631
>>8812654
*you lost me

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Can somebody explain how they determined the x-intercept to be -1/Km?

>>8812698
it's very simple just set 1/V0 to 0 and solve for 1/[S]
0 = Km/Vmax * 1/[S] + 1/Vmax
hence
0 = Km * 1/[S] + 1
so
1/[S] = - 1/ Km

>>8812711
Thanks, anon. Have a (you)

>>8811614
For that system to have infinitely many solutions equation 2 must be some linear combination of equations 1 and 3
i.e. A(x + y - z) + B(4x + y) = Mx+2y-3z
equating coefficients of y and z yields
A + B = 2
A = 3
hence B =-1
in which case M = -1
you can check this by checking that the determinant of the 3x3 matrix which represents this linear system is 0.

hey whats the website for textbook torrent again?

>>8813742
libgen.io