/sci/ - Science & Math

if i put an helicopter in a train and i let it stay in mid air ,when the train starts what will it do?

>>8902173
It will go to the back of the train

>>8902173
when accelerating it moves toward the back of the train

at constant speed, if it has walls around it it moves with the train

wtf why did the last thread get deleted?

How do I find the inverse function of [math]f(x)=2x+sin(x)[/math]?

How do I find out how much needs to be added onto a non-injective function to "stretch" it into an injective function?

>>8902203
/sqt/ was hijacked by an autistic "math oracle" poster who would repost threads before they hit the bump limit just to force his image

>>/sci/?task=search2&ghost=yes&search_text=&search_subject=sqt&search_username=&search_tripcode=&search_email=&search_filename=&search_datefrom=&search_dateto=&search_op=op&search_del=dontcare&search_int=dontcare&search_ord=new&search_capcode=all&search_res=op

give me best source you know to start with mathjax. i have a mission. im aware of coding and basic understanding. need sth like a sorted base for teh commands.

We have
[math] \lim_{s\to \infty} \zeta(s) = 1 [/math].

So do I approach sums over n involving factors
[math] \zeta(n) - 1 [/math]
as in pic related?

E.g
[math] \sum_{n=1}^\infty \zeta(2n) - 1 = \dfrac{3}{4} [/math]

I fail to see how..

In the induction section of Lang's Basic Mathematics.
I have a good understanding of how the binomial theorem works, but I'm unable to factor numbers into the desired result. Steps 1 to 2, and 3 to 4 as pictured in particular.
I've understood and solved all previous examples and exercises in the book, but clearly my understanding is still lacking.
Not asking for advice on the specific exercise, but looking for additional resources to improve understanding of this area in general.

In the induction section of Lang's Basic Mathematics.
I have a good understanding of how the binomial theorem works, but I'm unable to factor numbers into the desired result. Steps 1 to 2, and 3 to 4 as pictured in particular.
I've understood and solved all previous examples and exercises in the book, but clearly my understanding is still lacking.
Not asking for advice on the specific exercise, but looking for additional resources to improve understanding of this area in general.

[math] x = 1 [/math]


test.

>>8902283
Note: Tried Khan Academy on factorization, found it to be too simple

>>8902168
What is "compositional product", it sounds straightforward but it's only briefly referred to in the notes as an example and google doesn't provide anything obvious.

>>8902298
are there different tex2jax delimiters on 4chan?

im pretty sure ive once seen equations on /b/ but [math]... is not working. also the obvious ones.

why are heterohalidic gasses so rare?

>>8902283
In both steps, they just use

m! = (m-1)! · m

They use this 4 times.

E.g.
(n-k+1)! = (n-k) · (n-k+1)

>>8902283
In both steps, they just use

m! = (m-1)! · m

They use this 4 times.
E.g.

(n-k+1)! = (n-k)! · (n-k+1)

>>8902381
if this means molecular halides(cant find a proper translation) then check out molecular orbital theory.

>>8902283
Does anyone recall if there is a nicer proof for this. Maybe with some counting argument?

am i right in thinking the system is consistent if [math] \alpha=3,\beta=2 [/math] and if [math] \alpha\in\mathbb{R}\setminus\{3\},\beta\in\mathbb{R} [/math] or have i missed out another case? and also do the following look like the right the solution sets? [eqn] V=\{(-2\lambda,\lambda,1,2-\lambda):\lambda\in\mathbb{R}\}\,;\quad V=\left\{\left(2\frac{\beta-2}{3-\alpha}-4,2-\frac{\beta-2}{3-\alpha},1,\frac{\beta-2}{3-\alpha}\right):\alpha\in\mathbb{R}\setminus\{3\},\beta\in\mathbb{R}\right\} [/eqn]

>>8902298
just another test.

[math] \style{font-family:Arial}{T} = 1 [/math]

>>8902499
[math] T = 1 [/math]

[math]
\style{font-family:Arial}\mathrm{T} = 1
[/math]

[math]
T = 1
[/math]

T

[math]
\mathrm{T} = 1
[/math]

[math]
\mathrm{ \style{font-family:Arial}{Text.} } = 1
[/math]

[math] \mathrm{ \style{font-family:Arial Unicode MS}{TDH} } = T
[/math]

>Finished junior undergrad of B.S. Neuroscience program
>Competitive GRE scores but 3.23 GPA

a-am I gonna make it bros? I don't want to be a waiter at Applebee's....

[math] \mathrm{ \style{font-family:MathJax TeX}{T} } = 2T [/math]


[math] \mathrm{ \style{font-family:STIX General}{T} } = 2T [/math]

I have this binomial..
(x+x^2x^3...+x^7)(x^2+x^3+x^4+x^5)(1+x+x^2+x^3)

How do I figure out the coefficient of x^10 after expansion?

[math]
\style{font-family:STIX GENERAL}{T} = T
[/math]

[math] \mathrm{ {\sf T + 1} } = T [/math]

How do I find the interval for the definite integral?

[math] \color{blue}{Text} [/math]

>>8902590
it's probably arbitrary like 0 to 2pi

[math] \color{blue}{ \mathrm{ {\sf IM BLUE} } } [/math]

>>8902571
1) That's a polynomial
2) Choose a term from each of the three factors and multiply them. Count the number of combined terms which have x^10, and that's your answer.

[math] \small{\color{blue}{ \mathrm{ {\sf IM BLUE} } }} [/math]

[math] \footnotesize{\color{blue}{ \mathrm{ {\sf IM BLUE} } }} [/math]

[math] {\color{blue}{ \mathrm{ {\sf small{IM} } } } [/math]

[math] {\color{blue}{ \mathrm{ {\sf small{IM}} }}} [/math]

>>8902607
I didn't want to do that, it's rather tedious. Is there no way to solve this using pascals triangle or any other shortcut?

>>8902596
That's not correct.

[math] {\color{blue}{\mathrm{{\sf IM}}}} {\color{blue}{\mathrm{{\sf BLUE}}}} [/math]

>>8902625
then what? some kind of infinite series?

[math] {\color{blue}{\mathrm{{\sf IM}}}}/;{\color{blue}{\mathrm{{\sf BLUE}}}} [/math]

>>8902628
It's not some kind of infinite series. It's an actual interval. I just tried to plug in (0, 2pi) and I got the wrong answer. I'm particularly interested in figuring out the general method for solving these type of problems.

>>8902634
try 0 to pi then

Any algebraists here?

Need to see if there's a ring homomorphism f from Z_3 to Z_6, where f(1) = 1. So, f(1) being 1 makes everything determined by 1 (if that makes sense), so f(2) = 2 and f(0) = 0 (obviously). And that's that. Am I missing something?

Can someone explain why we need all these shitty tests for convergence/ divergence? Isn't it obvious what the sequence does just by looking at the terms or plotting a quick graph?

Are there any examples of sequences that look like they converge or diverge but actually do the opposite?

>>8902652
its all just nerd shit they do to feel important. you can tell by looking at the first 3 terms or so

>>8902652
[math] \sum {\frac 1{n^3\sin^2n}}[/math]

>>8902652
>>8902656
we don't learn sequences in Canada
that's a seperate course but my calc skills are good enough

How exactly does a PhD work? Like do you have to know your exact research topic as you apply for programs, or do you just apply for the concentration/advisor and then decide your topic later?

>>8902636
Not it.

>>8902684
fuck it's gotta be something 0 to a multiple of pi
0 to pi/2?

>>8902692
I don't know man. I'm confused. I don't really want to go at it by guessing. Just skipping this problem until later.

If money is the root of all evil,
it means that money squared = evil.

Is this why money is made either circular or rectangular?

How the fuck do I find the boundaries in problems where I have the find the area of a polar graph? This is fucking frustrating. WebAssign videos fucking blow so hard.

>>8902719
>rectangle
>squared
All squares are rectangles, but not all rectangles are squares, brainlet.

>>8902808
You are the one who is the brainlet here.
I clearly meant non square rectangles since i said squared money is evil

>>8902168
that rϕXrθ product is supposed to be =4sin ϕ

but i can't do it right always get wrong results

where am i screwing up?

>>8902216
This is injective. The derivative is 2 + cos(x), which is always greater than or equal to 1. So it's monotone increasing, thus injective.

>>8902641
4=1 mod 3, so 1=f(1)=f(2+2)=f(2)+f(2)=2+2=4, a contradiction.

>>8902652
A better question is why does it matter whether or not a series diverges?

>>8902844
its supposed to be a cross product, you did some weird term by term vector product.

I don't understand how the universe can function if two observers can look at the same thing and see different results

>>8902945
im pretty sure i used cross product

>>8902929
So that you don't waste time adding up tons of terms like a moron for nothing or a wrong answer.

>>8902168
Suppose that w=f(u) is a differentiable function. And that u = ax + by. Is the following computation always correct?

[eqn] \frac{\partial f}{\partial x} = \frac{\partial f}{\partial x} \frac{ \partial x}{\partial u} \frac{ \partial u}{ \partial x} = \frac{ \partial f}{ \partial u} \frac{ \partial u}{\partial x} [/eqn]

REQUESTING ALGEBRAIST

I have been doing this S I C C proof, and basically, all that is left to do, is this;
Ok, so I have show that an Ideal I is a prime ideal of a commutative ring A. I have also shown that any element not in I is a unit (in A), and now I have to show that I is a maximal ideal of A. How would I tackle this one? Feeling very stuck here. Perhaps try to show that A/I is a field? How does that even look like ..

>>8902915
Yeah, I figured that out, I was just too lazy to check the possibilities since I'm a dumb faggot.

Thanks anyway.

>>8903309
You've essentially got it. The set of units is multiplicative. So A - I is multiplicative, and so I is prime.

>>8903140
nigga the step in the middle is nonsense, don't treat derivatives like fractions
the outer equality is chain rule, yeah

>>8903309
clearly maximal because if you add any element to it then 1 would be inside

well you can also directly prove A/I is a field by considering the projection A -> A/I, see, every element will be u + I and inverses are preserved

>>8903348
>>8903355
YES, I GOT IT. Figured it out while taking a huge fucking shit (I always eat tacos before doing algebra for some reason, makes me think better). Thanks for the help, lads.

Also to >>8903340, what does it mean for a set to be multiplicative?

>>8903367
https://en.wikipedia.org/wiki/Multiplicatively_closed_set

>>8903372
Thanks.

Feels good to get a ton of help while I see many questions here passing by without getting any attention, kek.

So from what I understand, one-counter automata (PDA with a non-removable, non-placeable start-of-stack symbol and only one other stack symbol they can use) don't recognize all context-free languages. I believe counter examples include [math]\{ a^n b^m a^m b^n : m, n \in \mathbb{N} \}[/math] and strings of well-balanced brackets with two different types of brackets. How would I go about proving this?

is it possible to demonstrate that the cosine of any angle theta is equal the adjacent leg/hypotenuse of a right triangle or is it some kind of postulate?

>>8902675
could be both

>>8903505
you can draw a circle around a right-angle triangle, and you can draw a right-angle triangle in a circle, like pic related. the radius of the circle is the length of the hypotenuse. in the unit circle the radius is 1 so you don't need to divide by it (x / 1 = x) but if the radius is not 1 then the cosine is the adjacent leg divided by the hypotenuse.

>>8903348
But if the middle step is nonsense... how do you prove the chain rule?

how do i understand coordinate transformation? using the equations in pic related, doesnt that rotate the coordinates by -θ and not θ

I'm sorry guys, but i have been stuck on this part for atleast an hour now, and i don't even get it by looking it up at symbolab or wolfram.
Could anyone explain to me whats happening here? It should be so easy. But it can't get it right for some reason.

>>8903735
To be more specific here. I don't get the how it goes from the first part to the second part. The integral part from 2 to 3 is okey.

Anyone know how to integrate the floor function? Really at a loss with this one...

Pic related

>>8903740
>To be more specific here. I don't get the how it goes from the first part to the second part.
Making the explicit division of polynomials:
x^2-5x+6=(x-4)(x-1)+2

>>8903748
plugging in different values for x it seems to check out but i don't know how to show it in the general case

http://www.wolframalpha.com/input/?i=Integrate%5BFloor%5BLog%5By,x%5D%5D,%7By,2,x%7D%5D,x%3D0.25

>>8903755
I feel really stupid now. I should take a short break.
Thats super basic.

>>8903768
yes i agree, the first one i see now is incorrect but i do believe the second one. Again, no idea how to show it though...

>>8903773
see if this is of any help

http://functions.wolfram.com/IntegerFunctions/Floor/21/01/01/0001/

>>8903768
Try writing the floor as the exact value minus an error term bounded by 1, and use the formal definition of your integral (Riemann, Lebesgue, etc.) to derive the bounds.

how do i show that [math]\mathbf{a}=(1,2,1)[/math] and [math]\mathbf{r}=(1,0,1)+\lambda(1,2,1)[/math] are parallel? i know if two vectors are parallel, then [math]k\mathbf{a}=\mathbf{r}[/math] for some non-zero k, but idk what to do after that

https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem

this says a sample rate of (EXACTLY) 2B samples/second is sufficient, but other people have claimed that you need a sample rate GREATER THAN 2B (even if it's 2.000001). if you think about it, in the most extreme case of only having 2 samples in total to work with, you don't have enough information, you would need 3+ samples? so what's the deal, is EXACTLY 2B sufficient?

High school brainlet here can anyone help
Haven't started calculus yet so no shit like LH

If your hair grew half a foot overnight would you wake up dehydrated, or tired, or some shit?
I know that growing hair happens too slowly for any use of energy to be noticeable but didn't Harry Potter
grow his hair out a fuckload every time he tried to cut it? Wouldn't that give him a fucking hangover or something?

Prove that any set of n+1 natural numbers <= 2n contains a number that dividers one of the other members.

halp exam in an hour

>>8904170
https://www.quora.com/Given-a-set-of-n+1-positive-integers-none-of-which-exceeds-2n-how-can-one-show-that-at-least-one-member-of-the-set-must-divide-another-member-of-the-set

>>8904226
damn it , thank you

>>8903748
ln(x)/ln(y)=log_y(x)

solve for the values y_i so that log_(y_i)x=i, for each integer i>=2

then split up the integral to be a sum of integrals over each interval [y_i, y_{i+1}]

now each function inside the integral is constant over the region of integration

>Ethanol is water soluble, which means it enters the blood stream readily, there to be carried quickly to all parts of the body (most notably the liver and the brain). It’s also fat soluble;

How can a molecule be both?

No chemists on /sci/ atm so I guess I'll let the thread die and post it here again.

>>8903905
Multiply it

>>8902414
i meant something like ICl or BrCl or IBr

is 3 not just a consequence of the other axioms?
since a#0=a#(b-b)=a#b-a#b=0. i dont get why its included

>>8904335
Ye. Likely it's a stylistic choice to include it there given how glaring a hole (2) leaves.

Can somebody help me with my homework
P is a prime number and a and b are integers
a != 0
a | b is true
p | b is true
p | a is false
Gotta prove p | (b/a)

>>8904419
Step 1: Think about what "|" means (you were provided a definition)

>>8904335
>a#b-a#b=0
Which follows from what exactly?

>>8904422
a.p | b must be true right?

>>8904514
Yes, since that is what you're trying to prove

But I'm sure your prof told you what a | b means (hint: it starts with something like [math]\exists z \in \mathbb Z : \ldots[/math])

>>8904419
Since a|b, b=ka for some integer k. Since p|b but not p|a, it follows that p|k. Since k=b/a, we have p|(b/a)

>>8904540
>>8904547
Much love, thanks

What is it called when you have multiple equations like:

x + y = 12
2x + 3y = 48

and you have to combine them like

3x + 4y = 60

to isolate and get the value of a variable?

>>8904357
thanks it makes sense now
>>8904427
im pretty sure the proof was wrong, but i think the problem is with a#(b-b)=a#b-a#b. the step you pointed out follows from V,+ being a group with identity 0. i probably shouldve used a#b*(a#b)' or something to be in keeping with the picture as well

>>8904559
adding them? or solving by elimination in the specific case where one of the x or y terms cancels.
really it's just the property if a=b and c=d, then a+c=b+d, which i dont think has a widely used name. although ive seen it being called the addition property of equality in some places

>>8904559
combining them is not how you solve the system.
If you're talking about putting that in a matrix then it's called Gauss Jordan elimination.

In what context was this written?

What does it mean? Is it about permitivity?

>>8904559
In its most abstract form?
You are simply taking advantage of the fact that
>a=b and c=d
>implies a+c=b+c and c=d
>implies a+c=b+d
As for what to name that trick, something like "addition of (real-valued) equations" should be fine.

Can a biotechnologist do research in humans? If not what do I need to study if I want to research cures for aging, is medical school the only path?

>>8904574
>the step you pointed out follows from V,+ being a group with identity 0.
I think from that only follows that b-b = 0, not that a#b -a#b = 0

>>8904559
You combine them into a new equation with 1 variable less. For that you can for example calculate 2*(first equation) - (second equation) or the same with 3*(first) which gives you a value for the remaining variable. You can plug that value into one of the two equations then to get the second variable

>>8904668
im starting to think youre right, but isnt [math] a\#b\in V\setminus\{0\} [/math] and therefore it has an "* inverse"? also to be clear were talking about -(a#b) and not (-a)#b right?

>>8904744
>im starting to think youre right, but isnt a#b∈V∖{0}a#b∈V∖{0} and therefore it has an "* inverse"?
Yes, but I'm not sure how you would use the multiplicative inverse to prove that a#b - a#b = 0.

>also to be clear were talking about -(a#b) and not (-a)#b right?
To be absolutely precise, it would be a#(-b). Though I think this is equal to -(a#b), and (-a)#b

So, I'm trying to prep for my ODE course this fall, and I'm having a hard time with reading and understanding because I feel like there's a lot of steps misconstrued, or I'm just bad at reading.

I have a very small idea of what I'm doing, but I still don't really understand what I'm doing in terms off conceptual understanding. What is "g(y)" and what is f(x) aside from being a function to represent the outcome/integral of the differential f(y), and the differential itself (dy/dx or y') on #3 of the picture.

Also, what would be a good textbook to read through to get a better understanding, or what would be a better way of reading mathematical textbooks?

This also vaguely reminds me of how Energy is derived in terms of F=MA

TL;DR
what is g(y)*y'=f(x)?
what is a better textbook for ODE?
how do I read?

>>8904943
if you have the ODE y*y'+y^2*y'=x^3-x then you can rewrite this as f(y)y'=g(x) where f(y)=y+y^2 and g(x)=x^3-x

>>8904951
I see, that clears my confusion on the notation. Thank you!

>>8904775
i meant the general binary operation * as in the picture, which in this case is +

>>8902168
How in the name of jesus christ you prove shit like

((C ∪ B) ∩ A) ∪ (B ∪ C) ⊇ (A ∩ B) ∩ (C ∪ A)

((C \ B) ∪ A) \ (B \ C) ⊇ (A \ B) ∩ (C ∪ B)

((C ∩ B) \ A) ∩ (B ∩ C) = (A ∪ B) ∩ (C \ A)

>>8904996
just work with elements, these are trivial
((C ∪ B) ∩ A) ∪ (B ∪ C) is just (B ∪ C) anyway

I have no idea what the answer is

it's for my discrete math final

help?

>>8904996
by definition [math] X\subseteq Y [/math] if and only if [math] \forall x(x\in X\rightarrow x\in Y) [/math].
now if [math] x\in (A\cap B)\cap(C\cup B) [/math], then [math] x\in (A\cap B) [/math].
If [math] x\in (A\cap B)[/math], then [math]x\in (A\cap B)\cup (A\cap C)=A\cap(B\cup C) [/math].
if [math] x\in A\cap(B\cup C) [/math], then [math] x\in (A\cap(B\cup C))\cup(B\cup C) [/math]

>>8904996
By the definition of intersection, union, etc...

Why is the notation for limit a shorthand of an english word? Shouldn't something so common deserve its own symbol?

>>8902168
This is more of a request than a question.

Does anyone have an infographic on dependencies of topological spaces similar to this, only much larger? I remember seeing one posted here, but didn't save it.

>>8905039
What kind of discrete math question is this?

>>8905119
idk i go to community college and the teacher likes sports

i don't know the answer tho

>>8905072
It's not like it's unique in that regard. Everyone was just happy using [math]\lim[/math].

>>8905072
> Why is the notation for limit a shorthand of an english word? Shouldn't something so common deserve its own symbol?
blame the g*rmans:

https://en.wikipedia.org/wiki/Limit_of_a_function#History

>Weierstrass first introduced the epsilon-delta definition of limit in the form it is usually written today. He also introduced the notations lim and limx→x0 (Burton 1997).

>>8905121
This question is hideously ill-posed. Do you assume a 50-50 chance for both teams winning? What constitutes the early season?

Do you have a similar question he did in the notes/in class?

I'm assuming he's wanting you to do something with combinations, because sports seasons actually make good counting problems.

>>8905141
No it's in a series of questions like "what are the chances of you getting robbed in a bad neighborhood"

"what are the chances of a fatal car accident on a a holiday weekend"

I just don't know sports to say whether it's likely or impossible about the football game

What is the simplest and shittiest pi formula that people start with before deriving a better one?

>>8905147
I have know idea what the fuck he wants from you then. For what it's worth, it's not impossible that the Packers and the Steelers could play each other in the early season. And if I watched a Steelers-Packers game during any random NFL season, I wouldn't be surprised if either team won. Hope that helps.

Does the next formula work when [math]n[/math] is a negative number or there exist another for that case?
[math]\sum_{i = 0}^{n} b^i = \frac{1 - b^{n + 1}}{1 - b} [/math]

>>8905378
Factor out b^n and apply the standard formula to what remains.

>>8905147
Your prof is joking or punking you... or he's a moron.

>>8905147
>what are the chances of you getting robbed in a bad neighborhood
Can the neighborhood be guarded by a finite number of nearsighted policemen?

>>8902168
Is a good idea to learn proofs, logic, and set theory before learning calculus?

>>8905039
It's a bullshit question. If I were you I would make up a number (probably around 50% but not exactly) and then explain it by mentioning some specific athletes and how they run super fast or throw a ball really good.

If you know which team he likes then favor that one, otherwise guess.

>>8904996
>>8905043

What fucking class is this with fucktons of just unions and intersections? I'm taking Intro to Higher Math in the fall (basic set theory and rigorous proof-writing course). Is this what I'm in for?

>>8905378
>summing from i=0 to some negative number
Shiggy
You take sums over {0,1,2,3,...} my man
If you want the i to be negative in your b^i terms, rewrite the summand b^(-i) or 1/b^i
But to answer your question, no. Consider for instance .5^-i. Then your terms are 1, 2, 4, 8, 16, ... while the 1-b^(-n+1) term on the right would grow more and more negative with increasing n.

>>8905394
You don't really need to, and it won't help as much as you think. A book like Apostol relies on proofs and such throughout to develop the material, so you'd pick it up normally just going through that. Books at the "advanced undergraduate" level are almost always self-contained and have an introductory chapter on set theory and foundations that the rest implicitly relies on, too. You're not at risk of missing anything, or in a position to really reap any benefits. Especially if you're going to learn "cookbook" calculus. Which there's no real shame in, especially since it gives you an intuitive feel for basic analysis that makes it a decent place to get up to speed with what real math is all about. If you dive right in to heavy abstraction you might lose interest or have trouble seeing the big picture.
Though I can still recommend Smith's Introductory Mathematics: Algebra and Analysis. It's kind of like an extended form of those intro chapters I mentioned, and it's well suited for beginners as a foundation for further study, if you want to get a feel for how math works without having to first commit to a specific subject or build an intuitive sense of something through cookbook calc/LA/diffeq classes.

>>8905381
Thanks, anon, I got it:
[math]\sum_{i = 0}^{n} b^{-i} = \frac{1 - b^{n + 1}}{b^n(1 - b)}[/math]

just finished khan academy linear algebra as prep for a course.

is it really this easy? or did this gay e-learning shit lull me into a false sense of complacency?

Why does /sci/ get such a hard-on over topology? What makes it the most interesting field of higher math? Prior to visiting this board, I got the impression that Analysis was the way to go if you wanted to wave your brain-dick.

>>8905612
Topology is basically a generalization of analysis to deal with spaces other than R^n, by abstracting away unimportant details such as the Cauchy construction and keeping only the useful properties (such as existence of limits, definition of continuous functions, path-connectedness, etc.).

This is useful because you can then import principles from analysis into things that can't be parametrized into R^n in an obvious manner, such as the "separation" between two groups of people in social networks, or the "continuity" of a function [math]Automaton: \Omega \to \Omega[/math] representing a generic transition between states of a system.

It is precisely the ease of generalizability that makes topology a prime candidate for shitposting. About the only thing that we can faithfully model with R^n is physical space (and that's only after ignoring relativistic / quantum effects), while the topological axioms are general enough that you can (after abstracting away the details) transport insights from familiar fields like R^n into any other field of your choice and sound DEEEEEEEP.

>>8905612
Everyone gets memed by the non-physical objects and their wonky transformation.

If you want to wave your brain dick, it's all about algebra these days.

>>8905648
Is "turn a sphere inside-out" the "1+2+3+4+=-1/12" of topology?

>>8905696
I'd say homotopy type theory in general (of which sphere eversion is a special case) is the "1+2+3...=-1/12" of topology, because it abuses equality in a similar manner, and also because it's a /sci/ meme in the sense of >>8905653.

But I'm just getting into HoTT right now so I might be a little biased there.

>>8905707
>>8905696
Not exactly topology but Banach–Tarski paradox is a great meme

>>8902168
If I have a spray bottle and I know the pressure and volume of the spray bottle can I work out the speed of the spray exiting at the nozzle if it was spraying bug spray?

>>8904744
>>8904775
You're both right to realize that anon's original "proof" is not correct. However, 3. still follows from 1., 2., and 4.
Switching to standard [math]+[/math]/[math]\cdot[/math] notation.
[math]x \cdot 0 = x \cdot (0 + 0)[/math] since 0 is the identity element.
[math]x \cdot 0 = x \cdot 0 + x \cdot 0[/math] from distributivity.
[math]x \cdot 0 + -(x \cdot 0) = x \cdot 0 + x \cdot 0 + -(x \cdot 0)[/math] - adding the same thing to both sides.
[math]0 = x \cdot 0 \;\;\square[/math]

>>8904775
>Though I think this is equal to -(a#b), and (-a)#b
Yep. Because we can use prove that [math]-1 \cdot x = -x[/math] for all [math]x[/math].

[math](-1) \cdot x + x = (-1) \cdot x + 1 \cdot x[/math] since 1 is the identity element.
[math](-1) \cdot x + x = (-1 + 1) \cdot x [/math] from distributivity.
[math](-1) \cdot x + x = 0 \cdot x[/math]
[math](-1) \cdot x + x = 0[/math] from >>8905773.
Therefore [math](-1) \cdot x = -x \;\; \square[/math]

>>8905707
>HoTT
it is the future

What is meant by the last statement? That is exactly what H is, isn't it? It's literally defined as the subgroup containing the elements in G of order n. Is it some shit about G being infinite?

>>8905819
Wait, no that can't be, they say G is finite, so forget that.

>>8905819
My algebra is rusty but sounds like they mean prove that some but not necessarily all elements of G of order n form a subgroup of g, H.

>>8905826
of G*

>>8905819
Same rusty algebra fag. I think they want you to show basically that H is a cyclic subgroup of G.

>>8905833
Okay, I'll try that, thanks.

>>8905826
>My algebra is rusty but sounds like they mean prove that some but not necessarily all elements of G of order n form a subgroup of g, H.
wrong, they mean all, that's why H is defined that way

>>8905833
>Same rusty algebra fag. I think they want you to show basically that H is a cyclic subgroup of G.
also wrong

>>8905819
>What is meant by the last statement? That is exactly what H is, isn't it?
no, g^n =e doesn't mean that the order of g is n

just think about it

How do I add standart deviation to all the variables? Usually it is in the way by selecting all the means and standart deviations, but in this graph there is already a fixed value and I just can't understand, how do I get the standart deviation value for this value.

>>8905879
>>My algebra is rusty but sounds like they mean prove that some but not necessarily all elements of G of order n form a subgroup of g, H.
>wrong, they mean all, that's why H is defined that way

I guess I misunderstood the parenthetical comment.

do these just mean
scalar multiplication [math]\odot[/math] distributes over [math]\oplus[/math] and [math]\odot[/math] distributes over +?

>>8905930
yes
i.e. first one means a(v+w)=av+aw

>>8905930
yeah it is only with the tensor procuct that you only get one time the scalar inside the product

in mathematica, how do i assign the result of Integrate to a function?

i want to do something like this:
f[x_] := Integrate[......

>>8905981
ok it works like this:

f = Integrate[...., x];
f /. x-> 0

but can i make it so it's f[0] instead?

>>8902168
I'm currently in first semester, third year of a four year undergrad chemistry double degree.
The second part of my degree makes me feel like I really should have done physics.
Should I transfer, take as many physics courses as electives, teach myself some physics or some combination?
Opinions?

why is the 1b1 orbital in water nonbonding?

Its not a math question but do you guys listen to music in study hours?

my house is too loud

anybody knows a good list of exercises from a book or a mathematician website that has good exercises (I mean the idea behind the exercise) ranging from beginner to ultra advanced level involving: trinomial factoring; completing the square; square of sum and difference; cubes of sum and difference; difference of squares and sum and difference of cubes? It could have exercises from math competitions like AIME (I've seen and done the excellent exercise number 1 from AIME 1989 and liked it a lot).

because I studied in public schools my entire life and got interested in math too late in life I have a hard time dealing with these factorizations when they happen to show in the middle of exercises

anybody knows a good list of exercises from a book or a mathematician website that has good exercises (I mean the idea behind the exercise) ranging from beginner to ultra advanced level involving: trinomial factoring; completing the square; square of sum and difference; cubes of sum and difference; difference of squares; sum and difference of cubes?

it could have exercises from math competitions like AIME (I've seen and done the excellent exercise number 1 from AIME 1989 and liked it a lot). All lists of exercises about the subject I've founda and done in the internet are completely easy or medium at the most, with the same mechanical and repetitive idea behind the exercises

because I studied in public schools my entire life and got interested in math too late in life I have a hard time dealing with these factorizations when they happen to show in the middle of exercises. But now I'm dedicated to dominate it!

>>8905819
g could be of order n/2, but still means g^n = e

$testing lmao$

[math] like this? [/math]

>>8905581

answering questions on what is essentially a learning game with little fairy dust sounds to squeeze dopamine out of your reward circuit every time you get the right answer as well as the fact that khan academy is multiple choice and you would have to be R-E-T-A-R-D-E-D to not get the right answer AND the fact that any good university course is not going to be multiple choice especially if it is a MATH course and not a TEST TAKING course means you definitely have been lulled into a false sense of complacency and need to crack open a textbook like Shilov's (not silverSHIT's horrible english """"translation""""") and see how long it takes you to answer questions relative to khan-fairy-dust-multiple-choice-academy.

>>8905378
Normally sum and product are defined like this:
[eqn]\sum_{i=a}^b = 0, \prod_{i=a}^b = 1[/eqn] for a > b

>>8905819
Group order = number of elements in the group
Group element order = the number n such that g^n=e for an element g of the group, and "infinite" if no such n exists.

>>8906254
Smallest such number n.

Are limits spooks?
>spiritual lim human

>>8906263
>spookposting in /sqt/
Save it for the race threads nigga

Who else /severecitationanxiety/ here?
>Make observation based on experimenting with the mathematical model
>Write it down
>Wait fuck, that's definitely been observed before
>Dig through literature for hours to find someone to cite on it
>ALWAYS worried that I'm not making it clear enough what my sources are
>Never even gotten marked down for poor sourcing

Hey /sci/,

Practising some Fourier Transform problems.

In a solution to one of the problems they use the following simplification

[math] 1 + e^{-8 \cdot j \cdot \omega} = e^{-4 \cdot j \cdot \omega} \cdot (e^{4 \cdot j \cdot \omega} + e^{-4 \cdot j \cdot \omega} ) [/math]

I don't see how the two sides are connected.

What happened to the 1 on the left side?

>>8906419
1+e^{-8jw}
= e^0 (1+e^{-8jw} )
= e^(-4jw+4jw) (1+e^{-8jw} )
= e^(-4jw) e^(4jw) (1+e^{-8jw} )
= e^(-4jw) (e^(4jw)+e^(-4jw))

>>8905438
Thank you for the advice. So would some more in depth proofs and logic be a good next step after an intermediate undergraduate level of experience in calculus?

>>8906429
Thanks senpai

It seems like you guys are mostly math nerds but I'll ask anyway.

I want to make a walk-through metal detector. My plan is to make a wire loop around a door frame, which will serve as an inductor. When metal enters the loop, the inductance changes. I'm going to set it up with some capacitors to make an LC oscillator. The change in inductance will change the frequency of the oscillator.

From there, I haven't put a lot of thought into it. If it's slow enough, maybe I'll just ADC it and examine the frequency in a microcontroller. Or maybe I'll mix it with the typical resonant frequency and look for beats.

What do you think? Feasible?

>>8906461
try in >>>/diy/ohm

>>8906077
Herman, Kucera, Simsa - Equations and Inequalities: Elementary Problems and Theorems in Algebra and Number Theory

What exactly is the difference between Analysis and Calculus?

Here some engineers get "Analysis 1, 2 3" while others get "Calculus 1, 2, 3"

How would i prepare for an Analysis course without any prior Calculus knowledge?

Which of these 2 books is better? To do before working through a calculus book. Algebra and Trigonometry -Beecher, Precalculus - Stewart

>>8906042
I can only focus if I'm listening to music without lyrics, or with lyrics in a language I don't understand.

>>8906582
Analysis and Calculus are the same thing.

>>8906582
Europe calls their calculus courses analysis.

>>8906956
what do they call analysis?

>>8906956
But some degrees have to take Calculus while others have to take Analysis, in the same university.
So they can't be the same thing.

The reason I'm asking is because the ones that get Analysis are considered much harder so I need to know if a regular calculus textbook will be enough to prepare myself.

>>8906986
if you want to learn calculus read a calculus book

if you want to learn analysis read an analysis book

>>8906986
Check the course website?

analysis is different from calculus

Why is Turner syndrome considered the only possible monosomy?

>>8907070
because X chromosomes are redundant, just like women

What is the funniest thing that is available in "food grade" form?