/sci/ - Science & Math

Say you have a bunch of boxes that each contain randomly a red ball or a blue ball. You have a separate bunch of boxes that each contain a ball in a superposition of red and blue until the box is opened. Is there any way to tell which group is which, or does quantum fuckery only kick in once you introduce the other aspects of quantum mechanics into this scenario?

To start out the personal questions thread with a gold star, did you do well on that test yesterday?

>>11225448
Doesn't the concept of color already rely on energy levels?

Math questions:
>>11214727
>>11217334
>>11225374
>>11225391

Physics questions:
>>11213159

Chemistry questions:
>>11218694 (bond formation doesn't always release heat. enthalpy of reaction can be negative bby)

Biology and physiology questions:
>>11211671
>>11214681
>>11214769
>>11218331
>>11222696 (hope ur okay now)

Stupid questions/Use the sticky questions:
>>11213895 (no)
>>11214834
>>11215128 (LaTeX is ugly)
>>11216528 (that's not what superposition is)
>>11219357
>>11219803
>>11222483 (wikipedia)
>>11224306 (I'm interested in this)
>>11224376

lmk if i missed one

>>11225467
oof, no. the theory of boundary layers can rim me.

>>11225374
f(n+1)-f(n) should depend only on [math]n ~ mod ~ 30 [/math], unless I'm going completely insane. This means it has a period, you can interpolate with an appropriate function and then take the integral for f(n).

>>11225509
>n mod 30
*f(n) mod 30.

>>11225443
I know that the space of all differential forms on a manifold M is a [math] C^{\infty} (M)[/math] module. Is the same real for the space of all tensors on M? I can't see why not..

is
[math]\mathbb{R}^n|n\notin\mathbb{Z}[/math]
a thing

>>11225657
Yes, if you re-interpret [math]\mathbb{R}^n[/math] as the set (space?) of functions from [math]\{1, 2, \cdots, n\}[/math] to [math]\mathbb{R}[/math], then you can just change the domain.

>>11225675
I dont think that makes any sense

>>11225443
Is there a mathematical symbol for midpoint?

>>11225711
You can place a dot on the middle of the line segment and two hash marks on either side, indicating the two constituent segments are equal.

>>11225715
I know that, I was just wondering if there was a symbol indicating midpoint on its own. So like if you had a line or something, and then you listed things lower like:
Length: 5
Slope: 0.5
Midpoint: {3,3}
Is there a recognizable symbol I could use for midpoint rather than the word?

>>11225721
I don't think so. Feel free to invent your own.

>>11225725
OK. I was already planning to use it as part of another made-up symbol so I was hoping I could have a recognizable part lol

>>11225741
What are you working on, anon? What are your symbols for? What do they look like?

>>11225675
hm, i guess my question was more "is there ever a case where you would have a N-tuple where N is not a whole number"

>>11225746
Just tracking durations. Other symbols are pretty easy (Min, Max, Mean, First, Count, Sum) but I wanted to have a metric for sorted midpoint, which would be the duration that would be occurring halfway through the sections if they were sorted.

So if you had: 6min, 1min, 1min, 3min, 5min, 1min, 3min
You would sort them: 6min, 5min, 3min, 3min, 1min, 1min, 1min
And the halfway point @ 10 mins (because 20 minutes total) would occur during a 5min duration, so 5min would be the sorted midpoint value.

>>11225443
Is getting a math or physics degree actually pointless? Doubly so if they aren't coming from an ivy league school? I am so frightened to go into these then just end up as a barista at some starbucks.

[math]test +[/math]
[math]\[+\][/math]

[math]f(x)=1/(1+x)[/math] for which numbers c is there a number x such that [math]f(cx)=f(x)[/math]
[math]cx=x[/math]
so
[math]c={1,0}[/math]
Is this right?

>>11225995
I meant c can only be 1 and 0. I looked it up on stackexchange and there wasn't a concrete answer.

What is the evolutionary advantage of gender dysphoria?
What is the evolutionary advantage of homosexuality?

>>11225995
the question says: for which [math]c[/math] has the equation [math]\tfrac{1}{1+cx} = \tfrac{1}{1+x}[/math] a solution?

>>11225876
Depends on what you want out of life, in general, hire-ability is like so:

Pure Math < Physics < Applied Math

If you're not from an Ivy-League you're going to have to dilute your studies with something, whether it be finance, computer science, statistics, biology or something else. Really though, mathematics is not an undergraduate-only degree, your hire-ability goes up immensely after graduate school no matter your undergrad, but recognize that graduate level math is not easy, not easy at all.

>>11226017
I'm not even sure what I want to do. I for sure don't want to get into academia and I don't want to be a programmer either. I think I will just commit suicide if I can't find a job after grad school.

>>11226086

Family. Family is the purpose you are searching for. Get married and have kids.

>>11226022
>how long does it take to self study something like Spivak. or a textbook more advanced than spivak in general? Is it realistic to complete it in the same time as a regular semester (2/3 months) or is it possible in one month? By complete, I mean study the text properly and not skim it.

bump

>>11226010
There isn't one. It's a product of living in a cube your whole life.

For my English assignment I have to prepare short talk on subject related to technology or science. What should I talk about?

>>11225995
for any c, f(c*0) = f(0)

>>11225657
In physics:
>Many different types of regulator are used in quantum field theory calculations, each with its advantages and disadvantages. One of the most popular in modern use is dimensional regularization, invented by Gerardus 't Hooft and Martinus J. G. Veltman, which tames the integrals by carrying them into a space with a fictitious fractional number of dimensions" (Renormalization & Dimensional regularization).
>>11225749
[math]\mathbb{R}^n[/math] is not just N-tuples aka functions from [math]\{1, 2, \cdots, n\ [/math] to [math]\mathbb{R}[/math] (isomorphism in various algebraic structures). This object is something called manifold too, metric space and many other things. Calling [math]\mathbb{R}^n[/math] the set of real N-tuples is just lack of culture.

>>11225577
Bump

In case you're bored, here's some review (and some lore)

https://youtu.be/5zLr7hAnrZY

>>11226369
how old are you? Are you a grad student?

Where can I learn math? Iv decided to try and go back to college but I have a couple months before I can get instate tuition. What can I do to try and place into college algebra?

>>11226428
Have you tried googling "college algebra textbook"?

>>11225577
Tensors as in smooth sections of [math]TM^n \otimes TM*^m[/math]?
Yeah, pretty sure. Diffeomorphism to R^n, pull back local trivialization of the tensor bundle, define the action by multiplication on the basis. Trivially independent of chart, should preserve smoothness.
>>11225657
There are spaces of real non-integer Hausdorff dimension, i.e. https://en.wikipedia.org/wiki/Hausdorff_dimension , but I'm not sure there're ones considered to be R^a.
>>11225682
He's talking about infinite-dimensional vector spaces.
>>11225749
When N is the cardinality of a large set.
>>11226200
https://en.wikipedia.org/wiki/Tryon%27s_Rat_Experiment
>>11226428
Khan Academy.

How do you get to vh? va and l are given and alpha is 60 degrees.
It's vh=va/sqrt(3) according to the solution, but I've no idea what to do here.

i know that matter can't travel faster than light, but that's usually talking about linear motion right? what about rotational velocity? can anything spin faster than light? I like to imagine a hugeass record player spinning an oversized record, and everyone knows that a point farther away from the center of the record spins faster, so the actual record doesn't even have to be going very fast, it just has to have a big diameter. what would happen if we actually made a really oversized record and spun it really fast?

Is [math]f(x, y) = xy[/math] differentiable on [math](a, b)[/math]?

>>11226626
>but that's usually talking about linear motion right?
It's talking about any motion.
>what about rotational velocity? can anything spin faster than light?
No.
>what would happen if we actually made a really oversized record and spun it really fast?
It would take an infinite amount of energy to reach the speed of light. If the disk was somehow already moving at the speed of light, then the solution to the Ehrenfest paradox says that the disk takes the form of non-Euclidean geometry and therefore no point exceeds the speed of light.

One case that people sometimes mention is that of shining a laser somewhere far and moving it around (lighthouse paradox), but it's solved when we realize that the new image is formed by new photons that were sent by the laser instead of photons that were rotated around, so nothing goes faster than light again.

>>11226788
>it would take an infinite amount of energy to reach the speed of light
what if we just made a really big-diameter disc out of the lightest material possible, attached a handle slightly off center, and gave it a gentle push? bad ms paint to accompy

>>11226812
to tack onto this as a variant, let's say you are a really big disc already and you're rotating near the speed of light, and you had some sort of mechanism to "bring your arms in" (like a figure skater) to get to the speed of light. what then?

>>11226674
yes

>>11226830
Life over as soon as the rotational forces exceed your bones and organs ability to keep together. Your idea would be a neat death for a Dethklok song.

>>11226812
Each particle on the disk is gaining mass/energy as it being accelerated, which is just linear motion, since the moment of inertia/angular momentum depends on the mass, this means the disk will require infinite amounts of energy to have some particle in it reach the speed of light.

Otherwise I don't really get what you mean by giving it a push on an off center handle.

>>11226830
That's the second part of my post, i should have specified that happens for relativistic speeds already, but if, even if you get a disk to a point where it relativity becomes important, it becomes non-Euclidean, so the ratio of the circumference to the diameter changes and no point exceeds the speed of light, basically, the force the particles feel takes time to travel around the object, so part of it moves while the other doesn't. In short, there are no rigid bodies in relativity.

>>11226899
by non-euclidean, are you saying the disc no longer exists in space as we know it, but instead it exists some sort of (hyper/hypo)bolic space instead? and
>part of it moves while the other doesn't
is interesting, that'd mean my disc w/ handle would indeed accelerate from my gentle push, but only certain sections at a time to stay under FTL. is that a consequence of existing in a noneuclidean space?

>>11226931
>by non-euclidean, are you saying the disc no longer exists in space as we know it, but instead it exists some sort of (hyper/hypo)bolic space instead?
It still exists in space disk, but it changes due to length contraction/time dilation, the ratio of the circumference to the diameter being pi happens in a flat space, but due to the relativistic effects, this ratio changes, which means the disk becomes non-euclidean.

>is interesting, that'd mean my disc w/ handle would indeed accelerate from my gentle push, but only certain sections at a time to stay under FTL. is that a consequence of existing in a noneuclidean space?
Consequence of the speed of light being finite, this means the speed/force that each particle passes after each collision to the next one, ie a wave, is limited by the speed of light as an absolute maximum (in real materials this travels at the speed of sound in the material).

What books should someone interested in learning how batteries work, to the point of being able to make their own, read?

>>11227009
A physical chemistry text book, probably

>>11227019
Okay, which one?

>>11227084
Nigga, did you even try to use google? Theres a text called "Modern Batteries" by Vincent and Scrosati. Start there if you already know basic chem. If you don't, read an intro chem text.

where can i learn more about the weak and strong nuclear forces? most videos i look up just seem like clickbaity layman explanations with no actual maths on them. hell, the way they're described doesn't even sound like a force at all (i.e. the weak force lets particles decay but electromagnetism actually incites motion). I guess what I want to know is, if the force describing gravity is F = GMm / r^2, what're the equations describing weak and strong forces?

>>11225448
If you only consider the "opening of the boxes" as your measurements, I'm afraid there is no way to tell the difference, assuming that this system works as you precisely described. However, there is a profound difference between those two sets of boxes, since the balls in each one are in states of "different statistical nature".

Let [math] \left\lvert {\color{Red}{R}} \right\rangle [/math] and [math] \left\lvert {\color{Blue}{B}} \right\rangle [/math] represent the states 'red' and 'blue' of a ball.

The first set of boxes denotes what we call a statistical mixture of those states. Assuming that the colors are equally distributed, the balls in there are then described by [math] \displaystyle \Big\lbrace \left\lvert {\color{Red}{R}} \right\rangle : \frac{1}{2} \,\, , \, \left\lvert {\color{Blue}{B}} \right\rangle : \frac{1}{2} \Big\rbrace [/math]. Therefore, the density matrix of the ensemble is [eqn] \hat{\rho}_{1} = \frac{1}{2} \left\lvert {\color{Red}{R}} \right\rangle \left\langle {\color{Red}{R}} \right\rvert + \frac{1}{2} \left\lvert {\color{Blue}{B}} \right\rangle \left\langle {\color{Blue}{B}} \right\rvert . [/eqn]

In the second set of boxes, prior to any measurement, all the balls are in the same state (the superposition one), so, the ensemble is in a pure state. Each one of the balls are in the state [math] \displaystyle \frac{1}{\sqrt{2}} \Big( \left\lvert {\color{Red}{R}} \right\rangle + \left\lvert {\color{Blue}{B}} \right\rangle \Big) [/math]. Therefore, the density matrix is given by [eqn] \hat{\rho}_{2} = \frac{1}{2} \left\lvert {\color{Red}{R}} \right\rangle \left\langle {\color{Red}{R}} \right\rvert + \frac{1}{2} \left\lvert {\color{Blue}{B}} \right\rangle \left\langle {\color{Blue}{B}} \right\rvert + \frac{1}{2} \left\lvert {\color{Red}{R}} \right\rangle \left\langle {\color{Blue}{B}} \right\rvert + \frac{1}{2} \left\lvert {\color{Blue}{B}} \right\rangle \left\langle {\color{Red}{R}} \right\rvert . [/eqn]

>>11227288
Notice that the difference between [math] \hat{\rho}_{1} [/math] and [math] \hat{\rho}_{2} [/math] is due to terms that describe the interference of states with different colors. Hence, given any measurement, the first set of boxes will NEVER display interference properties between the states [math] \left\lvert {\color{Red}{R}} \right\rangle [/math] and [math] \left\lvert {\colorBlue}{B}} \right\rangle [/math], but this is something that can occur for the second set, if the measurement is capable of extract information about interference. So, since there is a difference between those sets of boxes, you could, in principle, tell which 'group' is which by setting up, if possible, a proper experiment.

>>11225443
How the heck do you integrate a function like dy/dx = xe^x^2? What is it called when the power has a variable and also has a power? I mean in such a case I feel like we're supposed to use integration by parts but that still doesn't solve the problem of what to do with this power of a power.

>>11227449
let u = x^2 and du = 2x dx
so 1/2 du = x dx

y = 1/2 S e^u du
y = 1/2 * e^u + c
y = 1/2* e^x^2 + c

check with symbolab

Why is Lang's "Basic mathematics" a meme book?

>>11227449
substitution

>>11227479
>>11227512
W-woah, I had no idea you could use substitution like that, thank-you so much!!

>>11227503
It isn’t people just enjoy torturing newfags, the book will help considerably with review of highschool and middleschool math while giving you a chance to try your hand at fairly easy proofs with motivation, unlike insipid nonsense like proof books, logic books, baby set theory trash. Using it as an immediate primer before attempting college level texts is a good idea for people who would otherwise be bored by khan academy. no aspect of it is a meme other than its being spammed on this board for years. If you are unchallenged by Basic Mathematics the natural progression is Apostol/Courant/Spivak

>>11213159 #
Yes Yes and Hell no

I want to stop wasting time
How?
NVM, don't answer me
Else I'll refresh the page again and again for a reply.
I'm addicted.
I'm shutting down all these websites cold turkey

I hate when books do this
oh my god just say why

>>11225448
If Erwin Schrödinger is right, then the wave function of probability of the balls in a state of quantum super position only collapses once you open the boxes to look at them(measure them)

>>11227719
That's the geometric series for an infinite sum.

>>11227727
I recognize it now. Thanks.

>>11225443
Why do /sci/ hate or have strong opinion on Computer Science?

is it legal to use diethyl ether as a psychoactive to get high?

>>11227181
>where can i learn more about the weak and strong nuclear forces?
From a book about particle physics, the standard model or specifically the weak and strong forces.
>what do I need to know to read those?
Download one and read the preface, the author should specify what he expects. Scheck, for example, quotes
>I assume that the reader is familiar with nonrelativistic quantum mechanics and
with the foundations of special relativity.
in his book on strong and electroweak interactions.
That might sound like a lot, but it really isn't.
>>11227503
Conjecture A: Basic Mathematics is a meme is derived from "Lang is a meme.", which appeared for other reasons (i.e. HIV denial, Lang's Algebra, etc)
Conjecture B: The average person who asks for advice on a korean blue whale hunting forum would struggle with Lang, and is better off with Khan academy.
>>11227828
A friend of mine studies computer science.
He said his class is mostly "I learned python at 12" arrogant twats.
>>11227932
Legal where?

>>11227719
why?

>>11227971
I originally came here in 2008 to improve my whale hunting skills, but ended up becoming an experts on continuous actions on wrapped Fukaya categories, wtf

Can I represent the identity as a non trivial power series? E.g.
[eqn]t = \sum_{i=1}^{\infty}a_it^i[/eqn]

>>11228210
No. t^n is linearly independent of t^m, m!=n. t^m, t^o, etc cannot be combined to make t^n.

>>11228210
No, because [math]\sum_{i=
1}^{\infty}a_i0^i=0[/math]
>>11228230
Nice reply faggot.

>>11228210
>>11228230
>>11228240
What the hell? It's the questions that are supposed to be stupid.
[math]a_i = 1[/math] if [math]i=1[/math], else [math]a_i = 0[/math].

>>11228249
That's why I asked for a non trivial power series.
>>11228230
Also not in the limit?

>>11228210
Not in that way because you can prove that the series representation if it exists, is unique. However, you can look at other power series representations. For example, the fourier series representation would be non-trivial. And Fourier Series are just power series of [math] e^{ti} [/math].

>>11228249
>non-trivial
>>11228210
Something something really long post about edge of the wedge.
>>11228267
If you take the n-th derivative, you'll notice it always zeroes at 0 for n>1, which implies all of the power series' coefficients larger than one zero.
>>11228098
At least derived symplectic geometry has extensive applications to hunting seals.

>>11225443
Can someone explain why multiplying a number N by, say 13% or .13 gives out 13% of the said number N?

>>11228484
Because 13%=0.13 by definition. This a very stupid question.

>>11228491
You didn't understand what I am asking. I'm asking why does multiplying 75 by .4 give 40 percent of 75, aka 30? Why does multiplying work? I'm not seeing why this works.

>>11228534
Because multiplying by .75 is the same as multiplying by 75/100.
So you have [math]\frac{a}{100} \times 75[/math]. Division by 100 naturally gives you one percent of a, and multiplying by 75 yields 75% of a.

>>11228545
Perfect. Thank you!

Hey /sci/entists, brainlet here. I need to make something that looks like picrel, just using a different color scheme, and different "camera" angle. Just a single frame, no animation.

I can code, and want to render this as an SVG image. I only know some high-school tier math :D

What kind of math do I need to produce something like this? As far as I understand it, this is just some plotted equation, but what's the equation, and how do I know where to put all the points and lines on a 2D plane? :DDDD

>>11226000
Solve the equation (1/1+cx) = 1/(1+x)

How do I find a complex number given n of its roots and the radius of the circle the roots are on and the angle of one the roots from the real number axis?

>>11228889
de moivre's theorem

>>11228633
>>>/3/

What's a good course to take to get a good first touch with physics, and retain the knowledge because it's well explained? I don't wanna straight jump into calculus based physics, I want to learn all of the concepts first.

>>11228897
I can't believe it's that simple.

>>11228947
Algebra-based physics is a waste of time, I discourage you from taking that. Learn calculus first or take calculus concurrently with a regular, freshman general physics course. Basic calculus isnt hard, and a great many of the core concepts require calculus. Newton's second law is a second order diff. eq., for ex.

>>11228960
It isnt exactly intuitive though, is it? yw :*

>>11228965
I concur, several physics concepts are unreachable without knowing even some basic calculus, and the stuff that you learn in algebra-based physics is better explained with calculus anyway.

>>11228965
>>11229017
Alright I see. Thanks for the advice. I'm studying calculus currently. What's a good calculus based physics course in that case? MIT physics? I'm self studying because I don't retain much during classes.

What is Dark Matter and Dark Energy?

Trying to prove that if A and B are countably infinite, AxB is countably infinite. Is it a good enough proof if I define K as the set of naturals whose square root isn't another natural, excluding 1 (with each element being named then k_n), and then say. Let a_n be the elements of A, b_n the elements of B, then the function that goes from N to AxB is f(((l_n)^k)-1)=(a_n,b_k). Therefore, AxB is countably infinite. Is this a good enough proof?

>>11229086
>define K as the set of naturals whose square root isn't another natural
Fuck, make it the set of naturals that don't have a root which is another natural.

>>11229086
dunno
you didn't define l_n, k, and b_k, so I have no idea what you're talking about

>>11229050
>MIT
Sure, why not? This looks good~ https://ocw.mit.edu/courses/physics/8-01l-physics-i-classical-mechanics-fall-2005/

>>11229116
Ah, fuck, replace l_n with k_n. b_k would be the same as the b_n, only with another letter to show that (a_n, b_k) don't share the same subindex.

>>11229135
and what does the k in the exponent mean?

>>11229146
We can see that K's elements are 2, 3, 5, 6, 7...
Let's start with the sequence of the exponents of 2: 2, 4, 8, ...
You can then say 1=(2^1)-1, 3=(2^2)-1, 7=(2^3)-1
In other words, 1=((k_1)^1-1), 3=((k_1)^2-1), 7=((k_1)^3-1)
Thus, f(1)=(a_1, b_1), f(3)=(a_1,b_2), f(7)=(a_1, b_3)...
Then, repeating for the sequence of 3's exponents
f(2)=(a_2, b_1), f(8)=(a_2,b_2), f(26)=(a_2, b_3)...
And so forth.

>>11225443
Why aren't more helicopters constructed with a twin rotor like an RC helicopter to appease Newton's 3rd law?
Also god jenny is a hot robot

>>11229180
Taking a quick look on
https://journals.sagepub.com/doi/pdf/10.1260/1756-8293.2.1.1

Gives me the idea idea that the main reason probably is increased complexity which means higher manufacture and maintenance costs.

>>11229159
oh I see
I don't think that works, because you need a one-to-one mapping.
And here f(63) for example could be either (a_1, b_6) or (a_6, b_2).

The best place to discuss Aerodynamics is through usually forums through AIAA or colloquiums at your nearby University

>>11229234
Which is why I brought up this change >>11229093 so that numbers like 8, 32 and such aren't part of K. Therefore, K goes 2 3 5 6 7 10 11...

>>11229180
Its exceedingly difficult to construct, but Sikorsky/Boeing are working on it

>>11229240
oh right, my bad
that should work then

How do you prove by definition that pic related is differentiable?
I used the limit on the definition and then proved that it was zero with epsilon-delta, is that ok?

>>11229261
btw I would've just defined a function like f((a_n, b_m)) = (n + m)^2 + n
seems easier

>>11229264
Calculate the total differential and plug in the definition.
>I used the limit on the definition and then proved that it was zero with epsilon-delta, is that ok?
Sounds right.
>>11229280
Watch this:
Assume, without loss of generality, that [math]A=B= \mathbb{N}[/math]. If they aren't, take the trivial bijection from [math]A \times B \rightarrow \mathbb{N}^2[/math]. Fix the lexicographical order on [math]\mathbb{N}^2[/math], and either:
Take the trivial order preserving map [math]\mathbb{N} \rightarrow \mathbb{N}^2[/math], or
Prove [math]\mathbb{N}^2[/math] satisfies Peano's axioms.

>>11226558
(sorry for late reply)
Let the y axis be vertically downward, and the x axis be horizontal and to the right. let the points A, B, C, and D represent the roller to the lower left, roller at upper left, pin at upper right, and pin at lower right, respectively.
The velocity at B is hence given by [eqn] \mathbf{v_B}=v_A\mathbf{\hat{i}}+v_H\mathbf{\hat{j}}=\omega_{BD}\mathbf{\hat{k}}\times\mathbf{r}_{DB}=\frac{\omega_{DB} L\sqrt{3}}{2}\mathbf{\hat{i}}+\frac{\omega_{DB} L}{2}\mathbf{\hat{j}} [/eqn]
Set like components equal to each other and divide out common factors and you get
[eqn] v_a=\sqrt{3}\ v_H [/eqn]

>>11226558
(sorry for late reply)
Let the y axis be vertically downward, and the x axis be horizontal and to the right. let the points A, B, C, and D represent the roller to the lower left, roller at upper left, pin at upper right, and pin at lower right, respectively.
The velocity at B is hence given by [eqn] \mathbf{v_B}=v_A\mathbf{\hat{i}}+v_H\mathbf{\hat{j}}=\omega_{BD}\mathbf{\hat{k}}\times\mathbf{r}_{DB}=\frac{\omega_{DB} L\sqrt{3}}{2}\mathbf{\hat{i}}+\frac{\omega_{DB} L}{2}\mathbf{\hat{j}} [/eqn]
Set like components equal to each other and divide out common factors and you get
[eqn] v_a=\sqrt{3}\ v_H [/eqn]

>>11229180
tail rotors are easy to construct

>>11229356
***x axis is horizontal and to the LEFT

Are non-local hidden variables just a matter of "we can't think of how to test it, so we don't waste time considering it" or is there more to it than that?

>>11229423
IIRC it was something like this:
Imagine you have a dice.
You can describe it's behavior probabilistically: a dice has 1/6 of a chance to fall on each side.
Or, you can describe it's behavior purely deterministically, the way God intended:at creation, a dice comes with an infinite sequence of integers between 1 and 6. The n-th time the dice is thrown, the n-th element of the sequence is the side that shows up. Naturally, there is no way of measuring what will be the n-th side other than throwing it n times.
What we do know, however, thanks to extensive statistical research, is that approximately one sixth of dice have 1 as the first side, one sixth have 2, etc.

If [math] 9|m [/math] and [math] 11|m [/math], show [math] 99|m [/math].

Not really sure how to go about this. I know [math] m=9x [/math] and [math] m=11y [/math] for some [math] x,y\in\mathbb{Z} [/math], but I'm not sure how to combine them to get the result

>>11229545
Look, I dont know shit about number theory, but if 9 divides m and 11 divides m, doesnt that mean both 9 and 11 are (prime) factors of m? If 9 and 11 factors of m, doesnt that directly imply that 9×11=99 divides m? Isnt this trivial?

>>11229560
9 isnt prime lol nevermind, but i think my logic stands

>>11229545
How about a contradiction?

Assume [math]99 | m[/math] such that [math] 9 \nmid m[/math] or [math] 11 \nmid m[/math]
Then
[math] m = 99k = 11 \cdot 9 k = 11k' = 9k''[/math] and poof

This is a magnetic field that attracts gold:
https://www.youtube.com/watch?v=-9e7DBzdpQY&t=6m

I don't get this, is it because the aluminum plate acts as a catalyst for the field and the gold coin or is it because the friction of the gold coin against the aluminum is causing some other effect?

>>11229596
Gold isnt ferrous. Look up eddy current forces.

>>11229545
I think I'm too tired to even notice what side of the implication I'm on

Assume that [math] 9|m [/math] and [math] 11|m [/math], thus [math] m = 11k,\; m = 9k' [/math]

Then
[math]\displaystyle \frac{m}{9} = \frac{1}{9}11k = 11k'[/math]
[math]\displaystyle 9 \frac{m}{9} = m = 9 \cdot 11 k' = 99k'[/math]

>>11227719
classic brainlet complaint

In school-level maths (that's as far as I got) we use ±i as the solution to √-1.

Is the way we extended our number system into 2 dimentions the only possible way of handling √-1?

For example I was looking at 2x2 matrices as analogues for the numbers, and I see that there are an infinite number of matricies that square to -I (identity matrix).
$$\begin{bmatrix} a & b \\ -(a^2+1)/b & -a \end{bmatrix}$$
They all have a determinant of 1.

>>11229997
[math]\begin{bmatrix} a & b \\ -(a^2+1)/b & -a \end{bmatrix}[/math]

What software do you use to visualize math stuff, like vector fields or parametric surfaces?

So I was trying to recreate Lloyd's mirror using a cheap laser diode module, precision polished metal mirror and a piece of paper as a screen in attempt to see the interference fringe pattern, but no matter what I tried I couldn't see any. Both direct and reflected beams just overlapped like normal. Was I doing something wrong, or is my laser just too shitty for that? It does produce distinct fringe around the shadows of objects in the beam though.

>>11230179
Brain is soft.

>>11229593
Why do you need contradiction? And haven’t you just shown that [math] 99|m [/math] implies [math] 9|m [/math] and [math] 11|m [/math]?

>>11229671
What’s the logic behind [math] \frac{1}{9}11k=11k’ [/math]? You seem to be saying that [math] \frac{k}{9} [/math] is an integer, which, if so, your proof doesn’t need to go further that [math] m=11k [/math].

>>11229356
Thank you very much for the reply, anon!

>>11230376
The logic I used is that 9 doesn't divide 11, so k has to since 9 divides m.
I don't see why I wouldn't have to go further though?

>Why do you need contradiction?
I realized I didn't need it after, but like I said in my second post, all I had shown is that [math]99|m \Rightarrow 9|m, 11|m[/math] not that [math]9|m, 11|m \Rightarrow 99|m[/math], so I wasn't satisfied.

>>11230381
yw~ hope it made sense even if I skipped a couple details

>>11228549
You're welcome.
>>11228960
Ladies and Gentlemen, it's that simple.
>>11229264
>I used the limit on the definition and then proved that it was zero with epsilon-delta, is that ok?
Sounds about right.
>>11229997
>Is the way we extended our number system into 2 dimentions the only possible way of handling √-1?
It's the only well behaved way, yes.

But there are quite a few ways of constructing the complex numbers, even if they are the same object. See https://en.wikipedia.org/wiki/Complex_number#Matrix_representation_of_complex_numbers , for example.

>>11230179
Mathematica, Matlab, Gnuplot, Python, Geogebra, Mathstudio express.

The surface area of a cube without one face includes the interior area?

>>11229671
this is nonsensical and doesn't work
you could use the same argument to prove that 2|m and 4|m implies 8|m, which isn't true (take m=12 for example)

>>11229545
m is divisible by 9, so it has 3*3 in its prime factorization
m is divisible by 11, so it has 11 in its prime factorization
therefore it has 3*3*11 in its prime factorization
therefore it's divisible by 99

>>11230545
what are you finding the SA for?

>>11230230
>in attempt to see the interference fringe pattern, but no matter what I tried I couldn't see any.

It could be that you need the slit, so that all light is from the exact same direction?

>>11230558
>you could use the same argument to prove that 2|m and 4|m implies 8|m
However in that case 2 would divide 4, which means that the only thing we can guarantee is that k/2 is an integer, not k/4, hence why I could assert that k/9 is an integer.

>>11230567
They are asking me to find the rate of change of the surface area of a box without a face and I don't know if I should count the area of the faces from the inside or not.

>>11230581
>box
Of course you should.
Besides, even if it's wrong, you just need to divide everything by two later.

>>11230584
fair enough
thank you anon-kun

>>11230558
Perhaps a cleaner way, in that it doesn’t involve the FTA, is the following:
9|m and 11|m, so 99|11m and 99|9m. Furthermore 99|44m and 99|45m by multiplying the respective dividends by 4 and 5. Then clearly 99|(45m-44m) and 99|m.

This works because Bezout’s lemma provides integer values x and y so that (9x+11y)m=m, which in turn works because gcd(9,11)=1.

>>11230573
I called it nonsensical, because this part is just plain wrong and doesn't make any sense:
1/9 11k = 11k'

For example take m=198, then k=18 and k'=22.
1/9 * 11 * 18 = 11 * 22
This is obviously not true.

>>11230627
Ah that part.

I just noticed I wrote k' instead of k''
ie
m/9 = 1/9 11 k = 11 k/9 = 11 k'' for some k'', integer, not the k' from m = 9k'
so 9 m/9 = 99k''

>>11230612
huh that's pretty cool

>>11230647
ooh gotcha

this is an odd question probably no one will answer, but
if someone has been smoking for about a year, and smokes one cig pack which contains twenty cigs, every two to four days (usually takes them three days to finish) how many cigs will they have smoked altogether after a year? approximate/estimate is fine

>>11230668
20 cigs/pack * 127 packs/year = ~2500 cigs/year

>>11230690
oh damn. 2500 doesn’t seem like that much in retrospect, thought it’d be kinda higher
thx tho

>>11230690
>365/3=127
>20x127=2500
Your approximations fucking suck, buy a calculator.
>>11230668
Around 2433 cigarretes a year, assuming a pack every three days.

>>11230705
What's the point of giving him four significant figures when his own estimate has an error of plus or minus 50%? Did you think about that, remiliaanon?

>>11230728
are you talking about the person who asked the cig question? or the anon who said it’d be 2500 cigs per year?

>>11230728
It's not a matter of precision, it's a matter of you somehow getting 365/3=127.

>>11230734
I mistyped, hun. It really doesn't matter. 2500 is a reasonable estimate.

>>11230739
I reserve the right to call you out for getting the second largest digit wrong.

>>11230744
k

>>11230746
100 cigarretes are serious business.
If my cousin Alejandro had 50 more cigarretes back in New Mexico, he'd still be alive.

>>11230756
And yet 100 cigarettes is an error of 4% while anon's estimate had an error of 50%
god i wish cigarettes weren't so expensive ;_;

How do I prove this? I'm thinking the integral form of the remainder, but I don't really know how to use it, am I supposed to find the nth derivative?

>>11230569
The whole point and its distinct difference from the double-slit experiment is that it doesn't. Direct beam interferes with its own (coherent) reflection that works as the second virtual source and forms fringes. Or at least should, but not for me apparently.

>>11230800
>write arctan(x) as integral of something from 0 to x
>write the sum as integral of something from 0 to x
>???
>PROFIT

Fuck yea i now understand the PLL. Just want others to know it.

>>11230829
Do you know why Alison was so mean to Hanna in regards to her going as Britney Spears for Halloween in season 2 episode 13?

>>11230829
Aria is my favorite~

I need help with a problem.
[math]f(x,y)=-\sqrt{1-x^2-y^2}[/math]
There is a point [math]P=(\frac{1}{2},\frac{1}{2})[/math] with a gradient [math]\nabla f(\frac{1}{2},\frac{1}{2}) = (\frac{\sqrt2}{2},\frac{\sqrt2}{2})[/math] and I need to find the directions in which the directional derivative on [math]P[/math] becomes 0, but I don't know how to do it or to prove that there is no such direction..

>>11231236
>I have a vector and I can't figure out what vectors are orthogonal to it
What did he mean by this?

>>11225443
Suppose I have a function f, but I want to smoothly "skip over" one of the integer values of x. For example, if I have the function f(x) = 2x, but I want to skip the point (3, 6), so that the actual value of the function at x=3 is 8. So make a new function h(x) which takes on the following values:
h(1) = 2
h(2) = 4
h(3) = 8
h(4) = 10
h(5) = 12
etc.

In pic related, I am almost there. I make a sigmoid function s(x) centered at x=2.5. And I make a function g which is just f shifted over to the left one. And I use the sigmoid to transition from one to the other. But this is not an exact solution- it only asymptotically approaches the exact values I want. I would much prefer an exact solution to this puzzle (which is still smooth). I think all I need is to replace the sigmoid with a smooth function that is exactly 0 at x ≤ 2 and exactly 1 at x ≥ 3.

Can anybody help me out here?

>>11231244
Why does it need to be exact? Just use tanh(x) with a small width

>>11231243
dont be mean to someone trying to learn.
>>11231236
but yes, any vector perpendicular to the gradient will have that property. think of a mountain: the gradient points up the mountain in the direction of steepest ascent. what direction has a slope of zero? the direction that is perpendicular to the direction of steepest ascent. this can be proven formally. im sure your vector calc text talks about it.

>>11231257
Because I want to do this sort of thing at many different locations along a function arbitrarily close together, and I don't want the errors to add up.

I tried to Google this, but the search terms turn up vague results unrelated to my question. In a nuclear reactor, are there names for the isotopes created when say, a silver or zirconium control rod absorbs all those neutrons? Or are neutron heavy control rods too varied in composition from reactor to reactor to a newly designated isotope? Perhaps there is a name for this conglomerate such as there is for melted reactors, that being corium. Is there? Thanks guys.

>>11231243
>>11231277
Holy shit, I just remembered that the dot product can be expressed as [math]||A||||B||cos \theta[/math]
I feel so retarded right now, maybe I should take a nap.

>>11231277
>dont be mean to someone trying to learn.
But I wasn't.
>>11231244
Take a smooth bump function [math]b(x)[/math] with [math]supp ~b(x) \subset (2, 3)[/math] set [math] \hat{b}(x) = b(x) / \int b ~ d \lambda[/math], and let [math]h(x)= f(x) + \int_0^x \hat{b}(t)[/math] dt[/math], the solution.
Alternatively, if you don't care what values the function takes outside of the integers (otherwise you're basically locked into the above approach), do some simple periodic function trickery.

I took ODEs a few years ago and I forgot most of it. I'm trying to teach myself some beginner level PDEs. Can someone explain why the answer to this is f(y)e^2x? Is separation of variables the right approach?

What's the mathematical relationship between absorption rate and absorption capacity?

So if Mars is 13 light minutes away, could the best personal telepresence communication method involve knocking the parties unconscious while the signal is en route, then waking them up for brief windows of hearing, seeing and responding?

>>11231795
what

How do you find the points on [math]f(x,y)=\frac{1}{xy}[/math] that are closer to the origin?
I'm trying to use Lagrange multipliers but I don't know what constrain to use.

>>11231626
>Is separation of variables the right approach?
Yes. You mistake was in the 3rd line, not including the "constant" of integration, which turns out to be a function of a single variable y.
[eqn] \frac{\partial}{\partial x}u(x,y)-2u(x,y)=u_x-2u=0 [/eqn]
Separate the variables and integrate and you get
[eqn] \ln |u|+C(y)=2x \implies \exp\big(\ln |u|+C(y)\big)=e^{2x} [/eqn]
so
[eqn] e^{C(y)}e^{\ln|u|}=C'(y)u=e^{2x}\implies u(x,y)=f(y)e^{2x} [/eqn]

>>11231827
That's because the question doesn't make much sense if you don't add constraints to the hypothesis, you can see that for any fixed x, f will always get closer to 0 when y grows indefinitely, and same if you fix a value of y and let x grow. If you don't have any constraints then there is no point that is the closest to the origin, and there are infinitely many points that are as close as you want them to be (without ever reaching 0 of course). There is no single constraint that will give you the point that is (globally) the closest to 0.

can anyone help me find a certain blog post from some anonymous professor? i think thats what it was anyway

he was making the case that college algebra (and even by extension super-remedial english classes) shouldnt be offered at unis because anyone who takes them shouldn't be at uni in any capacity anyway, and they will invariably end up slogging through 4+ years, always struggling, maybe graduating with a bad gpa, maybe failing to graduate, while the uni is $60k richer at their expense. thus cheapening both the overall education quality status-quo as well as the real-life value of having a degree.

>>11231499
Thanks, I didn't know about bump functions until your comment. Looks useful. What are the bounds on the first integral?

>>11231499
>>11231963
Nvm, I think I have it figured out. Thank you!

>>11231886
use google lol

Whats this thanks for the 4 thing

>>11232058
some genuine schizo thinks his "celestial french girlfriend" is communicating with him thru numbers

>>11232107
Thanks anon

>>11230569
>so that all light is from the exact same direction?
Isn't it already? A slit makes a pattern on its own, mirror ir not, but does nothing otherwise. I've seen someone somewhere suggested passing the beam through a pinhole to select a single mode from a multimode laser somehow, but unless I did something wrong again there was no difference either. I don't really understand this single/multimode thing, and I don't have any idea what laser do I have in the first place, aside from power and wavelength. I also tried it with my other lasers, green and violet, as well as using a polarizing filter, with no noticeable results. I wonder what am I doing wrong.

is this category theory?

>>11225876
Many CEOs are psychopaths so the answer is yes.

>>11225443
What will happen when the internet goes dead?

Forgive me for my lack of proper language as I am a layman. Hypothetically, if you constructed a case of calcium entirely around a compass, would it still function as a magnet? To go further, at what point does a magnet stop "functioning"(if that is the proper term)?

>>11232589
Magnets can create perpetual motion machines

>>11232655
get out of here ken.

I'm pretty much a Math brainlet, but I've decided to apply myself. I've already looked at the guide in the sticky, but I want to gain a deep and solid understandig of the matter to the point of it becoming intuitive, so I feel like I should start even pre-undergrad and put in the work instead of jumping off of shitty, half-assed education.
Any recommendations for this in terms of books or courses?

>>11233112
At that low of a level, literally just google "pre calculus text" or use khan academy

>>11233112
Pre college math is basically just computations, get a proof book and learn how to do that first, this will teach how to think about mathematics properly, like How to Prove It A Structured Approach by Velleman.

>>11225443
I'm taking Calc 2 next semester and I took Calc 1 last fall so there's a year gap (did take discrete math in the mean time but not related). Could anyone rec some good online resources to refresh my memory and rebuild up my skills/knowledge?

>>11233156
khan academy for refreshers on the content itself
The Organic Chemistry Tutor on youtube for content refreshers and well-explained, worked-out practice problems. I recommend this guy over Khan desu.

scientifically speaking, how do I break the "hand to wiener" opoerant conditionI've developed for when I sit down at my computer desk
I'll just idly start touching my dick and it's really annoying, I don't want to be a coomer

I'm trying to get to ω*, which is the angular velocity of the "holder of the three planets" to which the three planets are attached.

I calculated the velocity vm at the midpoint of the planets, whereas the radius is 0.5(a1+a2) and get ω*=(v2-v1)/(a2+a1) through ω*=vm/r
Apparently the correct answer is ω*=(v2+v1)/(a2+a1).
Please help.

>>11230945
>>11230952
I ment phase locked loop.

>>11231499
>do some simple periodic function trickery.
What is the periodic function trickery? I'm afraid I can't see it.

I just got done taking Signals and Systems and passed with a A, but my professor was extremely incompetent and I literally have no idea what the fuck that class was even about. I just memorized problem solving strategies and got lucky that the questions on exams were similar to the ones I studied. I don't actually know what the fuck a Fourier transform is or how to do shit to time signals.

My question is: will lacking an understanding of fundamental signal concepts bite me in the ass in my later EE classes?

>>11233173
For a wheel that is rolling without slipping (like a gear), [math]
v_{center}=(v_{top}+v_{bottom})/2 [/math]. The outside diameter of gear one has speed [math] v_1=\omega_1 a_1 [/math], inside diameter of gear 2 has speed [math] v_2=\omega_2 a_2 [/math]. Notice that these speeds are also the speeds of the corresponding tangents of the planets. So the speed at the middle of each planet is [math]v=(v_1+v_2)/2[/math]. The radius from center point of 1 to center of planets is [math] a=(a_1+a_2)/2 [/math]. Because [math] \omega^*=v/a [/math] we get
[eqn] \omega^*=\frac{v_1+v_2}{a_1+a_2}=\frac{\omega_1a_1+\omega_2a_2}{a_1+a_2} [/eqn]

>>11233251
I can't say much about EE, but yeah that's probably not good if you don't recognize what a FT does. Do you understand the Laplace transform? It's literally that, but with [math] s = j \omega [/math] giving you pure frequency response of the system.
In general, "lacking an understanding of fundamental [core] concepts" is bad news, bud.

How to go monk mode in maths? Is it worth it?

>>11233324
dont go monk mode unless you already have PhD
being a NEET is really fuckin gay

German speaking anons, what does luftkubik/m^3 mean?

>>11233335
luft is air and kubik is cube

>>11233339
so does that mean cubic air per m^3?

>>11233335
>>11233341
are you studying psychometrics? it could possibly mean "kilograms of dry air per cubic meter" but I don't speak German

>>11231963
The entire real line.
>>11231991
Also works.
And you're welcome.
>>11232572
No.
>>11233246
I don't remember. I think I had some general idea but no actual method.
My bad.

>>11233348
No, it's in a text about construction engineering i'm supposed to translate and honestly i'm at a loss, don't know wtf it means

>>11233356
can you post a pic of the page or maybe some more context?

>>11233322
Based. Thanks again, anon!
What's your major?

>>11233369
ME~

>>11233357
here you go

This is probably retarded, the notes from our professor say that the energy of a photon is [math]E_r=(1+\beta)E_s[/math] for a receiver moving with a certain relative speed with respect to the source. However wikipedia says that [math]f_r=\sqrt{\frac{1-\beta}{1+\beta}}f_s[/math] and if I multiply both sides for h i get [math]E_r=\sqrt{\frac{1-\beta}{1+\beta}}E_s[/math] which is different from the notes, so what happened?

I know its stupid question but I cant recall it myself - how do you compute integral of multiple functions? I need to calculate integral of f(x)*sin(2pixt)/x and no, it's not homework. F(x) is function of x but without given form, it's data collected.

>>11233573
numerically

>>11233573
>f(x) is a function of x but without given form
Numerically.

>>11233322
I'm not quite sure why vm is listed as a2ω2-a1ω1 in the solution. Also, how does one determine ω of the actual planet?
>tfw compulsory mechanics course and studying something unrelated

>>11233613
they have a minus sign in their eqtn for Vm because they are not including the sense of V1 and V2. My equation for V_center necessitates that you consider the direction of V_top, V_bottom.

I'm doing some graduate level courses in control theory, and even though I'm putting in the work it's still difficult to understand a lot of the concepts. Are there certain topics you are just inherently not smart enough to understand?

The first derivative is rate of change of a graph
The second derivative is the curvature of the graph
The third derivative is ____?

>>11233742
the rate of change of curvature, or jerk. civil engineers need to consider this quantity when designing transitions between regions of different curvature.

>>11233754
civil engineers designing sections of highway, that is

>>11233757
>>11233754
I got the jerk part, but when analyzing a graph, where does it manifest? You can visualize the 1st derivative by drawing a line tangent to a graph at a point, you can visualize the 2nd derivative by noting if that line is above or below the graph at that point, where does the 3rd derivative show up?

>>11233766
You can't visually determine the third derivative through some neat trick, it's really just change of curvature. Look at it and think about how it fails to be a parabola.

>>11233766
It's the rate of change of curvature. Say you have a smooth and continuous function on (A,B). That function can be graphed. The curvature at any point along that graph can be thought of as 1/R where R is the radius of the circle that just barely kisses (osculates) with that point. If the third derivative is positive, that means the curvature is increasing locally. That means the graph will intersect the osculating circle. If curvature is not increasing, the circle is not intersected.

>>11233140
brainlet

Hi,
Why cos(pi/4) = sqrt(2)/2 = 0.70710678118
but cos(45) = 0.52532198881 please?

>>11233996
put the calculator into degrees mode when putting in cos(45). The calculator interprets that as cos of 45 RADIANS

>>11233996
because you forgot to change your calculator from radians to degrees.

>>11233998
>>11234001
oh thanks!
it gives me the right answer when I turn the calculator in radians mode actually (google calculator)

Since you guys are the smartest board by far, I thought I would ask if anybody can solve this puzzle. I’ve been at it for a few months now and I’m convinced, since the developer is just some guy he might have overlooked that its simply impossible. Here ate the rules

Objective: slide the little penguin guy to his mom

Mechanics: pieces (penguin or snowball) can only be moved orthogonally. They continue to move in a straight line until they come up an obstacle. The edge is not considered an obstacle, only other pieces. In fact you cannot even dispose of a snowball by sliding it off the edge of the board.

I can seem to get to a part where the penguin is aligned with the mother but two snowballs are in the way. You don’t want to download the app because this is one of the last levels just use pencil and paper or coins or something.

>>11234105
>The edge is not considered an obstacle, only other pieces.
So you fall off?

What the FUCK is inter-universal Teichmuller theory about?

[eqn]\lim_{x \to 0}\frac{e^{\sin x}(x \sin x-1)}{\cos x}[/eqn] pls halp

>>11234128
Just break it up into:

lim (e^sinx) * (lim (xsinx/cosx) - lim(1/cosx))

1 * (0 -1)

-1

>>11234128
literally just plug in x=0

>>11234105
the snowballs don't slide off? just push centre one down and right, slide penguin into it and up.
pic related

>>11234112
>>11234156
I take that back. You guys are super dumb. I said the edge wasn’t an obstacle and I later alluded to the fact that its not legal to push snowballs off the edge of the board (implying that’s exactly what would happen if they came against the edge). Furthermore if the answer was that simple I would have solved it. According to the game, it says it takes at least 20 moves.

>>11234179
>you guys are super dumb
You can't even ask questions correctly.

>>11234191
Wrong

>>11234179
shut up you stupid frog

>>11234201
To say that something is “not an obstacle” literally means that it doesn’t “obstruct” movement. Yeesh...

>>11234264
https://math.stackexchange.com/questions/318555/prove-that-frac-d-dx-xn-nxn-1-for-all-n-in-mathbb-r

>>11234179
what is the game called so I can try the mechanics

>>11234264
Based

Has anyone here ever successfully proven a series doesn't converge through contradiction?
Specifically, something that looks like:
>suppose it converges
>then, it converges to a and to b, but a=/=b, so it doesn't converge
Or some similar Ramanujan-like trickery.

>>11234264
that's some very lazy memeing to get the desired negative sign

>>11234435
Pigu Puzzle

>>11234128
the function is continuous around 0 so lim f(x) = f(0)

why is it 105/252 and not 126/252?

>>11225443
I just decided to add fractions in fractional form rather than decimal for the first time in 20 years and used this calculator to relearn how to do it.

https://www.calculatorsoup.com/calculators/math/fractions.php

I had no issue relearning how to do it, but this one line in the instructions threw me off, "This is basically multiplying each fraction by 1." I completely fail to see how this is true, as 1/3 was multiplied by 7 and 4/7 was multiplied by 3. Where exactly did multiplying by 1 happen?

>>11235000
It is 126/252.

>>11234520
>laughs in a non-Hausdorff space

>>11235017
You are multiplying 1/3 by 7/7, i.e. 1, and you are multiplying 4/7 by 3/3, i.e. 1.

>>11235019
i thought so, man my prof is always putting wrong shit in