/sqt/: Stupid Questions Thread

>>8551660
Reposting my q

Seroius question: what is the average diameter of the human penis when erect

>>8551685
Integral of the diameter over the length of the penis, divided by the length of the penis.

>>8551696
Nigga u dum. dats da average diameter of A human penis, not THE human penis.

How do you use figures from other papers? Do I just screenshot them and give credit in the figure caption? I don't want to believe that I have to email the authors of each publication to use them. If it matters, the papers are typically published on arxiv so very open

anybody doping biophysics here? how do you like it?

>>8551703
THE human penis is my penis and I can confirm anon is correct

Copying my post


Someone wanna explain how to use the normal form of a transition matrix to solve differential equations?

Currently working on
[eqn] \ddot{x} + 2 \dot{x} + x = 0 [/eqn]
Letting [math] v := \dot{x} [/math], gives
[eqn]

\begin{pmatrix}
\dot{v}\\
\dot{x}
\end{pmatrix} =
\begin{pmatrix}
-2 &-1\\
1 &0
\end{pmatrix}
\begin{pmatrix}
v\\x
\end{pmatrix}
[/eqn]
Letting the matrix equation be [math] \dot{X} = A X [/math]
The characteristic values are both 1.

And that's about as far as I can get with repeated characteristic values.
How do I find the rotation matrix P such that
[math] P \dot{X} = P A P^{-1} P X [/math]
I know that the normal form of A should be given by
[eqn] J = P A P^{-1} = \begin{pmatrix} 1 & 1\\ 0 & 1 \end{pmatrix} [/eqn]
and that if I find P, I can define U such that [math] U = P X [/math],
and use some easier differential equation solutions to solve the new [math] \dot{U} = J U [/math]

How often do you masturbate? Do you find it easier to study when you masturbate frequently or when you abstain?

>>8552071
If it's not an equation with complex eigenvalues you shouldn't really need to find a diagonalized matrix... And even if you were to diagonalize it it would not require a rotation matrix.
This has a pretty obvious first solution, being Ce^(-t), and to find a second solution you need to find a generalized eigenvalue of that matrix- namely a value of lambda such that
[math]
(A-\lambda I)^2 = 0
[/math]

>>8552092
abstain ftw

>>8552093
sorry, determinant of that.

>>8552092
Abstaining works better because I can't stop masturbating if I start.

>>8552100
lel same

that's why i have to study at the library

>>8552105
Library doesn't work for me. I always end up figuring out a way to masturbate.

>>8552132
lel. i get distracted by qties

>>8552132
Same. I can't get myself to go to the library instead of masturbating.

>>8552093
Yeah the solution to this one is pretty easy. Just fixing up my notes, and would like an easy worked example.

[eqn] x = c_1 \exp (-t) + c_2 t \exp (-t) [/eqn]

I might have the signs wrong

>>8552137
>>8552132
Would you say you are addicted?

>>8552165
Yes.

Is it true that the geocentric model isn't exactly wrong, it simply leads to complicated math and retarded revolutions of the planets around the earth?

>>8552197
It's fucking wrong because gravity, nigga
Nothing intrinsic about the theory matters.

>>8551671
He just multiplied the top and bottom of the fraction by 2, and distributed the negative sign into the e^x terms.

>>8552217
Wow, great explanation, "nigger."

Black people should be banned.

>>8552231
>Implying I'm black
>>>/pol/


Models that don't accurately predict things thay they try to model are wrong. That simple. The trick is to know when the model's wrong or not.

>>8552197
The heliocentric model isn't quite right either. The Earth orbits the barycenter of the Sun-Earth system, which isn't always within the Sun.

You can construct the terran-centric model, but it's a non-inertial frame.

>>8552327
You're non-inertial, boyo.

>>8552197
Yes, you can construct a geocentric model that predicts the same observations a heliocentric model does. However it'd not be capable of explaining why the planets move that way, since it's complicated motions cannot be explained with gravitation or any know physical law.

>>8552231
First day on 4chan?

What are some useful tools or techniques to figure out how matric multiplication will affect vectors?
It's a total pain to calculate one possible vector at a time; can I make some sort of 3D map of vectors, rendered based on how the matrix would affect those vectors?

My problem is that when a vertex of an object passes off-camera, my maths causes that vertex to fuck off some random place which of course makes a total mess of rendering.

>>8552298
That gives me a basic understanding, but it doesn't let me understand why things happen like a vertex suddenly jumping to another place.

What's the difference between undergraduate and graduate school? In terms of content, material and grading on what?

Is there something like Gilbert Strang's series of recorded lectures about linear algebra, but for discrete math?

>>8552553
There's this: https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-fall-2010/
But these are actual classroom lectures as opposed to Strang's style

>>8552557
Looks interesting, thanks. I will miss Strang and his savant ability to explain various concepts and how they interact.

How are most of you formatting equations? Word? LateX?

>>8552529
undergraduate: emphasis on coursework
graduate: emphasis on research

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>>8552600

Can someone explain to me why this proof of the rational numbers between 0 and 1 has Lebesgue measure 1 is wrong? I know it is wrong as the converse is true, but the proof itself seems pretty satisfactory.

Suppose that the rational numbers between 0 and 1 have Lebesgue measure e such that e < 1. Then there exists a countably infinite sequence S of open intervals S such that the union of every set in S contains every rational between 0 and 1 and has measure e, which is less than any other possible union of open intervals that still contains all of the rationals between 0 and 1. We assume that the sets in S are disjoint; if not, an alternative sequence S' could be created such that for all n, S'n = Sn set minus the union of all of the intersections between Sn and the S'ms such that m < n; each set in S' would have less than or equal measure to its counterpart in S, so this sequence would have lower Lebesgue measure than S, which would contradict S's claim to have the least total length of any covering of the rational numbers between 0 and 1. We can therefore re-index S with indexing T such that for all j, the endpoint of Tj is less than the start points of all Tk such that k > j. Denote the endpoints of the various sets in T as a11, a12, a21, a22, a31, ... So S = T = (a11, a12) U (a21, a22) U (a31, a 32) U ..., with the endpoints of these intervals being of increasing order.

Now, take N = (0, 1) / T. This is clearly equal to (0, a11] U [a12, a21] , still with countably many intervals. As (0, 1) is of measure 1 and T is of measure e, N must be of measure 1 - e, which is greater than 0 as e < 1. So at least one of the intervals in N must have Lebesgue measure > 0; take that interval, note that since it's an interval it contains all numbers between its start and endpoint, produce a rational from density, and you obtain a contradiction.

I abused notation here a little with S and T standing either for a sequence of intervals or a union, but you get the gist.

>>8552327
>which isn't always within the Sun

How far out does it get?

>>8552777
>S'n = Sn set minus the union of all of the intersections between Sn and the S'ms such that m < n

An open set minus an open set is not necessarily open.

>>8552817
Thanks for this; this blows up my proof quite handily and allows me a greater intuition as to why the converse is true; the problem is that the sets are non-disjoint.

So I'm working on a problem, and I have an approximate solution from a slightly different problem which I'm working through for understanding before I get to work on my own one as I'm somewhat rusty on the math.

Basically I understand everything up to this point, where I get

[eqn]
S = 2 \epsilon_0 \epsilon_r \sum_{n=1\ (odd)}^{\infty} A_n (\frac{n\pi}{a}) cos \frac{n\pi x}{a} cosh \frac{n\pi b}{2a}
[/eqn]

Now, I also have as an approximation the condition that
[eqn]
S(x) = 1 \ for\ |x|<\frac{W}{2} \\
S(x) = 0\ for\ |x|>\frac{W}{2}
[/eqn]

Next the author says, "Equating these and using the orthogonality properties of the cos(n pi x/a) functions gives the constants An such that:"

[eqn]
A_n = \frac{2a\ sin\frac{n \pi W}{2a}}{(n \pi)^2 \epsilon_0 \epsilon_r cosh \frac{n \pi b}{2a}}
[/eqn]

And it's this step that loses me. I have no idea what it means for the cos term to be orthogonal (and thus magically turn into a sin?), nor how the overall jump was made from S=... to An=... . Does anybody know how the math would go in this? Or have something similar I can look at to see how it works so I can figure this one out? It's probably something quite simple but I've been at the overall problem for a while now and I'm just totally stumped.

>>8552817
>>8552825
Actually, wait a second; can't you induct upwards from S using the triangle inequality in such a way that each generation of a given element of S's sequence is either equal to the union of the corresponding element from the previous generation and all other elements that were not disjoint with it, or the null set if last generation's corresponding element was already pulled into some other element this generation? Because you've only got countably many sets, eventually you'll run out of non-disjoint sets and the process terminates, and it's a valid thing to do because the triangle inequality exists so each generation will have less than or equal measure to the last generation. So you'd still have gaps in the line that the complement can come in and screw you over with thanks to density.

>>8552838
I dunno but this might help: (scrolling down a bit) http://tutorial.math.lamar.edu/Classes/DE/PeriodicOrthogonal.aspx

Can you said that a vectorial space is a sub-vectorial space of itself or is it retarded ?

>>8552904
Yes, just like a set is a subset of itself. It's not retarded, but it's trivial. (also, in english it's a vector space not a vectorial space you silly frenchman)

>>8552898
Ahh that's actually quite helpful, thanks a lot!

Why is psychological addiction a thing?

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>>8552954
https://www.youtube.com/watch?v=36GT2zI8lVA

>>8552071
Bumpity

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>>8552784

>>8553003
Is there a mathematical model to predict the center of orbit on a flat plane from just those recorded points?

>>8552909
What if it's a set of all sets that don't include themselves?

>>8553080
That's not a set :^)

Where the hell is the ∉ key?

>>8553086
Sure it is. Let's call it R (like bertrand Russell).
R = { x | x ∉ x}

How is that not a set?

>>8553092
>How is that not a set?

Before we proceed, let's define "set." You first.

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>>8553112
That's pretty straightforward. It's a collection of objects. In this case, it doesn't really matter if it's a collection of mathematical objects, and a set itself is also an object.

Are we really gonna go down the rabbit hole and ask each other to explain set theory from the ground up?

>>8553144

>Are we really gonna go down the rabbit hole and ask each other to explain set theory from the ground up?

Yes, because the resolution to Russell's paradox is that you cannot construct the set of all sets that do not contain themselves from the axioms of ZFC. Also, "set" is undefined, like "point" and "line" in Euclid :^)

how would you prove the riemann hypothesis? if it's false, it would suffice to provide a single example of a non-trivial zero with a non-0.5 real part, right? but if it's true, what kind of proof would be needed?

i mean that's literally the million dollar question... but there ought to be some previous work/ideas on this subject to read about

>>8553162
Hehe that was fun

>>8553211
Let z be a zero of the Riemann Zeta function. (some equations or whatever) Therefore Re(z) = 1/2.

Alternatively, assume Re(z) is not 1/2. (some equations)
(a contradiction)

You're right about the false part.

>>8553011
Yeah. Check out the 2-body problem

>>8553211
Yes, providing a number that breaks the hypothesis would be sufficient. But that's not the only way to prove it's false; lots of disproofs of theorems are given without actually providing a counterexample (the first example of this I encountered in number theory is that pi(x) > Li(x) infinitely often, which was proven but didn't give an actual number, and it was 20 years before anybody even got a bound on where that number was)

Describing "what kind of proof" is needed in concrete terms is impossible. There's a decent probability it may not even be a direct proof of the original statement because there are six bajillion statements equivalent to the Riemann Hypothesis nowadays.
Nobody is close enough to doing it (as far as I know) to say with any heft that their approach is the right one. And even when (if) somebody finally does it the proof is likely going to be absurdly technical and inexplainable to anyone who isn't an expert in the particular subfield it came from.

I think I really fucked up...

How strict are colleges about deadlines? I just realised that a few of my college choices require a Math II subject test, which I never took. They sat scores are all due January 1st...will my application be canceled or can I still take the january sat subject test?

>>8553388
You may be fucked. Big administrations don't like making exceptions for people, especially when your excuse for needing the exception is either "I forgot" or "I didn't read the requirements".

That said they do want your money so you _may_ be able to arrange something, although don't count on it. Call the offices of the colleges you're looking at immediately and try to find somebody in admissions who can help you or confirm you're screwed.

any organic chemistry people here? taking org 1 and there's this one stupid question about diels alder reactions having two adducts that I can't get right for the life of me. It's this online homework site OWL, doesn't give great advice on the specifics you are getting wrong.

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Hey /sci/, I'm approaching the limit of transferable courses I can take at my community college. My problem is that I don't really care for getting my degree just yet, and would personally rather burn through my FAFSA taking all the classes I find interesting. I've yet to dabble into chemistry and philosophy at my community college, but doing so would put me well over the transferable limit, meaning some classes were essentially for nothing (though they also were free through FAFSA).

Anyone have any recommendations here? Should I just suck it up and move on to a four year, or should chill and enjoy life and soak up that dank free knowledge?

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Why does one whiff of pic related get me instantly high? Most inhalants, you have to huff for ten or twenty seconds to get anywhere.

>>8553162

>"set" is undefined

Thank GOD someone speaks the truth. I get so fucking triggered whenever one of my profs defines a set.

>>8552777
I don't know if I'm saying bs but maybe it is because Lebesgues' mesure of the sets containing the rationnal numbers in [0;1] is not the same as Lebesgues' mesure of the set of rationnal numbers in [0;1]

>>8552851
Can you spell that out more clearly? I don't know what you're trying to say.

Actually, the problem I pointed out can probably be fixed (using closed intervals is essentially the same) -- an interval minus a finite set of intervals is always a finite set of intervals. So, I'm not sure what the real problem is. I'm skeptical that finding a smaller disjoint cover is possible.

>>8553003
cool, thanks

>>8553162
That's only one possible resolution. The set of all sets that don't contain themselves DOES exist in NF. It uses stratified formulas instead of building up the set universe iteratively.

>>8553162
Wildmemer pls go

>>8553712
Wait, never mind. It doesn't exist in NF either but for different reasons.

Could someone give a good sample of TeX notations so I can right-click it and see the code? I'd like to see all the fundamentals so I can pick it up and use it quickly.

Y'know, fractions, abs, Boolean operators and equal sign variants, integrals (including contour and surface), matrices, vector notations, summations, pi product notations, probabilistic and set functions, subscripts, roots, derivative notations, unique symbols like the Laplace transform and the set of reals, size controls, and color palettes.

>>8553764
https://www.sharelatex.com/learn

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i have to write a script that computes the pearson correlation of two signals of different lengths using the conv function in matlab
im being told that if i do conv(x,fliplr(y)) that ill get the cross correlation, but when i do that i get pic
left being regular correlation and right being the conv thing
im very confused
any help much appreciated

I need some real advice in how to prepare for the EJU exam.
These are the syllabi:
www.jasso.go.jp/sp/en/eju/examinee/syllabus/index.html
(I only need

I would appreciate any (books, pages, study plan, schedule, whatever) recommendation!

I'm self studying and I'm free 24/7.

Sorry for asking this here, I don't know if it's the correct place to do so. If so, could you point me towards where I can ask this? (in my country there are no preparation courses decent enough)

[MATH] Euclidean division

n^5 + 5n^3 + 7n^2 + 8n + 19 = (n+7)q + r with 0 <= r < q


Someone has a method for do this kind of exercice ?

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Why can you not create a 100% pure solution of ethanol by distilling a mixture of ethanol and water? I get that water and ethanol form an azeotrope at 95.6% which has a lower boiling point than the individual components.
However, if you start, say, with a 50:50 mixture of water and ethanol, as the ethanol evaporates, you will never reach a 95.6% concentration in your heated flask.

>>8554327
You can create a ethanol solution that is very close to pure. Something around 99%. Chances are there will be some water that comes along for the ride.

If [math]4^x + 4^{-x} = 34[/math], what is

[math]2^x + 2^{-x}[/math].
Any help? The answer is supposed to be 6.

>>8554326

You're not too intelligent, you're just setting your expectations too high for others. You should learn to conceal your intelligence and blend in with people. This in itself is an interesting challenge to a certain degree.

>>8554394
Square the second expression.

>>8554394
[eqn]4^x+4^{-x}=2^{2x}+2^{-2x}=(2^x+2^{-x})^2-2=34[/eqn]

>>8554470
>>8554489
Thank you very much.

>>8554309
divide the long polynomial by n+7 using the division algorithm

or

write q = an^4+bn^3+cn^2+dn+e and match the coefficients

I have a function that outputs a binary value. Is this notation valid?

[math]f: R \mapsto \{0, 1\}[/math]?

>>8551670
>autosaging
It's called a bump limit... Faggot

>>8554739
Also what if a function outputs a value between 0 and 1? Can I [math]f:R \mapsto [0, 1][/math]?

>>8554739
Yes
>>8554788
Yes

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>>8554326
go into cocoon mode

focus on things you can do on your own that will help you become successful in life (building wealth, learning skills, improving your appearance etc)

>>8554326
You mean too unintelligent

please tell me that complex numbers aren't the final frontier of algebra

please

>>8554868
they're not

>>8554872
so, is there any operation that needs a new kind of number?
or are you referring to abstract infinite aleph shit?

>>8554885
what do you mean operation?

>>8554885
quaternions are 4d numbers if that's what you mean

>>8554885
you can extend the complex numbers by adjoining a solution to [math] z \bar{z}=-1 [/math]

there's also quaternions, octonions, the field of rational functions with complex coefficients C(t), the list goes on

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Need to provide a bijection of [0;1] into ]0;1[.

Check mine, but don't spoil it if it's wrong:

f(x) = x, except
f(0) = 0.1, f(0.1) = 0.01, f(0.01) = 0.001, ...
f(1) = 0.9, f(0.9) = 0.99, f(0.99) = 0.999, ...

>>8552448
bump

>>8554916
whay thehell does ]0,1[ mean

>>8554929
(0,1)

>>8554929
the range between 0 and 1 excluding 0 and 1 themselves

>>8554936
why why don't you use >>8554933

>>8554929
I thought it was novel notation for (-inf, 0] U [1, inf), but I guess it isn't.

>>8554916
seems like it works, there's a nice theoretical way to do it though using cantor-schroder-bernstein theorem

>>8554327
Not even fractionating columns save you from having to deal with vapor pressure. Sorry

>>8553609
It's really up to you, if you value the free education you're getting right now and don't care about retaking a few courses, I'd say stay. Otherwise leg it to uni

>>8554950
yeah, just use the identity from (0,1) to [0,1] and (x+1)/4 from [0,1] into (0,1), both injections, thus a biejction has to exist

>>8554941
because you have to learn some notation you fuck

>>8554966
your notation is gay and nonstandard. kill urself

>>8554968
>your notation is gay
science is gay
>and nonstandard
get the fuck out of my board

>>8554950
> theoretical way to do it
You mean prove they are equipollent without providing the bijection? That was not the point.

I did it by showing that (0,1) is a subset of [0,1] and [0.1, 0.9] is a subset of (0,1) that is equipollent to [0,1] by definition of continuum. Correct?

If matter can't be created nor destroyed, how does the universe keep expanding? Is it just stretching?

>>8554971
>You mean prove they are equipollent without providing the bijection? That was not the point.
the theorem provides the bijection, what do you mean by that's not the point?

>>8554999
It doesn't provide anything, it just states that a bijection exists. The point was to PROVIDE a bijection, not just prove it exists.

>>8555013
the proof is constructive...

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>>8551670
What field of science can I actually earn decent amout of money with a Bachelors degree in?

>>8555027
chemical engineering.

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>>8555027
Mathematics

>>8555022
Are you retarded or trolling? The proof doesn't PROVIDE a bijection, it only proves it's existence.

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>>8555027
engineering. civil, mechanical, or electrical. do literally anything you wan't after that. a BS in engineering is like packing a tradesman's van into your back pocket. you can literally take it anywhere in the world and make a decent living. if you really want to work for yourself its also the degree that facilitates that the best.

get your masters in theoretical underwater philosophy if you just have to have that academic fulfillment.

>>8555143
why are you so stubborn/defensive? you sound like an insufferable person

how exactly do you think the proof proves the existence of a bijection without giving you one? is this some weird non-constructive math you're working with?

>>8555143
>The proof doesn't PROVIDE a bijection, it only proves it's existence.
Now this here is a brainlet

>>8554993
energy can be created, emdrive is a proof of that

>>8555188
>>8555237
Jesus fucking H. are you two retarded. Go to wiki and see it for yourself.

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Is this for fucking real? Is the author trolling me?

Here I am, trying my best to study and all, and this shit suddenly shows up and ruins it. I think my mind is fried for the rest of today.

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>>8555271
>using wiki for proofs
truly brainlet behaviour, go read a book dumbass

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6 years ago I went to univerity for Social Work (You cannot shame me more than I have shamed myself). I dropped out after 1 year with terrible grades.

I am reapplying to university to study physics (I have the pre-reqs). Will my meme program's credits affect my average while I am in school for physics?

>>8555279
a) it's a soft book for retards
b) screen is fucking irrelevant

>>8555297
>a) it's a soft book for retards
what?

>b) screen is fucking irrelevant
feel free to read the book on a screen, this doesn't change the fact that the proof gives a bijection

try not being a dumbfuck and calling other people retarded because you think the proof on wiki is the only one, even though the wiki article literally says there's multiple proofs

>>8555297
Please stop acting high and mighty about first year mathematics, you're just embarrassing yourself

>>8555278
What? That looks like a good 'ol fashioned hairpin loop.

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How does this statement GIVE YOU ANY SPECIFIC BIJECTION YOU MORONIC FAGLET?!

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Spoonfeed pls

Length of A

Is it possible to get post-baccalaureate research experience in mathematics?

I participated in research my freshman, and sophomore years. I was diagnosed with a brain tumor my junior year. Afterwards, I never got back into research because I was just trying to get my degree, and get back to a decent state of health again.

Now, I want to apply to graduate school, but
1. My grades post-tumor diagnosis are mediocre as fuck. 3.1 GPA I think. Probably 3.5-3.6 from before it.
2. I haven't been involved in research for 3 years, and I want to go into a field unrelated to that research.

This should probably go in /adv/, but they're basically no help.

I just e-mailed a prof. at a large university local to me, and the plan is basically to ask him to take me on as a research assistant either with, or without pay, gain some relevant experience, and then re-evaluate what my options are.

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>>8555317
see
>>8555279
it's from kolmogorov/fomin's 'introductory real analysis'

the proof is basically a recipe you fucking moron
>input injections
>output bijection

maybe when you get past first year you'll learn to read the proofs before acting retarded

>>8555282

Is it the same school? If yes, then it could. If they never figure out you're the same person, then I guess you could dodge it.

If not, then no.

>>8554910
>>8554910
>you can extend the complex numbers by adjoining a solution to zz¯=−1zz¯=−1

Can you elaborate on this?

>>8555334

So I have to suffer for mistakes I've made 6 years ago?

AAAAAAAAAAAAAA

>>8555343

6 years ago? This is something you should e-mail their admissions/advisors about. You'll get a much more definite answer than you're gonna get here.

>>8555338
http://mathoverflow.net/questions/257317/what-structure-do-you-get-if-you-adjoint-a-root-of-z-barz-1-to-the-compl
http://math.stackexchange.com/questions/1902190/adding-a-root-of-z-bar-z-1-to-mathbb-c

>>8555278
Zinc dick

kek

Forgive me kek but I am curious enough to want to know this.

The problem: A poster in a 4chan's board will be assigned with a global number K that will be incremented by every post. Occasionally, the poster will get a "dubs" K = (...XX), "trips" K = (...XXX) or "quads" K = (...XXXX) where X is the repeated number in the least significant digits.

At first I was thinking that the probability for any c amount of repetition is simply:

9/(9n ), where n is the number of digits

because there's only 9 configurations where repeated number is possible for any size of digits:

|{11,...,99}| = 9

|{111,...,999}| = 9

...

but then I realize that this is very theoretical and that it does not take into account the speed by which the board is being posted on. So there must be someway to incorporate a function:

f(t) := the number of posts over a given time

and also the fact that over time it will get harder to get the magical numbers. It's been some time from my last probability class. Ideally, I would like to arise to a function:

f(a,b,c) where a is the current value of K, b is the rate of posts, c is the number of repetitive digits

Any help is appreciated!

>>8555328

Is this a brain cancer day or something?

> (0, 1) becomes itself
> [0, 1] becomes [0.1, 0.9]
Where's the bijection output? Why do I not see it? Oh yeah, that's because you're a pmsing fucking cunt. Check the iq boost recipe, down's.

>>8555278
It's Patrick's head from Square Pants. if it's a dick, how come there's no head?

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>>8555373
you obviously still haven't read the proof or even read the image >>8555279 that explicitly writes down the bijection

how much spoonfeeding do you need? you know when you get past first year people won't hold your hand every step of the way right?

>>8555356
hmm ok. Not very fleshed out but it shows it is possible at least.

>>8554961
I guess this was obvious from the start. I just wanted an artist to tell me how retarded I'm being by potentially wasting that kind of time (after all, sooner i get degree sooner I potentially get high paying job - so theres quite the opportunity cost really, especially considering I could simply self study whatever it is I want to learn).

>>8555392
What proof? The image makes no fucking sense since it's out of context.

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>>8555488
this is the last spoonfeeding i'll give you brainlet if you don't even know how to download a textbook yet

best of luck in second year, hope you take it more seriously than how you're treating your first year studies and you become more mature, math only gets deeper from here on

>>8555496
I know the fucking proof and it has nothing to do with the subject. You are so deep up your ass, you don't even know what we were talking about.

You got two fucking sets. You can prove they are equipollent using this theorem, but it doesn't contain a scheme to get the bijection between them. I can't believe I'm still talking to you, autist.

>>8555519
what part of 'here we can even afford the unnecessary luxury of explicitly writing down a one-to-one function' isn't good enough for you moron? am i really overestimating you undergraduates too much here?

>>8555519
There are multiple proofs of the theorem. Try Conway's "Division by 3" paper for the more explicit version which is based on a back-and-forth argument.

Does the measured space [math]\left( \mathbf N,\, \left\{ A \,\subset\, \mathbf N \left| \left(\frac{\mathrm{card} \left( A \,\cap\, [\![0,\, n ]\!] \right)}{n \,+\, 1} \right)_{n \,\in\, \mathbf N} \,\text{is convergent} \right.\right\},\, \mu: A \,\longmapsto\, \lim_{n \,\rightarrow\, \infty} \frac{\mathrm{card} \left( A \,\cap\, [\![0,\, n ]\!] \right)}{n \,+\, 1} \right)[/math] have a name?

How do you find how long it takes for two objects to collide in 1d space? Logic tells me you need to make some differential equation with newton's law of gravitation but im not sure where to go fromthere.

>>8555571
Hint: as long as your force depends on position or speed, Newton's second law of motion is a differential equation.

After solving your differential equation (calculating all the constants with the initial conditions), you solve [math]x_1 \left(t\right) \,=\, x_2 \left( t \right)[/math] for [math]t[/math] and that gives you the moment your two objects collide.

>>8555571

Do you know how fast the two objects are moving?

If the rate at which they're moving is an equation, try to see if you can put it in terms of "how quickly is the gap between them closing"

I.e. if they're both moving towards each other with a speed of 1, then the distance between them is closing with a speed of 2.

>>8555524
>>8555536
I honestly can't believe there are people this fucking retarded. The question WAS NOT ABOUT PROVING FUCKING C-S-BT, it was ABOUT A SPECIFIC CASE IT COULD BE APPLIED TO.

And what was needed is NOT TO JUST PROVE A AND B ARE EQUIVALENT, but to actually provide a fucking bijection. Your luxuriously unnecessary function is _NOT EXPLICIT_ you dumb fucking cunt. Why not take it a step further and provide a bijection F(A) = B without any more detail. CSBT is a given, so it must exist.
Only, see, THAT'S NOT THE FUCKING POINT YOU IDIOT.

>>8555635
no one's interpreting the question as 'prove c-s-bt' you fucking mongoloid

> Why not take it a step further and provide a bijection F(A) = B without any more detail.
because you havent listed any injections, have you still not read the proof? you input two injections and output an explicit bijection [math] \varphi [/math] which is literally given in the remark immediately after the proof

>>8555635
Is English your second language?

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>>8554916
>>8554966
>>8554969
>>8554971
>>8555013
>>8555143
>>8555271
>>8555297
>>8555317
>>8555373
>>8555488
>>8555519
>>8555635

>getting this fucking ass-blown over babby real analysis

KEK. Great job, guys. This was a fun read. What a fucking sperg.

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>>8555663
does elementary set theory even count as real analysis? we covered cardinalities in my first year calculus class

but i agree this sperg needs a few life lessons

I have to solve this system of non-linear differential equations:

[math]\frac{dx_1}{dt}=a(x_1x_2-x_3x_4)+bx_3+cx_4[\math]
[math]\frac{dx_2}{dt}=a(x_1x_2-x_3x_4)+bx_4+cx_3[\math]
[math]\frac{dx_3}{dt}=-a(x_1x_2-x_3x_4)-bx_3-cx_3[\math]
[math]\frac{dx_4}{dt}=-a(x_1x_2-x_3x_4)-bx_4-cx_4[\math]

I got the solution as t goes to infinity, but i need to calculate the time development of every element of x.

Is possible that the "grey aliens" are just genetically engineer monkeys made in Area 51?

>>8555702
shit. then a real sq: How do you write equations?
[latex]\frac{dx_4}{dt}=-a(x_1x_2-x_3x_4)-bx_4-cx_4[\latex]

>>8555702
>>8555714
use [/math] instead of [\math]

>>8555022
https://en.wikipedia.org/wiki/Schr%C3%B6der%E2%80%93Bernstein_theorem
>However, its various proofs are non-constructive, as they depend on the law of excluded middle, and are therefore rejected by intuitionists.
The kid's right.

>>8555726
explain this one:
>>8555496

>>8555726
The citation for that is by a 'scientific historian', not a mathematician

>>8555726
>>8555729
"Constructive" is a very technical term. Be careful with it. http://mathoverflow.net/questions/123482/is-there-a-constructive-proof-of-cantor-bernstein-schroeder-theorem

>>8555736
You might do well not to dismiss someone off-handedly like that, and instead considering you might be wrong.

>>8555702
>>8555725
thanks. so what do you do with non-linearity?


[math]\frac{dx_1}{dt}=a(x_1x_2-x_3x_4)+bx_3+cx_4[/math]
[math]\frac{dx_2}{dt}=a(x_1x_2-x_3x_4)+bx_4+cx_3[/math]
[math]\frac{dx_3}{dt}=-a(x_1x_2-x_3x_4)-bx_3-cx_3[/math]
[math]\frac{dx_4}{dt}=-a(x_1x_2-x_3x_4)-bx_4-cx_4[/math]

>>8555744
sure but the examples used for non-constructivity are contrived sets, not a unit interval

>>8555768
it shows that the proof is not constructive in general. giving an "explicit" surjection is not enough. it's on you to prove it's constructive in this case.

>>8555749
read a book on partial differential equations. you want to simplify the quadratic part, and bring it to a canonical form. in general solving whatever you get can be hard.

>>8555793
does it help if I know particular solutions and eigenfunctions?

>>8555784
if A=[0,1], B=(0,1), A1=B and B1=[1/4,1/2]

then using the construction above with
f: A -> B1 defined by f(x)=(x+1)/4
g: B-> A1 defined by g(x)=x
gives


[math] A_{2k}=[\frac{1-4^{-k}}{3},4^{-k}+\frac{1-4^{-k}}{3}] [/math]
[math] A_{2k+1}=(\frac{1-4^{-k}}{3},4^{-k}+\frac{1-4^{-k}}{3}) [/math]

[math] N=\{ \frac{1-4^{-k}}{3}, 4^{-k}+\frac{1-4^{-k}}{3} \mid k\in \mathbb{N}\} [/math]
[math] M=[0,1] - N[/math]

so the bijection phi(a): A to B given by
phi(a)={ (a+1)/4 , if a is in N; a if a is in M

>>8555834
({0,1} also in N of course)

>>8555371
The speed does not matter unless you take the current post number into consideration too.
The server recives posts, puts them in a queue and processes them one by one.

Your position in that queue can be considered random if them board is fast enough that you can not predict the number of posts that will occour between your posting and the server processing your request.

If that is not the case you have to modell the number of posts between your post and the server asigning you a number.

let k be the current post number and X be a random variable and consider for simplicity that X has bernoulli distribution 1/2.(This has very little to do with the actual distribution which depends on your ISP, the board itself, your distance to the 4chan servers and alot more)

This means that there is a 50% chance that when you post another poster posted before you (this means X=1) and a 50% chance that no one else posted before you (this means X=0).

Your post numbere will be:
k+X+1.

So P(k+X+1=dubs) is 0 if k does not end in dubs - 1 or dubs - 2 (e.g. k=63 or k =12312313 as there will only be at max 1 poster after you and it is impossible for you to get dubs)

If k ends in dubs - 1 (e.g. k=198)
P(k+X+1=dubs)=1/2 as you get dubs if no one posts before you

And if k ends in dubs -2 (e.g. k=42)
P(k+X+1=dubs)=1/2 as you only get dubs when someone posts before you.


Notice that the chance of geting dubs is the same for getting quads or any arbitrary post number because this modell does not assume that your post number is randomly generated but rather tries to predict what your post number will be.

>>8555642
You dumb fucking faggot.

I DID PROVIDE THE INJECTIONS >>8555373 as you can see

And as I hope you can also see, applying f([0, 1]) creates {0.5} and g((0, 1)) is an identity function after the first time. Don't just parrot out what you memorized - think, for one fucking second.

The "recipe" (fucking kek) they provide doesn't always apply. Just like in this fucking case. Which means - it's fucking useless, generally speaking.

>>8556539
" [0, 1] becomes [0.1, 0.9]" is not an injection moron, you haven't listed where a single element gets mapped to

you know to define a function you need to list more than just the domain and range right?

see >>8555834 for this recipe in action, maybe you can learn a thing or two

>>8556539
also what is f and g here? why are your posts so unclear? is this elementary set theory really too complicated for you to follow?

>>8556549
How is this not obvious you weak memory autist? AS I FUCKING WROTE IN MY OP >>8554916 and g is an identity function.


I'd look at the post you quote, but I prefer reading math syntax as opposed to latex code. Maybe you should learn basic latex before being a cocky ignorant cunt.

>>8556568
nvm latex was glitching.

As I said, this schematic DOES NOT work for every case.

Try applying it to >>8556568 and see for yourself.

>>8556568
how is that function from [0,1] to [0.1,0,9] if f(0.9)=0.99?

> but I prefer reading math syntax as opposed to latex code.
what does this even mean?

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>>8556574
also how do you STILL not understand this? i literally worked out an example and you still seem to think that both me and Kolmogorov are lying to you

>>8556575
Because f(1) is specifically 0.9 and f(0) is specifically fucking 0.1. AS. I. WROTE.

After that it's if it's smaller than 0.5, f(x) = x - 10^(r-1)*9
if it's bigger, f(x) = x + 10^(r-1)*9

or whatever. Can be literally anything, lots of ways to do it.

>>8556577
You're not lying, you're just being retarded or trolling progressively less subtle.

EXEMPLARY function on injections DOES NOT always apply, hence "in this case we can afford unnecessary luxury".

>>8556578
... are you fucking braindead

f can't be a function from [0,1] to [0.1,0.9] if f(0.9)=0.99 because 0.99 is bigger than 0.9

you seem to think that if f is a function from [a,b] then it has to map into [f(a),f(b)] for some strange reason

please tell me you realize 0.99 is larger than 0.9

>>8556579
the textbook doesn't use any 'exemplary function'... i used (x+1)/4 as an example to show how the bijection looks, but as kolmogorov writes this bijection is defined for any injections f and g

>>8556583
Okay, change that to f adding to a/subtracting from b d/10 where d is b/10.

So it's [0,1], [0.1,0.9], [0.11,0.89], ...

You still can't use the schematic on it.

>>8556579
also lmao did you ACTUALLY unironically add "in this case" to that sentence to suit your needs? jesus

>>8556599
>You still can't use the schematic on it.
why not? what's so special about your injection that it doesn't the recipe which is defined for arbitrary injections?

>>8556600
>>8556599
i.e. tell me at which part of the proof the schematic fails

>>8556600
Well try it and see for yourself, you god forgotten low level fuck.
> that it doesn't the recipe
Kek, relax, you're hysterical. In more senses than one too XD

>>8556604
>Well try it and see for yourself, you god forgotten low level fuck.
the recipe is defined for ARBITRARY injections, unless your function isn't an injection, it will work

tell me at which point of the proof your injection creates an issue that an arbitrary injection doesn't

>>8556599
>Okay, change that to f adding to a/subtracting from b d/10 where d is b/10.
>So it's [0,1], [0.1,0.9], [0.11,0.89], ...
you realize you're defining a different function for each interval here right, if the function depends on the endpoint 'b' of the domain's interval?

>>8556613
As much as I'd like to TELL YOU it's good for you to do exercises yourself. Maybe you'll improve your cognitive abilities to the point of not being a flaming retard with bright hints of autism.

>>8556617
It's original b. I wanted to add that, but figured you'll understand. Story of my fucking life: having high hopes for degenerates.

It's not a different function by definition of a fucking function. Is f(x) = x/x also a "different function for every argument"? Hahaha. Pathetic.

Hahahaha, holy shit. They're still going at it.

>>8556621
kek

define one injection for me and i'll gladly go through this recipe once more for you to make another bijection just to show you how confused you are

if you don't reply to this with an injection i'll assume you're trolling at this point

>>8556629
if f is from [0,1] and 'f adding to a/subtracting from b d/10 where d is b/10'
f(1)=1-1/10=0.9
and
f(0.9)=0.9-1/10=0.8 which is obviously not 0.89

>It's not a different function by definition of a fucking function. Is f(x) = x/x also a "different function for every argument"? Hahaha. Pathetic.
what are you even talking about here?

>>8556639
>f(0.9)=0.9-1/10=0.8 which is obviously not 0.89
I'll make it simpler for you so you don't have to use your tiny brain as much.

f(x) = x + d, if x < 0.5
f(x) = x - d, if x > 0.5

d = smallest element + 10^(rank of the smallest element - 1)

>>8556599
>You still can't use the schematic on it.
What do you mean when you write this?

You know the proof that shows how sqrt(2) is irrational by assuming sqrt(2) can be written a/b? Your argument here is analogous to saying 'I have an a/b that this proof won't work for'

>>8556657
smallest element of WHAT? what is rank? why is it so hard for you to define a function?

>>8556658
Fact is a fact.

>>8556669
>Fact is a fact.
Huh?

>>8556667
Of the domain you mindless bimbo.
> he doesn't know what a rank is
HOLD ME

I'VE BEEN TALKING WITH AN AUTIST WHO STILL HASN'T OPENED A CHAPTER ON REALS.

JESUS FUCKING GOD

>>8556674
is the function you want me to work with this?:

f(x) = x + 1/10, if x < 0.5
f(x) = x - 1/10, if x > 0.5

what obscure terminology are you using? there's not even a wikipedia entry for whatever you're talking about
https://en.wikipedia.org/wiki/Rank#Mathematics

>stupid question thread
>someone asks a stupid question
>everyone gets triggered

Never change, /sci/.

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>>8556679
i never thought someone could be so confused about what a function was

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>>8556657
this isn't an injection you stupid monkey, whatever d is you have

f(0.5-d)=(0.5-d)+d=0.5
f(0.5+d)=(0.5+d)-d=0.5

>>8556678
Effectively d is 10^(-1, -2, -3, ...).

> hurr durr its not even on wigipedia!
Hahaha what a silly slut. Rank is basically the biggest power of q (which in decimal system is 10) in a sum representation of the number.

So for 200 it's

2*10^2 + 0*10 + 0*1

r(200) = 2.

>>8556686
It will never touch 0.5 retard. It's gonna be 0, 0.1, 0.11, 0.111,... and 1, 0.9, 0.89, 0.889,...

>>8556691
>It will never touch 0.5 retard. It's gonna be 0, 0.1, 0.11, 0.111,... and 1, 0.9, 0.89, 0.889,...
i just listed two elements which go to 0.5

how will it 'never touch'? i'm done here if you don't even know what an injection is

are 0.5-d and 0.5+d not elements of [0,1]?

>>8556693
What a stupid piece of shit. f adds/subtracts only for least and greatest elements.

Just like with 0 to 10 bijection into 0 to 1. Only 10 changes to 1 and then all the in-betweeners take care of themselves.

>>8556703
> f adds/subtracts only for least and greatest elements.
then why write 'f(x) = x + 1/10, if x < 0.5'
you realize 0.5-d is less than 0.5 right? is it this hard for you to be explicit about what function you're working with? you wouldn't get any marks on a homework or test if you handed this in

if f only changes the least and greatest elements of [0,1] then you're saying f(1)=0.9 and f(0.9)=0.9 since 0.9 isn't the greatest element of [0,1], so f still isn't an injection

try again

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>>8556712
>>8556703
any independent observer want to chime in here? i'm not sure how to get through to this poor brainlet, he's more confused than anyone i've ever had in office hours or tutoring

>>8556720
I dunno man, but I applaud you for the successful troll. Very subtle

>>8556724
What troll?

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>>8556703
do you want me to use the function
f(x)=0.8x+0.1? because that's an injection sending 0 to 0.1 and 1 to 0.9

i'll keep guessing if you want, i just want you to understand why you can't find an injection that somehow magically makes this proof which works for arbitrary injections not work

Looks like >>8554916 is where it all began.

That's not a bijection by the way, because it's not an injection.
Let x1 = 1, x2 = 0.9
then f(x1) = 0.9 = f(x2) but x1 != x2

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>>8556736
I don't think he will ever get it at this point...

I thought things like injections were covered in most high schools but I guess not all of them, I just hope he invests in a tutor before getting slammed on an exam

>>8556745
Nigga what kind of fucking high school did you go to? Most high schools only go up to fucking trigonometry and shit, math for literal babies. I don't think the majority of kids going out of high school would be able to tell you what an injection is

>>8556736
>That's not a bijection by the way, because it's not an injection.

Yes it is, f(0.9) = 0.99, not 0.9.

>>8556759
I went to a shitty public school in Ontario

Injectivity was taught as 'one-to-one' and surjectivity as 'onto'

In grade 12 we did
Functions
Polynomials
Rational Functions
Trigonometry
Exponential and Logarithmic Functions
Combination Functions

Limits and Continuity
Derivatives
Curve Sketching
Calculus Applications

Basic Vector Operations
Working with Lines and Planes in 3 space
Testing for Collinear and Coplanar Vectors
Distance between Points and Lines
Intersections of Lines and Planes

>>8556768
Okay nevermind, that seems pretty standard to me.

My only quip is that the particular terms "injectivity" "surjectivity" etc. aren't usually taught (in my experience). But the ideas are.

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>>8556771
>>8556771
>My only quip is that the particular terms "injectivity" "surjectivity" etc. aren't usually taught (in my experience)
fair enough, I don't think I heard the words until going to university

meanwhile there's russian high schools where the students are already learning about manifolds and algebra :/

>>8555371

f(a,b,c) = [math]Prob(|W_a| \leq 1/10^c)[/math] where W is a Wiener process with standard deviation [math]\sigma b[/math]

You'll need to provide one more parameter [math]\sigma[/math] which is the frequency of posting surges -- if a board has lots of HAPPENINGS then the probability becomes very close to the theoretical ideal 1/10^c.

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

I know they do this sort of thing in mathematical finance, but I never took those courses. It's a long shot, but /biz/ (of all places!) might be able to help you out. Tell them that you're looking to insure yourself against failed dubsgets and need help pricing the option, or something like that.

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>>8556703
still waiting on that injection monkey

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I left uni for some strange reasons. I plan on continuing education later, but right now I need some recommendation letters.
Is it weird to ask for a recommendation letter from a professor whom I didn't met for 2 years? I aced his class, and he was very positive about me (to extent of organizing a well paid internship for me). I'm afraid I'll look like a failure who needs a recommendation letter after 2 years, though I could have achieved much more.

Also,
>autosaging
picreleated

>>8556768
One-to-one is a bijection you dumbbell.

Anyway, it's

> f(x) = x + d, if x < any other element
> f(x) = x - d, if x > any other element
> f(element that's gonna become 0.5) = basically any irrational number
> f(another element that's gonna become 0.5) = any other irrational number

> d = 10^(rank of the smallest element - 1)

FOR EXAMPLE (specifically for retarded cucks like you):

f(0) = 0 + 10^(0 - 1) = 0 + 0.1 = 0.1

f(0.9) = 0.9 - 10^(-1 - 1) = 0.9 - 0.01 = 0.89

>>8556932
i'm aware one-to-one sometimes refers to bijectivity, my school used non-standard terminology, sort of like your rank

why is it so hard for you to define a function without turning it into a mess? i bet if anyone else came into this thread they would have no idea where your f sends a given element

if
>d=10^(rank of the smallest element - 1)
then why do f(0) and f(0.9) subtract different amounts? is the smallest element of [0,1] not 0? why does the rank change depending on the input?

>>8556932
Not that guy but if you have two irrational numbers that both get sent to 0.5, then how is it still a bijection?

>>8556932
also this is exactly what i meant by
>you realize you're defining a different function for each interval here
because you're defining a new function every time you shorten the interval

>>8556949
More precisely, if a function f is bijective then it has an inverse (call it F) that is also a function, such that f(F(x)) = x = F(f(x)) for all x in [0,1]

So what is the value of F(0.5) in this case?

>>8556944
> why do f(0) and f(0.9) subtract different amounts?
of course here i meant add and subtract
as in if f(0)=0+d and f(0.9)=0.9-d, why are your d's different?

>>8556944
Because the DOMAINS CHANGE YOU AUTISTIC EMPTYHEAD

When 0 is the least element the domain is [0, 1] hence the rank is 0.
When 0.9 is the greatest element the domain is [0.1, 0.9] hence the rank is -1.

>>8556949
> two irrational numbers
> both get sent to 0.5
Is this a fucking joke? Is the punchline "the barman says "back the fuck off""?

What are other places you can ask stupid questions on apart from /sqt/?

>>8556986
if the domain changes it's not the same function you fucking idiot... why are you using the same f?

i asked for ONE injection, not multiple

you should put down zorich and go read the definition of a function somewhere, you know that expression you need to learn to walk before you learn to run?

>>8556989
>>8556735

>>8556997
HAHAHAHA so if I have f(x) = x*2 that's defined on naturals, applying it to primes would make it A DIFFERENT FUNCTION?! For fucks sake read a textbook for a difference. Not your colgohomorov shit. Clearly it's too difficult for you.

>>8557015
not the same thing obviously since the function doesn't depend on the domain

you're giving me a function f: [0,1] -> [0.1,0.9] defined by 'either adding or subtracting 1/10' right?

restricting this f to [0.1,0.9] is still 'either adding or subtracting 1/10' map

but you're defining a new function which adds or subtracts 1/100

is this really too difficult for you to see?

>>8557028
It's not 1/10 and 1/100 it's AN EXPRESSION THAT USES ELEMENTS OF THE DOMAIN AND IS EQUAL TO 1/10 and 1/100. There's a difference.

>>8557048
how can the smallest element of the domain be both 0 and 0.1?

give me ONE bijection f from a subset of [0,1] to (0,1) and ONE bijection g from a subset of (0,1) to [0,1] and i will produce a bijection from [0,1] to (0,1) using cantor's theorem exactly as done in the textbook i quoted

>>8557058
> give me two bijections and I'll give you one bijection
Hahaha I don't like that price. How about two injections for a bijection AS YOU CLAIMED YOU CAN DO using your BS-C T magic?

>>8557064
jesus you're not this lost are you, can you not read the word subset? an injection from [0,1] to (0,1) is the same as a bijection between [0,1] and a subset of (0,1)... and an injection from (0,1) to [0,1] is the same as a bijection between a (0,1) and a subset of [0,1]...

>>8557064
that's clearly what he meant, do that so he can show you and you can fuck off

>>8557076
i don't think he gets it if he still thinks he can magically come up with injections that break a >100 year old theorem with several proofs

>>8557058
Eh, I'll give one then.

g: [1/3, 2/3] -> [0,1], x -> 3x-1
f: restriction of g to (1/3, 2/3)

>>8557081
ok, so inverting your functions to fit into the notation of >>8555496

let [math] A=[0,1], B=(0,1), A_1=(1/3, 2/3), B_1=[1/3, 2/3][/math]

then using the construction with
[math] f: A \to B_1[/math] defined by [math]f(x)=(x+1)/3 [/math]
[math] g: B \to A_1 [/math] defined by [math]g(x)= (x+1)/3[/math]
gives

[math] A_{2k}=[\frac{1-3^{-k}}{2},3^{-k}+\frac{1-3^{-k}}{2}] [/math]
[math] A_{2k+1}=(\frac{1-3^{-k}}{2},3^{-k}+\frac{1-3^{-k}}{2}) [/math]

[math] N=\{ \frac{1-3^{-k}}{2}, 3^{-k}+\frac{1-3^{-k}}{2} \mid k\in \mathbb{N}\cup \{0\} \} [/math]
[math] M=[0,1]-N [/math]

and so we get the bijection
[math] \varphi: [0,1] \to (0,1)[/math] defined by
[math] \varphi(x)= \begin{cases} (x+1)/3 & x \in N \\ x & x \in M \end{cases} [/math]

sin (x) = sin (x+30*)

How would one solve this without looking at the unit circle

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>>8557108
woops, forgot to apply [math]g [/math] for the way back:

the
[math] A_{2k}=[\frac{1-3^{-2k}}{2},3^{-2k}+\frac{1-3^{-2k}}{2}] [/math]
[math] A_{2k+1}=(\frac{1-3^{-(2k+1)}}{2},3^{-(2k+1)}+\frac{1-3^{-(2k+1)}}{2}) [/math]

[math] M= \{ (\frac{1-3^{-(2k+1)}}{2},\frac{1-3^{-2(k+1)}}{2}), (3^{-2(k+1)}+\frac{1-3^{-(2(k+1)+1)}}{2},3^{-(2k+1)}+\frac{1-3^{-(2k+1)}}{2})\mid k\in \mathbb{N}\cup \{0\} \} [/math]

[math] N=\{ [\frac{1-3^{-2k}}{2}, \frac{1-3^{-(2k+1)}}{2}], [3^{-(2k+1)}+\frac{1-3^{-(2k+1)}}{2},3^{-2k}+\frac{1-3^{-2k}}{2}] \mid k\in \mathbb{N}\cup \{0\} \} [/math]

[math] \varphi(x)= \begin{cases} (x+1)/3 & x \in N \\ 3x-1 & x \in M \end{cases} [/math]

>>8552197
Tychonic system

>>8557159
[eqn]\sin(x) = \sin(x + \frac{\pi}{3})[/eqn]
Cancel the sines
[eqn]x = x + \frac{\pi}{3}[/eqn]
Subtract the x's
[eqn]0 = \frac{\pi}{3}[/eqn]

>>8557159
sin(x) = sin(x+30)
sin(x) = sin(x)sin(30) + cos(x)cos(30)
sin(x) = sin(x)/2 + cos(x)cos(30)
sin(x)/2 = cos(30)cos(x)
sin(x) = 2cos(30)cos(x)
tan(x) = 2cos(30)
x = arctan(2cos(30))
x = pi/3

ez pz lemon squeezy.

But, if you know trig m8 then you know that the solution is actually

x = pi/3 + npi where n is any integer

>>8557199
wtf?

>>8557199
0 = pi/3 is not true, yet the answer is pi/3 ? Is it usually like this?

Good explanation, i have just gotten started with radians, and it seems to simplify stuff alot.

>>8557223
Thanks

>>8557238
pi/3 is 60 degrees, not 30 degrees, >>8557199 is wrong

>>8557238
>0 = pi/3 is not true, yet the answer is pi/3 ? Is it usually like this?
>Good explanation, i have just gotten started with radians, and it seems to simplify stuff alot.

No, his solution is wrong.

The solution pi/3 but he just lucked out.

His problem is that he used the arcsin function, which is just defined from -1 to 1, which is why you get a contradiction.

There is no solution from -1 to 1, which you can check graphically.

That is why I used arctan, which is defined from -infinity to infinity. Basically, that guy either knows no trig or is trolling you.

>>8557223
That's the wrong trig identity senpai. You did it for cos(a+b)

>>8557281
this

now i want to know the real solution

Euclidean division (with n a natural number):
2003 = n * q + 8
3002 = n * q' + 27

How find the value of the divisor n ?

Thanks !

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>The left hand is divisible by p, while the right hand side is not.

I'm really not getting this. I don't think it's hard but I don't understand what Hardy is getting at in this point.

How do rotational coordinate transformations work?

I understand how a vector can naturally be represented using sine and cosine, but I have no idea how you'd derive the rotation matrix (This one: https://en.wikipedia.org/wiki/Rotation_matrix)

>>8557420
cos(a + b) = cos(a)cos(b) - sin(a)-sin(b)
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

a is the original orientation of the vector
b is the amount of rotation
a + b is the new orientation of the vector
then to get the new vector you multiply (cos(a + b), sin(a + b)) with the magnitude of the vector

>>8557443
>cos(a + b) = cos(a)cos(b) - sin(a)-sin(b)
cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

>>8557397
after establishing the identities p_m=q_m for every m=1,...,k (k=j), he wants to establish the powers of each prime are the same on each side

if you have p_i^a_i on left side and p_i^b_i on right side, and a_i >b_i then you can divide each side by p_i^b_i and leave p_i^(a_i-b_i) on the left, and no p_i on the right

but now the left hand side is divisible by a prime that the right hand side isn't, which is a contradiction

hence you must have a_i=b_i

>>8557420
let the unit vector in the x axis (1, 0) be
⌈1⌉
⌊0⌋
and the unit (basis) vector in the y direction be
⌈0⌉
⌊1⌋
Then the matrix A(ϕ) that rotates (counter clockwise) a vector by ϕ will take the unit vector in x direction to
⌈cos(ϕ)⌉
⌊sin (ϕ)⌋
and takes the y vector to
⌈-sin(ϕ)⌉
⌊cos(ϕ)⌋
Thus A(ϕ) equals
⌈cos(ϕ) -sin(ϕ)⌉
⌊sin (ϕ) cos(ϕ)⌋
Therefore the unit vector at θ to the x axis will be rotated to θ+ϕ after applying A(ϕ)
⌈cos(ϕ+θ)⌉=⌈cos(ϕ) -sin(ϕ)⌉*⌈cos(θ)⌉
⌊sin (ϕ+θ)⌋=⌊sin (ϕ) cos(ϕ)⌋*⌊sin (θ)⌋

>>8557368
n is a divisor of 2003-8 and 3002-27. find the gcd of 2003-8 and 3002-27, n must divide that. it's 35, so n divides 35. you can't determine n though, it could be 35, 7, 5, or even 1.

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I'm getting back into math after not doing it since highschool years ago. Playing around with khan academy, everything was going great until I hit pic related.

How do I know to rearrange the final line as "-5r + 16 = 1" . Up until now I've just been drawing the numbers down as they are presented in order. So I ended up writing "16 -5r = 1" without a operator. How do I know which way to order the numbers in? Why did the "-5r" get listed first in the last line?

>>8558095
It's a fairly common style that in introductory algebra books/courses the authors are very autistic about always putting the variable first for some reason (possibly not to confuse students by arranging everything into the exact same form)

16-5r = 1 is exactly the same equation as -5r + 16 = 1

>>8553609
Be aware that some components of your financial aid have lifetime limits. I'm not sure what state you're in, but my state grants have a credit cap after which they stop funding.

>>8558095
it's technically the same thing but the convention is that you put the highest powers first like 3x^2 + 5x + 1 for example

I got a C- in Calculus 1. Is there any hope of me getting a STEM degree?

>>8558162
Yeah, just don't fuck up that bad again

>>8555371

>>8556816
interesting answer, but I don't immediately see how this leads to a Wiener process

since the posts are discrete events, I think a Poisson process would be more appropriate

something along these lines:

suppose you observe the current value of K at time t=0, then compose your reply and hit Post a time T after your observation (for simplicity, assume T doesn't vary appreciably for different people)

then the value of your post will be K+1+N, where N is the number of posts made in the time interval [0,T) (i.e., in the time between when you observed K and made your post)

if you model the posts as a poisson process, then N has a poisson distribution with parameter bT

(of course, this is a simplified model because it doesn't take into account posts already in the queue)

>>8558208
The Poisson process is too simple.
It's a martingale and models posts as zero-measure points, so would advise the poster that observing N is useless due to homogeneity, while predicting a flat probability of 10^(1-c) of getting c repeating digits.

How come the use of modulo/division remainders is relatively rare in mathematics in general but extremely common in computer science?

>>8558347
number theory

computers can generally only do integer arithmetic precisely (within a certain range) since operations on reals are always limited in precision

>>8558347
because you haven't taken many classes in abstract algebra or number theory or cryptography

>>8558366
bad answer

inclusion of those fields does little to affect the proportion between the prevalence of modulo in computer science and mathematics in general

the correct way to look at this is that computer science is simply much more limited than mathematics in general and happens to be limited (especially when applied) to fields where modulo is essential while mathematics encompasses a vast number of fields where it's irrelevant/undefined

>>8558373
wrong

taking something 'modulo' something else is extremely widespread in mathematics every time you take a quotient of any algebraic structure, whether it's vector spaces, rings, groups, modules, monoids, etc., it doesn't need to be limited to integer division

these structures appear all over the place in linear algebra, geometry, number theory, manifolds, singularity theory, cryptography...

>>8558162
No. Relearn that material or you're fucked. Really.

>>8558052
Ok thanks !
n must be superior to to 27, because the rest of one of the division is 27 so n = 35.

ok sci,

im 27, no gf, no kids, little to no work experience and attending a CC as a math major (master race desu) but im afraid im running out of time, i know education isnt a race and older people go back to school all the time but i mean i don't have good grades for my major to get into a good school, i have A's and B's in general education classes but when it comes to my major it's all C's and on B, and my GPA? oh lord, at its highest it was a 3.5 but i wasted a lot of time on classes i didn't need, they helped me as a person and i think they've made my life better but not for my academic career. I lost financial aid because of it but thank god I'm only down to my last hand full of classes so i can ask for financial help from my family, I'm just worried that i wont get into the school i want because of the C's i got on my transcript i don't want to go to some random ass school, i want to go to a school from my list.

my list is like this:
top tier schools that i know i have no chance but emailed them and going to give it a shot anyways cause you never know, fuck it am i right.

semi-top tier which is i have a shot but still very low chance i get in

and then there is my bottom plan C schools, where i can get in most likely but the grades are what decide if i do or don't. They're not the best in the country in terms of my major but their reputation is at least good and i can do some self study if i want to get better at my craft, and i can network and work hard enough to get a good job (this is my goal if everything else fails, i do not want to fall below this because one of them is very local and i do not like to travel far from family)

then there's the random ass school - literally last resort to say at least i went to some college, i dont want to end up here, please tell me there is hope.

i don't know what to do /sci/ please tell me one of you guys that go to state uni's or good schools got C's at some point in your lives.

>>8558497
tl;dr

compress your blog post into a question

>>8558508
what do?

27, have C's on transcript, dont want to go to no literal who school, i want to get into a decent school with a good rep. is it still possible? am math major. am i fucked? got lik 4-5 classes left with a 2.8 gpa.

>>8558511
Depends on a couple things

one what you mean by "decent school". Harvard, Berkeley-tier stuff? Probably not. Ohio State? Better shot.

also where your Cs are timewise. Do they occur early on or late? Early bad grades aren't nearly as concerning.

>>8558514
well now that you say that, im just hoping i get in to any school now. m in California so, UCLA, USC, CSULA, Dominguez hills, northridge, Pomona, cal poly. Any school thats the best for mathematics, and if they don't accept me then whatever is closest to me to be honest.

Grades? well fuck me, its late in th game for me man. I'm getting C's in intro to physics, Cs in Calculus, but i had some shit professor man, i know thats not an excuse but they were bad. but whatever it's in the past an i got C's, i sitll need linear algebra and physics 2, but cal 1 and 2 were C's. put it like this major stuff i got C's.

>>8558519
Maybe you're just not cut out for math? If I were you I would have gotten a tutor a long time ago. Getting Cs means you probably don't understand the material very well. Try your best and go to whatever school is available but you are asking to get more than you put in.

>>8557926
Ah, thank you anon. The index in the left hand kind of confused me but now it's clear.

>>8559005
right hand* I mean

Is there anyone here who understands Illumina sequencing?
I still don't get it.

>>8551670
Question:

A club athletics team consisting of 1 male and 1 female long distance runner and 2 male and 2 female sprinters is to be selected from 5 male and 7 female long distance runners and 3 male and 6 female sprinters. The team captain must be one of the female sprinters. In how many different ways can the team be formed?:

What does one of the female sprinters needing to be the captain mean for this problem? am I overthinking it?

>>8551670
If action is the integral over time of the Lagrangian, how does one quantify stationary action?

>>8559389

with a functional derivative equal to zero? what do you mean by this?

>>8551778
Best case request the replication data, and remake the table yourself. Worst case, yeah, a screenshot is fine.

>>8559381
I doubt it means anything unless you already have a female sprinter who is the captain, who is then preselected and you can't make a choice in that regard. Do you understand the basic premise of the calculations and theory or do you need a refresher?

>>8559408
[eqn]S[ \gamma ](t_1, t_2)= \int_{t_1}^{t_2} L \circ T[ \gamma ][/eqn]

Where the action is [math]S[ \gamma ][/math], [math]L[/math] is the Lagrangian, and [math]T[ \gamma ][/math] maps [math]\gamma[/math] to a tuple of functions of [math]t[/math] [math](t, \gamma (t), \frac{d \gamma }{d t}(t))[/math].

>>8559434
Are you sure it wouldn't mean removing one female sprinter from the pool because she can't run while captain?

Why put that there if it is redundant?.

I think I have it but you tell me.

Would it just be 1x1x5x7 x 2x3x2x6?

>>8559455
Disregard this post, It's all good.

>>8559381
Maybe if you have the same people with a different captain it's considered a different team. If that's the case they probably should've pointed it out though

>>8559449

this notation looks like it is straight out of structure and interpretation of classical mechanics, a well known fag textbook. watch yourself, we'll have no trouble here.

but I know what an action is, that's not an issue, I don't understand what is meant by quantifying stationary action.

>>8559474
I mean, what makes an action stationary?

>>8559486

a path through time with a big ke, and little pe, clearly, but also things like the variation of the functional evaluated at the extremal path is zero. I'd wager you already know this, so there is probably not much more I can say.

why does every dude on numberphile looks like a fucking retard?

Is algebra solved?
What are some unsolved algebra problems?

What can I do with a PhD in photonics?

Is it a meme field?

And is the semiconductor manufacturing industry really that bad?

is it bad to switch majors after you've spent time on one for a long time?

>>8559545
>implying you don't look like a retard, yourself

For those of you who took calc 1 and calc 2 in uni, which class was "harder"? I am asking because I just got a B in calc 1 and it wrecked my GPA (I go to an easy/shitty school), and I'm wondering if calc 2 is gonna wreck me even more.

>>8559632
Calc 2 is definitely harder than calc 1. But it's not that the concepts are difficult to grasp, it's just that there's a lot of them to learn. So, get your shit together and prepare your anus.

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So I will be taking a discrete math course soon and I am fairly new to math, any resources that could help me get a leg up on what I may be learning?
I will also be taking a calculus 1 course at the same time

>>8559721
For calc, look at Khan academy. I recommend brushing up on your algebra and trigonometry, and make sure you know the stuff in the "precalc" section. You'll be using this stuff a lot in calc so it's good to be fluent in them before you start.

For discrete math, you can look through the lectures and lecture notes here: https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-fall-2010/
Look up some stuff on basic set theory, logic, and mathematical proofs. The first part of this free book will give you that exposure: http://www.people.vcu.edu/~rhammack/BookOfProof/

>>8559732
Thanks anon

>>8559545
i'd say they look mostly normal except like 2-3 of them

even on those 2-3 i think it's mainly their mannerisms like exaggerated facial expressions rather than their physical appearance

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Why couldn't you line up 2 particle accelerators side by side, with one going clockwise and the other anti-clockwise. Then when the particles are at half the speed of light (relative to the stationary accelerators), when the two pass each other at their closest points, they'll be going at the speed of light relative to each other. As such they are going at the speed of light.

What is the flaw in this?

>>8560292
delet this

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it is clear Q could be force or torque among other things, but is always a scalar quantity, why is this?

>>8560292
because they are NOT traveling at the speed of light relative to each other. relative speed, this is a concept called galilean invariance that does not apply when particles approach the speed of light. this is the foundation of relativity

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What is the value of x and how do I find it? Help I never studied math.