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Board
/sci/ - Science & Math

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Finite set edition.

Talk math/maths.
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>>12367198
I am retarded, the previous thread is >>12360554. Disregard the link on the OP.
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learn theoretical physics
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It's been taking me several hours to work through a given section (about 10 pages) on Linear Algebra Done Right, and doing a couple problems.

Makes me feel retarded, but I guess everything is fine.
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>>12367236
Nah, learn agda instead. Proving things to a formal verifier's standards feels really rewarding.
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Is there an axiom of finiteness? What makes a set finite?
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>>12367265
Finiteness doesn't need an axiom, it's an arbitrary property.
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>>12367265
yeah the ZFC contains the axiom of finiteness, namely: the one element set is finite
then you have the axiom schema of finite multiplicativity: it states that for any finite set x and any number n, if set y is n times larger than x then it is finite
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>>12367265
A set is finite if it is in bijection to a bounded subset of the naturals.
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>>12367246
Getting paid is rewarding in its own way.
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>>12367236
>learn jewish physics
No thanks.
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>>12367242
I have OCD and re read things over and can’t concentrate so I know how you feel.
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>>12367256
It's a good example of a right answer not meaning a good argument. If it didn't bring up the Zeta function I would argue it should be taught in primary school as a lesson in humility

>>12367236
The book "a new kind of science" by stephen wolfram has a really cool section on thermodynamics and relativity. The rest of the book is more computer science fare but I genuinely enjoyed the section I mentioned. There are torrents up on PB if you want it for free.
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do you guys study math for fun or do you study math for fun as a student ?
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>>12367384
Could you clarify your question? If this is your actual question, yes.
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>>12367211
>I am retarded
We know. You are on 4chan.
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Is there a clear cutaway between Riemannian geometry and relativity theory?
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>>12367455
what do you mean by cutaway? english not my first language
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How do you draw good graphs, /mg/? My graphs are usually inaccurate because I have no concept of scaling and they usually look like shit as a result.
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>>12367455
Riemannian geometry is essential to manifolds and differential geometry, which essentially is general relativity. Special relativity is easy
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>>12367455
What do you mean?
GR essentially says that space time is 4dim pseudo riemannian manifold with a (3,1) lorentzian metric, is that what you're getting at?
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>>12367242
keep it up, it'll be easier.
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>>12367319
delet
Seriously fuck OCD, but it gets better as you become older (usually).
>>12367242
It's normal speed.
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>>12367455
Riemannian geometry, while not dealing with Pseudo-Riemannian metrics of Lorentz signature, still plays an important role in GR. E.g. on Cauchy hypersurfaces.
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i got filtered by homology, help me /mg
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>>12367455
>is there a clear cutaway between orange juice and coke diet?
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>>12367660
To understand homology, you must become the homo
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I wonder when the first good post in this shitshow of a "math" thread will be made.
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>using $\Xi$ for any reason ever
We have 26 English letters in two cases, 23 other Greek letters in two cases, several fancy cursive fonts, boldface, Fraktur, even autistic shit like Hebrew letters, there is no possible excuse in any context for your variable to be three fucking lines on top of each other
People who use $\Xi$ will go to the circle of hell where they make you debunk proofs of RH for eternity
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>>12367736
when the geometers wander over. It’s delayed by every CSnigger post.
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>>12367749
Don't talk yourself into a meme.
Both geometry and CS is fine and interesting.
It's not the subjects that suck, it's the people.
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>>12367745
Listen here frogbro, I want to use a large letter for my functional. Since it is expressed as either a sum or integral I want to use something like an 's'. But I'm not going to use large sigma because I'm already using that for free entropy. Everybody can read the greek alphabet anyway so there's nothing wrong with using $\Xi$.
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>>12367772
>. Since it is expressed as either a sum or integral I want to use something like an 's'.
Here's an idea
use a fucking S you dingaling
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>>12367771
You will never be a mathematician or a real woman.
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>>12367745
>tfw I used $\Theta$ extensively in my latest paper
it's not my fault that computational focused geometry needs a billion symbols
fuck it next time I'll use nordic runes
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>>12367782
Thanks god, in that case I might actually get a decent job.
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>>12367789
>computationally focused
Not science or math
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>>12367789
OH FUCK ME ment to write $\Xi$, but yeah $\Theta$ was also used lmao
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>>12367780
Already using that for another purpose too, not gonna introduce inconsistencies
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>>12367792
go back to your archery club and shoot some cats
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>>12367806
I would never harm a cat, a CSnigger however...
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>>12367809
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>>12367319
I don't have OCD but I also feel the urge to reread from page 1 as soon as I start having trouble following along.
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>need to learn chapter 6 of book
>obsessive feeling I'm not doing it properly until I start from page 1
It drives me fucking insane just picking out little chunks of books/papers instead of reading them linearly through. I've finally managed to be mostly comfortable skipping the "chapter 0 where we sketch bullshit you already know" but it took me ages to get here.
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>>12367856
I'm autistic too, anon.
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>>12367660
Apparently sometimes easier to calculate than homotopy directly, can then be used to get info on homotopy via e.g. Hurewicz theorem.
Changing the name from combinatorical into algebraic topology was a mistake, now every faggot obsesses about muh functors in topology lmao instead of focusing on actually working with the constructions.
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>>12367242
yeah you're fine. people here just like to brag and make everyone else feel bad when they can't instantly derive all of analysis and LA in 2 hrs. Is it at least rewarding so far?
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>>12367917
that’s not autism it’s just being neurotic
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>>12367938
>sometimes easier to calculate than homotopy
Consistently easier to calculate than homotopy excepting special occasions where the fibration sequence applies, plus probably a couple other cases I'm not aware of.
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>>12367246
>(((Agda)))
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>>12368025
Something wrong with it?
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>>12368062
The triple parenthesis is a neo-Nazi indicator that the thing in question is of Jewish origin or influence.
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>>12367246
>Proving things to a formal verifier's standards feels really rewarding.
Is this the most autistic sentence ever written?
>it makes me feel good to nitpick an obvious proof into completely illegible symbols for hours on end until it's so drained of meaning that reading it is literally a mechanical process
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>>12368093
Sometimes I wish it wasn't against my principles to save basedjacks so I could post one right now.
Not even the guy who posted it but it's a joke in this case. Don't take the bantz to heart anon.
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>>12368110
Anon... Why do you think meaningful things can only be said unclearly?
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>>12367242
Several hours for 10 pages isn't a bad pace by math standards. It's basically a universal phenomenon among new students that they expect to be able to sit down and continuously read their math book like it's a novel and then think they're retarded when it takes them forever to read anything.
Eventually you figure out that you're (probably) not that much more retarded than anybody else and math is just hard. It takes everybody forever to read math texts except the top 1% fuckheads playing their lives with cheat codes enabled.
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>>12368124
Why do you think pages and pages of formalized autism code are "more clear" than plain English?
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>>12368152
Natural languages are such fuzzy bullshit, they cause misunderstandings all the time.
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>>12368169
>so uncomfortable with human language it makes him feel good to transcribe it into machine language
See? Autism.
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>>12368174
Well yes, this is sci. Go back to the humanities if you don't like it.
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Which math concept is more fundamental to reality: quantity or distance?
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You don't have any homosexual contractions in your invariants, do you /mg/?
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>>12368198
Isn't distance just a special case of quantity? Or do you mean discrete quantities/counting? In that case I'd say amplitude is more fundamental than either.
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>>12368110
>Is this the most autistic sentence ever written?
Not the autistic poster, but indeed proving stuff in a proof assistant has a very addictive nature to it, very similar to video games. It's a meme in the ITP community.
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What does /mg/ think of Uncle Ted?
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>>12368116
It's all so tiresome.
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>>12367242
Do you like the book so far tho?
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>>12368093
i was literally just shitting on Agda for being a gross language
go back
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>>12367856
It's it a book your class follows?
I have the same thing but with books recommended by the class. They usually have a different enough take to be annoying
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>>12367975
>>12368500
it's fun. proofs took some getting used to, but now im enjoying working through them, it's like a game. im enjoying understanding a lot of the things id previously memorized.

it's also the best textbook ive ever read so far. clearly a lot of thought and care went into it, which makes struggling through parts much easier
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>>12368537
LADR is a good place to start abstract math, I think. Axler is a really good writer and the subject matter of baby linear algebra is the best place to learn abstraction and proofs because everything works as smoothly as math can possibly work.
Just remember that his DETERMINANTS R IMPOSSIBRU rhetoric is a meme he made up to market his book, please don't join the cult.
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>>12368511
I think you guys need to find yourselves a new dogwhistle if you're going to freak out when somebody even recognizes what it means. It's not like anyone even got mad or told you to fuck off, he simply pointed out that the jew brackets are jew brackets.
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>>12368732
>It's not like anyone even got mad or told you to fuck off
he called me a Neo Nazi, what world do you live in where thats not being mad
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>>12368739
A world where neo Nazis spam their propaganda on every board without getting banned. It's just a fact of life at this point.
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>>12368739
He did not call you a neonazi, he said ((())) is neonazi slang. And I live in a world where this is, in fact, neonazi slang.
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>>12368604
> the subject matter of baby linear algebra is the best place to learn abstraction and proofs because everything works as smoothly as math can possibly work.
As a mathlet, I agree. Linear applications and such are really intuitive and fun to play around with.
I do think Axler is sincere about determinants though.
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>>12368739
Nazis on 4chan have been common currency for a while now
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>>12368511
Do you have any concrete criticisms of agda?
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>>12368767
Do you call every word with a latin etmology "Italian slang"? Every word with a Norman etymology "French slang"?
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>>12368829
Are you really going to feel better if I agree with you and say "okay, ((())) is not neo-nazi slang, it has neo-nazi etymology"?
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>>12368821
>Do you have any concrete criticisms of agda?
yes, its aesthetics
>>12368861
if you argue ((())) is neo nazi slang then you should argue that greentexting is as well
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>>12368799
>I do think Axler is sincere about determinants though.
I have a hard time believing he's entirely sincere about it, although autism is common among mathematicians so he could be.
It's just such a trivial hill to die on that I feel like he's seriously exaggerating how important it is, and so much of his railing against them is either empty sloganeering (saying "determinants are hard" or "determinants are often taught badly" as though those are arguments for not using them) or ad-hoc attempts to dodge around determinants where they naturally show up. I've never read one of his nu-proofs (and there are really only a handful in the first place) where his attempts to avoid using them don't feel more unnatural than their (often perfectly natural) appearance in the standard proof.
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>>12368871
>if you argue ((())) is neo nazi slang then you should argue that greentexting is as well
No, I should not.
And you should actually respond to what I post instead of entirely ignoring it so you can post a completely new train of stupidity every time you see a (You)
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>>12368894
ok retard
>>12368829
wasnt me, doesnt even have the same writing style
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>>12367198
Guys, so I decided to help out this normie in my Calc class and now he treats me like I'm his personal tutor. It's so annoying when he spam texts me every step of a question. This is why you don't help people with math. Also, why do normies have such a hard time learning math?
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>>12368767
Go back to >>/r/eddit
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>>12369328
i don't think it's surjective, that's why u have problems
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>>12369352
Yes, I'm extremely retarded
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>>12369345
Have you tried not being a big floppy meatflap pussy?
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question about the formula for the determinant of a nxn matrix. Does the sign alternate between + and - ? For a 3x3 matrix, it goes like:
a1(b2c3 - b3c2) - a2(b1c3 - b3c1) + a3(b1c2 - b2c1)
the sign alternates - to +. How would the sign behave for a 4x4 ? - + - ?
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>>12369406
Yes, that is how it works. An intuitive way to see this is to look at the calculation method where you calculate the $n-1 \times n-1$ sub matrices.
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>>12369411
Thanks.
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>>12367366
Where?
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>>12367796
>>12367745
>People who use Ξ will go to the circle of hell where they make you debunk proofs of RH for eternity
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how does one read this and where can I learn how to read math notation?
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So... did we finally figure out an aliquot sequence for 276?
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I want to construct an isomorphism:
$\frac{\mathbb{R}[x,y,z]}{\left< z + 5y -15, z+3x -15 \right>} \mapsto \mathbb{R} [t]$
But I'm struggling to get started, anyone have a hint that they could share?
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>>12369613
Actually, I could set the Ideal beneath the line as the kernel of the function, and let $\mathbb{R}[t]$ be the image.

Now I need to find such a function
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>>12368473
This guy is well-known as a retard. He keeps posting blatantly false ramblings about type theory on various online channels and is excessively proud about it. His blog is a wonder of stupidity.
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>>12368388
pretty based
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I'm having trouble with algebraic numbers again.

I know exp(z) is transcendental for all non-zero algebraic z, but does this mean that the real and imaginary parts of exp(z) must both be transcendental? It seems odd that one of them would be algebraic and not the other, but I can't convince myself that it's impossible either.
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>>12367198
I've learned absolutely 0 in calc3. it's just an application of calc1 and 2. double and triple integrals can be a bit trick though to set up.
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>>12369833
It could be that one of them is transcendental and one of them is algebraic: simply take z to be the real number algebraic number. Then imaginary part of exp(z) is 0 which is algebraic but exp(z) is not.
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If I have a bunch of positive semidefinite matrices $A,B,C$, how can I relate $\mathrm{trace}(ABAC)$ to $\mathrm{trace}(BC)$? I need some inequality
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>>12369974
No such thing.
Set $B=C=I$ and $A = 0$. Then $tr(ABAC) = 0$ but $tr(BC) = n$.
Showing that the opposite can also happen is left as an exercise to someone else. I'd recommend using B as diag(1, 0) and C as diag(0, 1). The choice of A isn't coming to me right now.
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>>12369974
Eigenvalues lol.
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>>12369985
Never mind, set $A$ as the all ones matrix.
>>12369989
That's just for positive definite matrices, he doesn't have a non-zero lower bound on the eigenvalues to exploit.
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>>12369985
>>12370011
hmm that's right. is there any good inequality when all are positive definite? or at least A is positive definite.
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>>12370018
As the other anon pointed out, the trace is the sum of eigenvalues. Those are all positive, so if you have a positive lower bound on A's eigenvalues (because it's positive definite), I think you can get something like $tr(ABAC) \leq \lambda^2 tr(BC)$, with $\lambda$ being $A$'s smallest eigenvalue.
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>>12370037
Correction: $\lambda$ being the largest eigenvalue.
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serious question. Is this good or a meme, or both?
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>>12370075
Both.
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>>12367198
>Finite set edition
Assume the Axiom of Pairing, Infinity and Separation and the Law of Excluded Middle.
Denote by ${\mathbb N}$ our model of the naturals and denote the Continuum Hypothesis by ${\mathsf{CH}}$.

Consider
$S_{\mathsf{CH}}:=\big\{n\in{\mathbb N}\mid (n<5) \lor {\mathsf{CH}}\big\}$,
a subset of ${\mathbb N}$.
Either $\neg{\mathsf{CH}}$ or ${\mathsf{CH}}$. In the first case, $S=\{0,1,2,3,4\}$ and in the second, $S_{\mathsf{CH}}={\mathbb N}$. The identity in either case is a bijection to a finite resp. countably infinite set.

We conclude that $S_{\mathsf{CH}}$ is either a finite or an infinite set.

Do you agree with this fine piece of math?
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>>12370113
No. You see, $0 \notin \mathbb{N}$.
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>>12369949

That's true. I should have said non-zero algebraic, since that's the case I was thinking about, I.E. when z is a complex number off the real line.
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>>12370113
How do you express CH as a first-order sentence, as required by Specification?
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>>12368093
kill yourself you fucking faggot tourist
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>>12367749
Any ETA on geometers wandering over and the thread becoming good?
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>>12370137
"normally".
I.e. with ${\mathsf {FOL}}$, $=$ and, to do set theory, $\in$. You don't need any axiom to express propositions (that may or may not be inconsistent once axioms are adopted.)

But to be concrete and answer your question, define what a bijective function is in the usual was (for all..there exists a unique...), then characterize the naturals N as least inductive set (as in {} is in it and all its successors), and define ${\mathsf {CH}}$ as saying that there is a set X which has the properties of N (as above) and whos power class is in bijection with the set W1 of hereditarily transitive countable sets (countable being defined in terms of the same X as we go).
Some functions and X then exists (trivially) when adopting infinity. (Also W1 will classically be the ordinal, $\omega_1$, tautologically depending on your definition, and the power class will be a power set in ZF. But that's not really necessary to assume)
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>>12370133
The same argument holds: The sum of a transcendental and an algebraic is transcendental so if you take x a real transcendental number, then x+i must again be transcendental.
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>>12370171
You'd need at least Foundation or something equivalent to it to characterize inductivity, as well as Powerset to prove the existence of $\beth_1$. At the very least, pairing, infinity, separation and LEM alone won't cut it.
Also, I'm fairly sure that W1 (the hereditarily transitive countable sets) doesn't have order-type $\omega_1$, even classically. What little ordinal analysis I do know is telling me that it's probably $\epsilon_0$.
In any case, I don't see a need to bring in W1 if you just want CH, since $\aleph_1$ can be simply defined as the Hartogs number of (the cardinality of) N.
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>>12370037
>>12370040
where do you need invertibility of A to show that $tr(ABAC) \leq \lambda_{\max}(A)^2\, tr(BC)$? I'm preeeetty sure it always holds if $A,B,C\geq 0$
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>>12370168
Give it a day, they’re a slow and dawdling people.
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>>12370248
There's literally a counter example in >>12369985 and >>12370011
Set $A$ the all ones two by two matrix, which is positive semi-definite and has largest eigenvalue 2 https://www.wolframalpha.com/input/?i=is+%5B%5B1%2C+1%5D%2C+%5B1%2C+1%5D%5D+positive+semi-definite , and $B = diag(1, 0)$, $C= diag(0, 1)$.
Then $BC = 0$, but https://www.wolframalpha.com/input/?i=%5B%5B1%2C+1%5D%2C+%5B1%2C+1%5D%5D*%5B%5B1%2C+0%5D%2C+%5B0%2C+0%5D%5D*%5B%5B1%2C+1%5D%2C+%5B1%2C+1%5D%5D*%5B%5B0%2C+0%5D%2C+%5B0%2C+1%5D%5D has clearly non-zero trace.
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>>12370075
It’s a good meme.
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I'm trying to find the kernel of the map $F(p(x,y)) = p(t^2, t^2 - 3t)$ but i'm very dumb and cannot figure it out.

With $F: K[x,y] \mapsto K[t]$ of course
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>>12370232
You don't need any axioms before writing down a property - a property is a string of symbols in the language.

And yeah possibly W1 and \in doesn't give you the ordering to get ω1 on the nose, but it's really about the small size of W1 and not ordinals.

Also, clearly CH is just a dummy ZF-undecidable statement here, don't get hung up on it.
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>>12369464
>where can I learn how to read math notation?
a math class.
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>>12370292
Let Z = (X- Y)/3
Then F(Z)=t
so F(X - Z^2) = F(Y - (Z^2 - 3Z)) = 0.
I'll let you continue.
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>>12370302

Thank you very much fren
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>>12370296
>a property is a string of symbols in the language.
Definitions that confuse semantics with syntax are never a good idea. Would the "string of symbols" in Skolem's paradox constitute a definition of uncountability?
>it's really about the small size of W1 and not ordinals.
And it would be wrong, because $\varepsilon_0$ is countable, so even if you were granted that "properties = string of symbols", having a cardinality of $\aleph_0$ implies that the string of symbols you wrote is not CH but a provably false statement in ZF. If you just want an undecidable sentence of ZF, go with Con(ZF); it's specifically constructed to avoid logical gaps like the ones that I've pointed out.
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>>12370339
>Definitions that confuse semantics with syntax are never a good idea
I didn't get semantics into the picture here. We define some class {n | n<5 or CH} where CH is the abbreviation for an express involving only a handfull of symbols (bracket, implication, \in, =, ...). It's some logical formula that in ZF we'd understand as the statements about cardinalities. In the context of some theory, this may be provable, disprovable, or otherwise, but I don't need axioms to write it down. E.g. I don't need Regularity or Induction to write down the formula that in ZF says that some set is the smallest inductive set. The latter interpretation being realized isn't necessary to tell you which property I mean.

I don't know whether it's ε0 or not - but you already know that CH isn't the point here. Where does this desire come from?
Since we're anonymous here, nobody will take away how smart you are making points about things nobody even asked about
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>>12370193
Sorry for being dense, but where is the exp function in this?

Just to be clear, what I'm wondering is this: if z is an algebraic number with non-zero imaginary part, can exp(z) ever be a complex number with algebraic real part and transcendental imaginary part or vice versa?

I we look at log(z), then it appears that both parts must be transcendent in this situation, but I don't suppose that proves anything for the inverse.
>>
Will Stewart's Single Variable Calculus 6e do as well as 3e?
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>>12370384
>some logical formula that in ZF we'd understand as the statements about cardinalities.
>tell you which property I mean
And this is where the semantics comes in. Without interpretations, you cannot tell if a given string of symbols represents the Continuum Hypothesis, or some exotic mathematical object cooked up as a counterexample to some ZF-conjecture. You could try to skirt around this by an informal appeal to some kind of pre-axiomatic "standard semantics of set theory", but as far as I know this isn't how set theorists think about their subject, and it does nothing to help whatever point you were trying to make in >>12370113 with your undecidable statement.

>Since we're anonymous here, nobody will take away how smart you are making points about things nobody even asked about
Skolem's paradox, the countable ordinal $\varepsilon_0$, and Con(ZF) are all basic concepts of mathematical logic, and I gain no credibility from demonstrating my knowledge of them. On the contrary, you lose credibility by making statements like "such-and-such formula represents CH" that anyone with a passing familiarity with ordinals can see to be false. I point this out, and suggest Con(ZF) as an alternative, to provide you with an avenue for you to fix your mathematical mistakes in >>12370113 and >>12370171.
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>>12370490
I would say yes. If it's for class then the exercises are probably different so make rich friends.
>>
$\text{Let } \alpha \in \mathbb C \text{ be a root of the polynomial } 1 + 4x +6x^2 +3x^3 \text{ and let } \mathbb Z[\alpha] \text{ denote the smallest subring of }\mathbb C \text{ containing both } \mathbb Z \ \& \ \alpha. \text{ Is 7 prime in }\mathbb Z [\alpha] ?$
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>>12370452
Here's your hint: cos(t) and sin(t) are algebraically dependent by the Pythagorean identity.
>>
Is it just me or is this book absolutely fucking kino?
Any other anons read this? I've literally been reading it 8 hours per day the past two weeks
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>>12370950
try again
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>>12370825
Right. Okay. For z = a + bi, we have one part being exp(a)cos(b) and the other exp(a)sin(b), and cos(b) and sin(b) are algebraically dependent. I've been hung up on the exp(a) bit, but I guess it doesn't matter what that number is? I'll have to mull this over some more. Thanks.
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>>12370825
This doesn't help.
>>12371123
cos(b) and sin(b) are algebraically dependent but not necessarily exp(a)cos(b) and exp(a)sin(b).
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>>12371138
Yeah. It clearly does matter what exp(a) is. Like, pi and pi squared are dependent, but multiplying both by 1/pi gives 1 and pi which are not. Think I'm gonna have to give this up.
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>>12367198
Does anyone ITT know where I can learn real analysis tricks for math competitions?
>>
>>12371178
Check out the Gelfand-Schneider theorem.
>>
>>12371197
>>
>>12370950
indeed, it is
>>
>>12371198
I have, but I don't see how it would help here.
>>
>>12371197
go through math competition problems with solutions
>>
>>12371197
There's a whole subfield devoted to party trick mathematics. It's called chaos theory.
>>
>>12370823
Use the correspondence theorem.
>>
>>12367242
>>
>>12370075
Axler must write a book on classical determinant theory (with applications to the LA of his first book) and multilinear algebra, as continuation to this book.
>>
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>>12371549
>>12367242
lol exactly. i am actually beginning to study out of this book as well and the student preface explicitly tells you this.
>>
If I have a subset of vectors, <(4,3,1,3), (3,2,1,4), (5,4, a, 3), (1, x, 4a, 4), (5 , 2,1,6)> for example.
If I want to put them in matrix form, to apply the Gauss Jordan method, is it the same if I write the vectors as columns or as rows in all cases?

It doesn't matter?
>>
>>12368520
I feel the same. In my probably class we started with Durrett and have since moved on to a new book every few weeks. It drives me mad.
>>
Did the animefag who subscribed to the arxiv mailing list and occasionally posted random articles die?
>>
>>12372163
one can hope
>>
any russians here? which university should I go if I want to get my sissy western brain filtered by the soviet rigor
>>
>>12371257
what the fuck are you talking about, brainlet? Nonlinear dynamics is one of the most useful fields of mathematics, even enginiggers and CStards use it. This general is so disgustingly algebraist and topologist dominated sometimes I just wish you'd all die.
>>
>>12370823
Use that 7 isn't prime (nor irreducible) in $\mathbb{Z}[i \sqrt{3}]$.
>>
>>12370950
what fucking book
>>
>>12368537
It's a great book! I had the same experience proving LA stuff after intro. Definitely just enjoy it and in general, don't ever take what other people say about difficulty here seriously.
>>
>>12372271
Kill yourself.
>>
>>12370113
>we conclude that this set is either finite or infinite
You assume LEM in this proof, so that statement is just a tautology
>>
Every time I start looking for hints or even the solution to a problem I'm having trouble with I find replies that make things way way way more complicated than they need to be. Especially on StackExchange or whatever it's called.

Is this common?
>>
>>12372671
I agree that his presentation either is, or is not, a fine proof.
>>
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>>12370292
>>12370823
i was able to do this 3 years ago, but I forgotten everything now
fuck
>>
Hey nerds EE here.
>differential eq defning system is a little too spicy to solve
>backflip into Laplace domain
>solve algebraic eq
>somersault back into real time domain
>problem solved

Can one of you explain wtf I'm doing on a conceptual level every time I do this. It feels like cheating out the imaginary roots of a polynomial with no real roots except worse because you get a very real result at the end.
>>
>>12371679
you can use gauss jordan without putting it in matrix form.
>>
what's the point of null space? Why would you want a vector x such that Ax=0 ?
>>
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How do I perform the equivalent of an element-wise function application f(x) in the spatial/time domain, but on a frequency domain signal, without first transforming it back to the spatial/time domain?
>>
>>12372994
>Why would you want a vector x such that Ax=0 ?
Because if you have a vector such that Ay = b, for whatever b you're interested in, and you want to know some more solutions, you could also use A(y+x) = b. And in fact, if you know just one solution to a linear system, adding nullspace stuff to it is the _only way_ to produce more of them. So knowing the nullspace tells you most of what you need to know about any other solution set.
The key point that makes the nullspace special is that the solutions of Ax = 0 form a subspace (whereas the solutions of Ax = b with b=/=0 do not).
>>
are chinks really smarter than whites?
>>
>>12373271
is a calculator smarter than a person because it can do math faster?
>>
>>12373313
yes, look up mochizuki for example
>>
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>ywn study 宇宙際タイヒミューラー理論 with 望月新一senpai
>>
>>12373313
strange analogy, but i was thinking more in terms of them being severely overrepresented in academia (including math)
>>
>>12373331
There are five billion chinese on God's green earth lad, of course they're overrepresented.
>>
>>12373343
look at the sat scores then
>>
What type of job can you get if you study Operations research and mathematical optimization?
>>
>>12373434
This is not career advice general. Also you can probably do all kinds of shit because for the most part your undergrad doesn't matter and you're going to learn most stuff on the job anyway. I can imagine the move to software dev positions being easy with an optimization background, even more so with data science or machine learning-based positions. I don't know if companies still hire 'operations researchers', but this at least used to be a thing like 20 years ago or so.
>>
Be straight with me /mg/, when is it too late to start a math degree for someone who wants to become a mathematics professor?
>>
>>12373669
Never
>>
>>12370950
Well now I'm curious
>>
Just got my first few lessons of tautology and other shit, what do I have to do to negate whole statement like
~p=>(q∧~p)
using the proper laws?
>>
>>12373127
>The key point that makes the nullspace special is that the solutions of Ax = 0 form a subspace (whereas the solutions of Ax = b with b=/=0 do not).
Is there not much to say about lineal varieties? I basically never see them in any LA book
>>
>>12372279
>Caring about whether something is useful.
Maybe /g/ is more your speed.
>>
>>12373669
If you start your PhD after 24 it’s over. Don’t listen to the copers who tell you otherwise.
>>
>>12373669
Let me break it down for you
>5-6 years of phd
>6-9 years of postdoc
>6 years of tenure track
Best case scenario: you'll spend 25% of your life working toward full professorship. That's assuming no break years, no time off for marriage + kids, no time wasted figuring out who you want to work with and what you want to work on, getting extremely lucky during each application process, etc.
>>
first year of uni and I'm already struggling with the complex numbers. i have a lot of trouble finding their arguments and anything related to trigonometry. fuck, i feel so weak
>>
>>12373830
Money or time isn't the problem, i want to be a professor either way but if i'm too old for math i might look into some other filed in stem.
>>
>>12373846
Why don't you want to simply self-study?
>>
>>12373867
I want an official research position so i can publish papers that will actually be taken seriously and so i can interact with other academics. I also don't believe teaching oneself advanced, research level mathematics is possible and some guidance is necessary past a certain point.
>>
>>12373876
> I also don't believe teaching oneself advanced, research level mathematics is possible and some guidance is necessary past a certain point.
>he thinks random things are impossible without even trying
You don't have anywhere near the correct mentality and your reasoning is stupid, give up.
>>
>>12373900
Maybe not impossible, but highly unlikely. I'm not a genius and even Ramanujan had serious gaps in his mathematical education that were only being corrected after he went to Cambridge.
>>
>>12373909
Ramanujan wasn't studying by himself, he was figuring things out on his own.
You have internet access, you can actually work your way through some books in your preferred subject and then try your hand at reading recent articles in it. It's not anywhere near as hard as you're making it out to be. At least attemp and fail before declaring it "highly unlikely", pussy.
>>
redpill me on springer, are they superior to wiley? or is it a meme
>>
>>12373925
They're book publishers, dude.
>>
>>12373922
I'm not going to waste years of my life figuring out if it's possible or not when i can just go to college like a normal person
You utter retard
>>
Man people in this thread are lucky, I wish I'd been born smart
>>
>>12373946
I feel the same way
You can/should really just make the most of things
>>
>>12373846
>Money or time isn't the problem
Your attitude will change on this eventually.

>>
>>12373736
>what do I have to do to negate whole statement
You take
~p=>(q∧~p)
and turn it into
~(~p=>(q∧~p))
>>
>>12373736
What's "the proper laws"? LK? NJ? Curry combinators? Lambda-mu calculus? Boolean topoi?
>>
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Help me out here please, fellas. I know this goes to infinity because I wrote a code for this, but I cant really wrap my head around the proof. I understand that this is simply a set of numbers that add together and without any miracles it adds up to infinity, but not sure how to prove it formally.
>>
>>12374152
nevermind, i made a mistake in understanding these series and writing the code, and understood how to prove it in the process
>>
When you’re finding sample proportion how exactly does that work for a Yes/No question? Like if 33 people said yes and 7 said no, how can you calculate that little p-hat? I know its x/40 but I have no clue what x even is
>t. graduated with a history degree and cant help his lil bro with basic math
>>
>>12374152
The limit is 1/2, not infinity. It's the integral from 0 to 1 of x, which is precisely 1/2.
>>
>>12373669
What is your background? You can't just be a mathematics professor for the sake of being a professor. Age doesn't matter but a correct mindset does.
>>
why are there so many trans folx on math twitter? Is this just a result of the correlation between transgenderism and autism?
>>
>>12374414
In a sense, this line of thought is correct.
Basically, whatever reason it is that they don't get laid like normal people pushes them towards math, transitioning, etc.
(unironically - except for adding "normal", that was just to troll around)
>>
>>12374414
What area are they in? I've never even met a gay mathematician, let alone a trans one.
>>
If I get a PhD in pure math but end up failing in academia, how difficult is the transition to industry?
>>
>>12374447
You should transition to the afterlife instead.
>>
>>12374447
worked for me
>>
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>>12374414
that's because both mathematicians and trans people are smarter than average
>>
>>12374491
what do you do for a living?
>>
>>12373736
Psst...are you interested in a $\neg$?
Also have a $\Rightarrow$ and a $\wedge$ for free on top!
>>
>>12374492
>trans people are smarter than average
Do you have evidence for that?
>>
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>>12374492
based
>>
>>12374492
There's clearly no argument to support that transitioning is a smart move.
You grow up a man till and age a woman - worst of both worlds, and struggle in the public face. It's a terrible move, actually. To smartness isn't the origin.
I'm not even denying twitters trannies are on the smarter 50% of the population.
>>
>>12374177
X = 33 for the sample proportion of ‘yes’ answers and

X = 7 for the sample proportion of ‘no’ answers. Hope that helps nigga
>>
>>12374683
Thats not even close to being correct you fucking moron.
>>
>>12372994
suppose you want to solve max cTx s.t. Ax=b. Given feasible solution x, directions d s.t. Ad=0 are directions such that A(x + d) = b, if cTd > 0 you can show that your problem is unbounded. That's just one example, but like >>12373127
said its basically a convenient way to move around a convex set defined by Ax=b.
>>
>>12373776
>>12373830
I started my PhD at 27, but
>the standard duration for a PhD in my country is 4 years
>post-doc is not quasi-mandatory to compete for a professor position in a uni
>once you get a position, things aren't the best at first but it's almost impossible to be fired

How fucked am I?
>>
>>12374492
>>12374522
Turns out trannies are overrepresented here too lmao
>>
>>12374414
>>
>>12374177
>>12374414
They’re overrepresented because they have nowhere else to go. The general body of mathematicians is dominated by straight white men.
>>12374492
>>12374834
These are both true as well.
>>
>>12374815
How far are you into your PhD? Have you published anything worthwhile?
>>
>>12374953
No, I'm in my first years. I'm mostly doing courses and preparing for qualification.
>>
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>>12374830
not a tranny but i wish i could fuck a hot tranny though (yes i know these are almost nonexistent)
>>
>>12375027
I'd have sex with a futa. Trannies suck though
>>
I'm looking into mathematical physics graduate programs. It seems that most are geared towards mathematicians instead of physicists, with most subjects being bone dry definition-theorem-proof mathematics. I've had some real and complex analysis, linear algebra, ODE/PDEs and perturbation theory, but none of it was particularly rigorous. Can I realistically follow these graduate level courses after a couple months of preparation?

>Differential Geometry
>Topology
>Lie Theory
>Homological Algebra
>Complex Geometry
>>
>>12375100
If you study hard and always ask the prof every question you WANT to ask (NOT just every question you NEED to ask), then you can realistically follow those courses with 0 months of preparation.
>>
OH GOD, I'M GONNA, I'M GOOONNAA I'M GOOONNAAAA.....APPLY ZOOOOOORN'S LEMMA
>>
>>12375100
Personally I'd think you'd need quite a bit more preparation than a few months to be able to follow those courses. Like at least a year imo.
>>
>>12375100
What did you do in
> real and complex analysis, linear algebra, ODE/PDEs
? They should be proof based (at least mostly), but you say
> none of it was particularly rigorous
so what did you do there? Solve integrals and apply Gauss Jordan? If those were purely calculation based you will probably lack the foundation.
Otherwise you should be able to follow those courses with basically 0 preperation.
>>
>>12375106
I doubt some of those are introductory courses though, and I'm pretty sure I don't have the necessary background for those that are.
>>12375119
For this particular program I think I could squeeze through with just 3 of those, very likely differential geometry (for GR), Lie theory (for symmetry groups) and perhaps Topology. Do you have any thoughts on preparation time for those?
>>12375149
Somewhat proof based, but outside of first year filter real analysis (axioms, bolzano weierstrass, cauchy sequences etc, certainly not Rudin tier) proofs themselves were low priority, most of the theoretical focus was on relevance to physics. Random example, properties of conservative vector fields are incredibly interesting and relevant, while proving those properties hold true is much less so. Needless to say, I've never written an original proof myself, if we aren't counting epsilon delta limits.

Considering I'm interested mostly in perturbation theory (Bender book is great), I might just go for quantum which should have plenty of that.
>>
>>12375100
Sure, I don't see why not.
>>
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/vg/ here.

Need a bit of math help coding my game.

I have an 8 directional character walking.

How do I make it so I move up the camera and I look down in 45°, and how do I modify my walking code so my character is at 45°, like zelda, but also having the front angle in all the 8 directions?
>>
>>12375283
>>
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>>12375292
look up zelda on the SNES.

The camera and world is 45° but the characters are also oriented towards the camera.

I have a character movement working top down, I just want to rotate it 45° like zelda.
>>
>>12375283
projective transformation.
>>
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Hello dear friends,
Could anyone help me find where I am going wrong?
>>
>>12375309
have you tried applying the gram-schmidt process to obtain an orthogonal basis and then normalizing it to obtain an orthonormal basis?
>>
>>12375315
Yes, that's what the work shown is.
>>
>>12375319
>>
>>12375319
Have you tried applying it correctly?
>>
>>12375320
>>12375323
Based and nothelpingretardswithhomeworkpilled.
>>
Alright thanks guys, I guess I'll go ask on reddit where people actually know how to do math.
>>
>>12375410
No problem, I'm always here to help.
>>
>>12375422
But you didn't help.
>>
>>12375428
...then why did you thank me?
>>
>>12375459
kek
>>
>>12375459
I was being passive-aggressive, much like you're being.
>>
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>>12373012
pls respond
>>
>>12373271
>>12373331
There's a strong cultural factor, though. I wouldn't be surprised if they're more overrepresented than ashkenazi jews, even though the later have superior average IQ.
>>
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I don't know what a number is or how to do operations. What's the quickest way for me to get from knowing nothing to calculus?
>>
>>12375871
reincarnation
>>
>>12371612
>>12367242
>>12368135
Here's how you read a math book.

Go through a chapter, look at the images, graphs, etc, don't read them. Takes less than a minute. Go to the end of the chapter and read the review problems, but don't spend more than 2 minutes reading them.

Go back to the beginning of the chapter, read the titles, the subtitles, bold, highlighted or otherwise marked for notice text. Don't read anything else. If a chapter summary is provided at the end of the chapter read that as well.

Go back to the beginning of the chapter, read the section summaries if they're provided, otherwise otherwise find breaks in the text where a concept is introduced then finalized and just read the introduction, and the finalization and ignore the bulk of the text.

Now, you have broken down the chapter in a systematic way, into smaller pieces that you have made a mental map out of. Now, you can speed read and do the problems. Because you broke down the chapter into a mental map you won't have to do any rereading.
>>
>>12375296
Not to be mean, but this is really more appropriate for /vg/agdg or /sci/sqt/. But I'm an amateur gamedev and I like answering these questions so you get lucky this time, punk

So the important thing here is fundamentally you don't change anything, the physics of a Zelda game are exactly the same as a top-down game. The drawing of the art assets on the screen, however, is quite different.

To explain, first we talk the physics. Link's bounding box is at the base of his feet. This is not quite his hit box: Link can be hit at the top of his head. But look at the black pixels that pool around Link's feet, that black oval, his "shadow." That's his actual bounding box that determines whether or not he's colliding with "walls" or generic barriers in the game. This shadow is drawn in game and gives players a convenient visual representation of what Link actually looks like from a gameplay perspective, and as players walk around the game world they become comfortable with the idea that Link's bounding box is at his feet and not the entirety of his body. This kind of thing applies to ALL objects in the game

Okay, the bounding box is a "squashed oval" so when Link collides with walls on the left and the right there's no issue since he doesn't intersect with these objects at all

However, Link can walk in "front" of objects and also "behind" objects. This causes an issue for the program that draws the scene: does it draw Link's sprite on top of the sprite of the object, or below it? The reality is that without defining some value, some kind of function, very carefully, you'll just get "bad" drawing behavior, or undefined drawing behavior more specifically, where whenever Link's visual body intersects with a visual object in the game world it will flicker back and forth between them.

The answer to this is not too hard: depth checks. Every object in the game has some kind of depth in proportional to its $y$-coord.
>>
>>12375933
So in Zelda it's not too hard. It depends on your coordinate system (traditionally in mathematics $y_1 > y_2$ implies $y_1$ is "higher up" than $y_2$, and I will follow this convention)

So think: You can draw Link first, and the object second, or the object first, and Link second, where being drawn "second" will look like being on "top" of the object. What kind of a relationship would you want for your depth checking function with relation to Link's and the objects $y$-coordinate? Once you figure that out, you'll be able to sort out the details (there might be some finicky bits of what $y$-coordinate you want to "associate" to Link, and what $y$-coordinate you want to associate to each object. But the fundamental idea here is to understand that video games have two different programs running simultaneously: one that computes the physics of the scene, and one that draws the scene, and your job as a programmer is typically to get these two things to match up in a way that makes sense.
>>
>>12375924
>review problems
>graphs and images
>chapter summary
>read the book like you would a biology textbook
lol
>>
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Can we have a "is maths created or discovered" discussion? My opinion is that it is absolutely created by humans. My reasoning for this is practical; once I stopped thinking that maths were discovered, and instead created, I started to be able to think metamathematically. That is to say, I stopped trying to figure out how to communicate with some kind of transcendent other world of math (that is actually ultimately unreachable), and just started to trust my own logical skills. Before, concepts like infinite series or infinitesimals didn't really quite "click" - because I kept thinking they were something more than I thought they were. Now, I just understand them as human creations and it feels as if they simply "are what they do", or even more abstractly "they are what they are", purely immanent concepts. My concept of mathematics now is just creation of new tools by way of demonstrating equivalences, and the amount of equivalences you can construct are ultimately inexhaustible, so the maths we make are just like the tools we make: useful things for what we want to do.
>>
I just spent a couple hours trying to rederive the point slope formula because I was too stubborn to look it up when it slipped my mind. Couldn't do it and ended up googling.

Can I put this on 3 hours of sleep or should I turn in my badge and gun?
>>
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>>12375924
im going to be honest im not going to read that
>>
>>12375924
This is so wrong lmao holy shit
>>
>>12376022
>Can we have a "is maths created or discovered" discussion?
No.
>>
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>>12375924
>>
What's a good book-pathway (or other learning resource) for someone looking to pick math back up?
I was never particularly good at math in school, I failed trig (I could never get the right sin/cos/etc) and forgot all but the most basic algebra, but I feel like I should understand it better now I'm older. I'm a (mediocre) programmer and don't want to be a codemonkey for the rest of my life so I feel like I should get some general calculus under my belt at least.
>>
>>12367198
Any probability theory bros here got any recs for learning SDEs and Brownian Motion (or just Continuous Time Stochastic Processes in general)

My measure theory is alright and I’ve done the introductory course on measure theoretic probability
>>
>>12376735
Well, there is pretty classic book by Karlin-Taylor but honestly I never studied from it, just used it as a reference or worked through some occasional section if I needed to use something similar.
>>
>>12375924
there's truth to this - getting an impression and overview for the content before you real from page one
>>
>>12376123
definitely better than reading linearly word after word starting at page 1
>>
>>12375606
That's a very rude accusation, I've been nothing but honest and straightforward.
Being passive agressive is for women.
>>
>>12376735
>>
Do you guys LaTeX your solutions?
>>
answer me this. if i = 0 to n in a summation formula. will I assign i to 0 in proving the base case in induction?
>>
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>I was being passive-aggressive, much like you're being.
lel what a faggot
>>
How many types of right triangle are there with side lengths x, x^0.5 and n, where n is an integer? Is it three?
>>
If I started to flip a coin, then continued forever, is it possible for me to only get "heads" for an infinite span of time? Or only any finitely large amount of time?
>>
What is the benefit of a maths + philosophy undergrad track vs just pure maths?
>>
>>12377168
what have you tried?
>>
>>12376291
What is your current level of skill?
>>
>>12377179
Sorry, disregard that. I pulled an all-nighter.
I recommend Paul Forester's Algebra i Expressions Equations and Applications
>>
>>12377117
For what? I only type up what I plan to publish...
>>12377176
Nothing, take the Arnold pill and go math+physics, they are inseperable and inspire each other.
>>
What is lim x->infinity for $(1+\frac {1}{x+2})^{2x+1}$? I tried graphing it but can't do the algebra.
>>
>>12377187
use $f(x)^{g(x)} = e^{\ln f(x)^{g(x)}} = e^{g(x)\cdot\ln f(x)}$
>>
>>12377184
Foerster*
>>
>>12377117
If you want to train your $\LaTeX$-fu, why not?
Never did that for classes, though, and I wouldn't recommend it, except if there are bonus points in it for doing it.

Are you thinking about it, because classes have largely turned online-only with solutions handed in digitally instead of on paper?
>>
>>12377185
>they are inseperable
Math has infinity and infinitesimals and tries to live with them, while physics tries its best to explain those singularities away.
>>
>>12377171
No. If you throw a coin a hundred times one of the throws will inevitably be a tails.
>>
>>12377216
wrong
>>
>>12377200
>>
[eqn]a^2b=21 ,\;a^2+b=21[/eqn]
Is there only one solution?
>>
>>12377242
No there are four solutions
a^2b = 21
a^2 (21 - a^2)=21
a^4 - 21 a^2 + 21 = 0
which has 4 roots.
>>
>>12377219
Can you point to a single example of anyone rolling 100 heads in a row?
If not, why do you think it's possible?
>>
Why, if m^2 is divisible by two, must m be divisible by two?
>>
>>12377338
No. Take m=1+i in Z[i].
>>
>>12377338
If m is not divisible by two, then its of the form 2k+1, and (2k+1)^2 = 4k^2+4k+1, which is always odd.
>>
>>12377354
>If m is not divisible by two, then its of the form 2k+1
Prove it.
> 4k^2+4k+1, which is always odd.
Prove it.
>>
>>12377348
(1+i)^2 = 1+2i-1 = 2i
You are probably using shorthand notation of x^2 to be |x|^2 which isn't strictly what was asked
>>
>>12377364
2i is divisible by 2. 2i= 2*i.
>>
>>12377338
>>12377348
If you're allowing for bullshit answers, then any grassman number is a counterexample as any grassman number ^2 is 0, divisible by 2, but the grassman number isn't
>>
>>12377187
$(1+\frac {1}{x+2})^{2x+1}$
$=(1+\frac{2}{(2x+1)+3})^{2x+1}$
$=(1+\frac{2}{y+3})^y$

I'm confident that it's $e^2$.
>>
>>12377371
But all grassman numbers are divisible by 2 since they are over the field C.
>>
>>12377382
What?
>>
>>12377227
Where in physics have singularities ever prevailed?
So far it always turned out in the end, that there was a better explanation that didn't need those.
What makes you think that development will stop?
>>
$\bullet$What textbooks, papers or text did you read today?
$\bullet$What non-textbooks did you read today?
$\bullet$Did you write something today?
$\bullet$Did you do some programming today?
$\bullet$Did you build something today?
$\bullet$Did you clean up something today?
$\bullet$Did you plan something today?
$\bullet$Did you manage to work off some bureaucracy/paper work today?
$\bullet$Did you practiced any skills today? If so, which?
$\bullet$Did you do sports/cardio/weightlifting today?
$\bullet$What were you eating today?
$\bullet$How much sleep did you get yesterday?
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How would you rewrite this triangle problem as a non-graphical word problem of the form: "The triangle ABC blah blah blah, find x".?
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>>12377473
a triangle's inner angles are equal to 40°, 65° and (2x+10)°. find x.
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>>12377479
The (2x+10)° isn't an inner angle.
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>>12377264
>if you've never walked to the other side of this particular room before why do you think it's possible
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>>12377473
abc is a triangle and acd is a straight line, with c between a and d. Given the angles abc = 65, cab = 40, dcb = 2x + 10, all in degrees, find x.
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>>12377264
if n heads in a row are possible, then so is n+1. one head in a row is definitely possible. therefore n heads in a row are possible for all natural n. in particular it holds for n=100.
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>>12377707
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>>12377641
You can try it as long as you like, you will never roll 100 heads in a row. It's empirically impossible.
However, if you try to walk to the other side of a particular room, you will succeed, so it's possible.
There's no comparison between the two.
>>12377665
>if n heads in a row are possible, then so is n+1
False assumption. 1 head in a row is possible but not 100 heads in a row.
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>>12376022
i think youre a faggot
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>>12377242
Just graph it.

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