/mg/ math general

Why is she so cute?

Can you really blame him? It's not like animals such as himself are even conscious.

>Any interesting insights you'd like to share?
I believe everyone would like to read this preprint: arxiv.org/abs/1707.06615
>The unreasonable power of the lifting property (orthogonality of morphisms in a category) in elementary mathematics
>For a property [math] C [/math] of arrows (morphisms) in a category, define:
> [math] C^l = \{ f : \forall g \in C\ \ f\ {_{^⋌}}\ g\} [/math]
> [math] C^r = \{ g: \forall f \in C\ \ f\ {_{^⋌}}\ g\} [/math]
>where [math] f\ {_{^⋌}}\ g [/math] reads "[math] f [/math] has the left lifting property w.r.t. [math] g [/math]"
>A number of elementary properties can be obtained by repeatedly passing to the left or right orthogonal [math] C^l,\ C^r,\ C^{lr} \dots [/math] (etc) a single example of the [starting property defined for a simple class of morphisms]

Because she is in love.

I just proved a nice formula

Theorem: [math] n^n \equiv n \mod (n-1)^2 [/math]

Proof:

[math] n^n - n = n(n^{n-1} - 1) = n(n-1) \left( \sum_{k=0} ^{n-2} n^k \right) [/math]

And [math] \sum_{k=0} ^{n-2} n^k \equiv \sum_{k=0} ^{n-2} 1 \equiv n-1 \equiv 0 \mod n-1 [/math]

Therefore [math] \sum_{k=0} ^{n-2} n^k = \alpha (n-1) [/math] so [math] n^n - n = \alpha n(n-1)^2[/math] so finally [math] n^n - n \equiv 0 \mod (n-1)^2 [/math]

@9059900
put in some effort next time you enormous faggot

I think i might have an unconventional idea to prove the riemann hypothesis but i suck at maths so i cant really work out the details. but i have an equation, which is (in my mind) only solvable for a real value of 1/2 in a really unconventional and reality bending way. The only problem is, i cant really derive it 100% clean and it breaks the math in my little brain.

I was trying to work it out the last 3 days, but im so unsuccessful and im doing so many errors on the way its not even funny.

I really want to solve the riemann hypothesis.
But alas, it BREAKS the maths.
Its like a quantum mechanical generator of 0s and 1s.
Anyone else got that vibe when thinking about the riemann zeta functions 0 crossings for re(s) > 0 ?
Am i just going insane ?
fuck my life

What's [math]\alpha[/math]?

Some integer. See that I proved that [math] \sum_{k=0} ^{n-2} n^k \equiv 0 \mod n-1[/math] so (n-1) divides that sum.

Therefore that sum is some multiple of (n-1). And I just call it [math] \alpha [/math].

>using mod

compsci fag pls leave

I'm not compsci. What notation do you use then?

x=0
x=x^2 divide by x
1=x is a neccessary condition

--> 0=x=1
since when is 0=1

>Why has posting in /mg/ slowed down to a crawl in the last few days?
fear of getting hit with pic related

your mind is too weak for math

>tfw differentiated a function all on my own for the first time
it certainly wasn't hard, but having to self-teach basic math that my basic schooling failed me on up to this point, it feels like something of a milestone.

Youre wrong.
My knowledge and training is too low for math.

I'd fuck Lurie hard in the ass if I could desu

[math]\frac{x}{x}=x[/math] is only true when [math]x \neq 0[/math]

I'm worried about him. He sounds like he has asthma.

Meant [math]\frac{x}{x}=1[/math]

very wrong post

>replying to low effort bait
y u do dis

Can somebody recommend me a good textbook for linear algebra?

I'm gonna have to take a first year university calculus course this fall, and I'm a bit nervous. I did well in high school calculus, but that was 4 years ago, and I don't remember shit. What should I learn to be prepared. Pls help.

>What should I learn to be prepared.
open a calculus textbook

Axler is very good. Everybody agrees with that. Very good textbook

which one? I only have a month to prepare.

>which one?
whichever book your course uses

>What should I learn to be prepared
"How to prove it"
>which one?
Open Spivak's Calculus or Apostol's

>Everybody agrees with that.
That's quite the claim.

keep in mind, I'm taking Calc 1. That book seems kind of complex.

>That's quite the claim.
Sure, that one is obviously false. The rest of my post is solid though - as everyone would agree

>I'm taking Calc 1
it still could be with theory but I figure now that's not the case
Well then don't read anything just do khan academy then maybe - to refresh on what you learned

Just finished linear algebra, what should I study next ?

>as everyone would agree
I disagree.

if you know calc 1/2 you can learn calc 3
if you know group theory you can learn representation theory
multilinear algebra is good to know

Differential equations.

nonlinear algebra

open world algebra

first person algebra

Topological Algebra

Universal Algebra, Differential Algebra

bullet hell algebra

curved algebra

naval algebra

computational algebra

FUCK YOU HE SHOULD STUDY DIFFERENTIAL EQUATIONS REEEEEEEEE!!!
Like it's been done historically. Learn calculus as you learn ODEs.

recreational algebra

anime algebra

cat algebra

we did it reddit XD

Thanks for the input, I'll start with Calc 3 and differential equations.

Highschool algebra

Can anyone here actually prove that [math]1 \neq 0[/math] ?

If you have 1 apple, you can eat that apple
If you have 0 apples, you cant eat that apple because there are none

you don't need to prove anything, they're not equal by definition
en.wikipedia.org/wiki/Peano_axioms

This is a good informal argument, but it's not a proof.
Bad post. You should feel ashamed of yourself.

Easily provable in Peano arithmetic.

Suppose that [math] 1=0 [/math]. Then [math] S(0) = 0 [/math].

This contradicts the axiom that says [math] \forall n \in \mathbb{N}, S(n) \neq 0 [/math]

Good. And what about some other systems where it isn't an axiom?

>it isn't an axiom?

But it isn't an axiom lol. I proved that it contradicts an axiom. Back to logic 101, compsci kiddy.

>But it isn't an axiom
I clearly meant the axiom which it contradicts. Do you have reading comprehension problems? There's a thread for people like you.
>lol
Really now?
>compsci kiddy
An interesting assumption. So what are you trying to achieve again?

>I proved
you didn't.

Posts like this are the second biggest cancer haunting Veeky Forums, right after /pol/tards.

Using von Neumann's construction of the natural numbers:
[math]0=\varnothing \\
1 =\{\varnothing\}\cup\varnothing=\{\varnothing\}\neq0[/math]
It follows immediately from any valid definition of the natural numbers.

OH FUCK REALITY IS DISINTEGRATING BEFORE MY VERY EYES JUST BECAUSE I COULD NOT PROVE [math]0 \neq \operatorname{Succ}(0)[/math]

Good job, user.
>I COULD NOT PROVE [math]0 \neq \operatorname{Succ}(0)[/math]
I feel sorry for you.

nonassociative algebra

Define 1 such that [math]1*x = x \ \forall \ x[/math]
Now define 0 such that [math]0*x = 0 \ \forall \ x[/math]

If [math]1 = 0[/math] then necessarily [math]x = 0 \ \forall \ x[/math]
So the existence of a single nonzero number x would contradict the assertion that 1=0.

But alas, I don't know how to prove the existence of a number whose only property is that it's not zero, especially when operating under the assumption that 1=0, which implies that every number is zero. How can I prove that at least one number is not zero when I've made an assumption that implies ALL numbers are zero?

I'm thinking this is one of those "unprovable but true statements" Godel was going on about...

I don't know if this is a shitpost or just retardation.

It'd have to be a very severe form of retardation considering the thicc thinking meme.

I'll be done all the "general" requirements for my mathematics degree next semester (top 50 university, so nothing that good). What emphasis area should I do?

1. Abstract
2. Applied/Computational
3. Actuarial/Financial
3. Computer Science
4. Operations Research/Management
5. Statistics

Why do you think this is an appropriate question for this thread?

>Reminder: Veeky Forums is for discussing topics pertaining to science and mathematics, not for helping you with your homework or helping you figure out your career path.

>If you want advice regarding college/university or your career path, go to /adv/ - Advice.

fine

What a vacuous construction.

n = 2
4 ≡ 2 mod 1
4 ≡ 0
???
Is there something I'm missing here?

>Is there something I'm missing here?
4 is congruent to 2 mod 1, what's the issue?

>4 is equivalent* to 2 mod 1

>being this retarded

>he doesn't think 1 divides 2
>being this retarded

All integers are congruent to 0 modulo 1 you dumb-asses. So every integer is congruent to every other integer modulo 1.
[math] 4 \equiv 2 [/math] because [math] 4 \equiv 0 \equiv 2 [/math].

>All integers are congruent to 0 modulo 1 you dumb-asses.
Did I say otherwise? Why did you quote my posts?

Daily reminder to work with physicists.

>work with physicists
>work with the brainlets that pollute mathematics

>image: Quantum Fields and Strings: A Course for Mathematicians
>This series of courses was intended to teach mathematicians [...] physics, [...] and consequently there is considerable diversity in mathematical rigor among the courses recorded in these volumes.
>considerable diversity in mathematical rigor among the courses
I'm not going to drop this because I'm not even going to bother to pick it up. Eat shit.

>>>/pg/ - Physics General

ncatlab.org/nlab/show/Quantum Fields and Strings
>While advertized as “A course for mathematicians”, experience shows that it is not really suited for pure mathematicians without previous exposition to and tolerance for physics
A bad sign already: the bullshit, hand-wavy distinction between "pure" and "applied" mathematics is taken seriously by evangelisers of the text. (No, you assholes: mathematics is mathematics is mathematics! If your shit lacks rigour you're not doing "applied" mathematics, you're doing only pretending to be doing mathematics.)
>But it is much better than the average physics text.
>If you only ever touch a single book on string theory, touch this one.
Interesting. So it's garbage pseudo-mathematics, but not as putrid as all the other unrigorous junk out there, which makes it worthy of being read.

Thanks but no thanks. This looks like another attempt by physishits of trying to get mathematicians to fix the mess they created.

I took a course in abstract algebra for mathematicans (I'm CS and we use mod notation in CS courses too) where we used mod notation. What other notations are there?

>physicists' work pollutes mathematics
at least they work

What is /mg/'s opinion on Advanced Calculus by Loomis and Sternberg?

Hey, im the guy from yesterday who was talking about the riemann hypothesis.

I think i have proven it now.

What should i do now to get 1 Million ?

try to publish it so everyone can have a good laugh