now, for a bounded sequence that do not converge, the proof is simple:

a bounded sequence that do not converge has two converging subsequences that converge to different limits

do you agree?

No.

then I give up

Do you have Bolzano-Weierstraß?

@ACuriousMind No.

I do, the class doesn't.

you're doing analysis the masochistic way

For the unbounded case, can't I just use the converse of "convergent sequences are bounded"?

i.e. somehow show $x_n+y_n$ is not bounded if $y_n$ isn't?

@yuggib Seems like it

Doesn't make much sense to show this statement before BW, does it?

@ACuriousMind In my opinion, it doesn't

@0celo7 yes, it is essentially what I did above

This problem set is due Tuesday and we don't get to BW until Thursday/Tuesday after.

The exact problem statement is: Give an example of each of the following, or state that such a request is impossible by referencing the proper theorem(s):

And the part I'm suck on is

I still think that for bounded, non-converging, sequences it's really painful to prove it without BW

and I have no intention in trying

:-P

Theorems I have: Uniqueness of the limit, boundedness, algebraic limit theorem, order limit theorem, monotone convergence

I think one can deal with the unbounded case separately

Then maybe use uniqueness of limit for the bounded case

@Danu but still you need BW

Sorry, what's BW?

oh

bolzano weierstrass

perhaps

Just prove BW by hand first lel

it's not too hard is it?

yeah, but it seems a little bit far fetched for an exercise

it's a whole section in the textbook

I doubt they want the reader to prove it as an exercise two section in advance

@yuggib ;D

Still, it's not too hard.

Also, weren't you doing courses on PDE's? Surprising that this material would not be prerequisite...

even Bourbaki it's not too hard

I just looked at the proof and it's too hard for me

@yuggib Wow I really need to know if $0\in\mathbb{N}$ for this problem

you always need to know ;-P

not that it matters, I can't solve the problem either way.

I just realized I actually have HW to do

lel

Exercise: Given $a,b\in\mathbb{Z}$ with $a\ne 0$, $\exists !q,r\in\mathbb{Z}$ s.t. $b=qr+r$ and $0\le r<|a|$.

You mean...long division?

Like exactly the thing we proved in class?

Ok.

I just produced a positive number smaller than a negative number. I just disproved long division.

I just managed to install Linux on my calculator

and play doom on it

I'm done for the day

I'm about to prove if $a>0$ then $a(b,c)=(ab,ac)$

any second now

I learned some integrals today

@BernardMeurer any interesting ones

imgur.com/a/QrGAb

can you do $\int_0^x\mathrm{e}^{-t^2}\,\mathrm{d}t$

@0celo7 Nothing special, just how to solve some basic ones

did you steal my calculator

@0celo7 I think I could but

Yes, yesterday on skype

@BernardMeurer really?

pls do it

They've always said it cannot be done, but I think that's BS

Ha

nice trap

@0celo7 He stole your calculator and installed Doom on it, be a bit more thankful!

Having an algebra class taught by a number theorist is the worst thing ever

It's sooooooooooooooó boring

What's a cool integral to solve for begginers practice @ACuriousMind?

...who else would teach algebra?

He's so enthusiastic about fucking integers, it's gross

@BernardMeurer The concept of "cool integral" doesn't exist in my world

@ACuriousMind A geometer. He teaches the three things I need and then does Morse theory for the rest of the semester.

@ACuriousMind seconded

although have you need the math chat

I suspect what bores you might be algebra itself, not the lecturer :P

they do nothing but integrals there for hours and hours

@ACuriousMind I found them cool today :c

@BernardMeurer It's fine, and many do seem to derive pleasure from solving integrals. I'm not one of those

@ACuriousMind We haven't done any algebra. Seriously. My notes are all: $n>2$ is either a prime or a product of primes, $(a,b)$ is a linear combination of $a,b$, $ar+bs=1$ iff $(a,b)=1$ and other crap

If $p$ is prime then $p\mid {p\choose i}$

E.g. the "long division" you did is algebra - it's showing the integers are a Euclidean domain. I suspect your teacher might be introducing all the concepts they can with the integers, so you have an example to abstract from.

who the fuck cares??

^ sent too late

@ACuriousMind The only fun thing about this problem set was noting that $rab+sac$ sounds like "Rabbi's sack"

And that's not even really fun

@ACuriousMind OK, let's return to HE.

So we had $\alpha(s,t)=\exp_p(sv(t))$, right?

Nah, not in the mood to decipher that now

bruh

@ACuriousMind I derive pleasure from recompiling the kernel

@BernardMeurer That's a euphemism, right?

@ACuriousMind I really do enjoy it

It's always a thrill, what will you fuck up next?

You know what is a thrill

Guessing RAM usage while avoiding more algebra proofs

Dude, this calculator has 64MB of RAM

and it runs Doom

my laptop has 16GB

and doesn't run the witcher 3

;_;

I bet my calculator does

f u

As soon as the cable I ordered arives I'll be running xorg on it

also, it managed to run python

just now

I still can't figure out how to calculate these damn pushforwards

It has to be trivial

Got Pokemon Emerald to run on top of an emulator

on my TI

nerd

Proudly

@BernardMeurer BF4?

@0celo7 I want to, but I'm stuck at work discussing magic

aka. UNIX and POSIX

...the game or actual magic?

Ah.

@ACuriousMind Do you playe the game magic?

No

Are you an actual magician?

@ACuriousMind Skype call

@BernardMeurer perhaps

@ACuriousMind Doesn't like us @0celo7

oh ffs Jost does the Gauss lemma by looking at a pullback bundle or some crap

That's in italic, I take it as an insult

that's even less understandable

@BernardMeurer I don't know what we did to upset him like this

at least he didn't verbally abuse me this time, just you

Me neither @0celo7, I'm searching my heart to find out how I hurt him