Mathematics - 2017-07-04 (page 7 of 9)

Ted Shifrin

20:00

Even Milnor makes the obligatory pun. "This approach to the problem runs into manifold difficulties."

Typhon

@TedShifrin I swear one of these days someone is going to make a graphing calculator named manifold destiny.

Ted Shifrin

Graphing calculators aren't too good with manifolds.

Typhon

wait

nvmd

for some reason your pun confused me

s.harp

hard to graph something more than 2 dimensional

Typhon

and I thought "manifest destiny" was "manifold destiny"

so the pun was totally lost

XD

Faust7

20:02

@TedShifrin i tried a few different things i said $ (1+\frac {1}{n})^n=c $ then tried to ln both sides and take the limit of n to infinity to try and show that ln(c)=1 so $c=e^1 $ but it just didnt feel like it i wasnt breaking some logarithmic law when i was putzing around with it. i think it might be easier to show $ (1+\frac {x}{n})^n = e^x $ at least then i could use the MVT and FMToC any hints how to approach this better?

Ted Shifrin

What's $\lim\limits_{h\to 0}\dfrac{\ln(1+h)-\ln(1)}h$, @Faust?

Balarka Sen

If I believe Akiva's intuition, I should look for framed torii in S^4 which are not framed cobordant to sphere.

Ted Shifrin

@Faust: Then set $1/n = h$ and see this is the same thing.

Typhon

@TedShifrin is the arf invariant used when making subwoofers?

red_trumpet

Hey, why is there math.stachexchange.com and mathoverflow.net? What are the key differences?

Balarka Sen

20:05

Latter is mathoverflow, the former is mathunderflow

Typhon

@red_trumpet mathoverflow is intended to be an eventual replacement. snigger

in all seriousness

MO is for research or reeeeeaaally complicated things

MSE is for people wanting help with this, that, and their mother.

Mike Miller

@BalarkaSen Sure, that's what you're doing

Faust7

my problem is oddly what the $ \lim_{h\to 0}\frac {\ln (1+h)} {h}$ is it looks undefined to me

Ted Shifrin

@Faust: It should look a lot like the definition of the derivative.

Balarka Sen

I am... underflowing?

Faust7

20:06

it does

Typhon

@BalarkaSen no

Ted Shifrin

So what's $\dfrac d{dx}\ln(x)$?

Typhon

underflow is completely irrelevant

Dis-integrating

hi guys. I want to a paragraph that basically introduces my passion and understanding in mathematics.

Typhon

Math overflow is a reference to stack overflow

Faust7

20:07

$\frac {1}{x}$

Dis-integrating

any suggestions?

Typhon

and stack overflow is a computer science bug made into a cute name

Ted Shifrin

And at $x=1$ that is ... ?

Mike Miller

@BalarkaSen trying to find tori etc

red_trumpet

@Typhon ok, thank you. I actually like the design of MSE better, would be sad to find it replaced...

Typhon

20:09

@TedShifrin is is undefined

@red_trumpet except MO is a paid service

or used to be back in the day

people used to have to pay to create communities on here

Balarka Sen

@MikeMiller right, i was making a stupid joke

Typhon

this site may one day become....

Ted Shifrin

Imagine that.

Typhon

Pay per view

user80108

hey, question for y'all: if $n \equiv 0$ (mod $3$) and we are considering polynomials over $\mathbb{F}_3[x]$, is it true that $\text{gcd}\,(x^n-1, x^m+x^k+1) \mid x^{n/3}+x^{2n/3}+1$ for every choice of distinct $k,m \in \mathbb{Z}/n\mathbb{Z}$?

Ted Shifrin

20:10

It would curtail all the homework-askers.

Balarka Sen

So, it's interesting to think about this. I don't know if it's visually apparent to me of such a framing on the torus (say)

Typhon

@TedShifrin yeah but guess what, it is 10 cents per post here.

we'd all be bankrupt

jk

actually we'd all leave

D:

Ted Shifrin

I wouldn't be. Answerers wouldn't have to pay.

Typhon

@TedShifrin no 10 cents per chat post

and I mean 99 cents per every page load

Ted Shifrin

I'm outta here.

Typhon

20:12

@TedShifrin heheheh

glad that is unlikely

but fun to speculate

SteamyRoot

Well, in some ways, that's how life is if you want to read some papers the legal way.

If you university isn't subscribed to the journal it was published in, you have to pay.

Tobias Kildetoft

@SteamyRoot Unless it is on arXiv, which it usually is these days

Typhon

@SteamyRoot pay per google

SteamyRoot

True, and that's a lifesaver.

Typhon

pay per email

SteamyRoot

20:16

But for papers that aren't on arxiv and you're not subscribed to, you pretty much only have the title and abstract to tell you what's inside.

Sometimes that's fine, but if you're looking for an obscure lemma or example...

Typhon

@SteamyRoot pay per page; pay per reload; pay per operation in calculator

I keep coming up with more ideas to torment people with horrible real life drm.

Balarka Sen

@MikeMiller @TedShifrin Ok, turns out the framed cobordism group of surfaces in $\Bbb R^N$ is generated by the torus with it's Lie group framing. This was proved by Pontryagin, using the Arf invariant.

@AkivaWeinberger I guess that means generic preimage of your map is indeed the torus.

I have no idea how to prove any of this and would love a reference.

Mike Miller

Google andy putman pontryagin thom

Typhon

3

Q: Proof for elements of $\textbf{Z}[\sqrt{3}]$ regarding the existence of the norm.

So for some context, I was in a proof writing class a couple months back. I really liked it and did quite well, but midway through the course we were doing things regarding the norm of these other kinds of integers (elements of $\textbf{Z}[\sqrt{3}]$). Basically things like the fact that there is...

Balarka Sen

Got it, thanks.

Typhon

20:28

correct me if I am wrong, but would any ring created by appending solutions to polynomials also have the same norm property assuming it had unique prime factorization up to units?

Tobias Kildetoft

@Typhon Not sure what you mean by "norm property"

Typhon

read my question

it should be clear from context given what the question is asking

Alessandro Codenotti

Rehi chat

Tobias Kildetoft

No, it is not at all clear what "norm property" you are asking about here.

Alessandro Codenotti

Just parked a car for the first time in my life, scary experience, but went better than expected

Balarka Sen

20:32

You need to drive like Arturo Benedetto Giovanni Guiseppe Pietro Archangelo Alfredo Cortaffoli da Milano [EDIT: minor typos]

who even cares about parking?

Alessandro Codenotti

Parking is like the brakes, superfluous?

Balarka Sen

exactly

Alessandro Codenotti

Does anyone have an intuitive explanation for the central limit theorem? It feels way too much like dark magic to me

Dis-integrating

could anyone help me write a short sentence that captures something cool about mathematics or why it is interesting?

s.harp

@Alessandro put a bunch of stuff in a pot and it diffuses out and loses all edges

Typhon

20:40

@Dis-integrating "Math is cool"

I hate writing but if I must.

Dis-integrating

i feel like you're going to write something here

or was that it?

either way, thanks

I'm actually dying here though

I want to apply to cambridge

Alessandro Codenotti

@s.harp eh

Not sure how serious that was, but I didn't get it

Balarka Sen

@s.harp lol

fpqc

Hello world

Balarka Sen

hi

fpqc

20:47

Man I have not been on in years

@TedShifrin You still using MO?

wOW

I guess I don't really come on math.se anymore

Balarka Sen

i don't recall you

from here

fpqc

Bro I was active in like 2011-2012

@BalarkaSen e.g. this was me: math.stackexchange.com/a/178381/165083

Balarka Sen

"huh"

Typhon

@fpqc yer a newb

fpqc

@BalarkaSen I deleted my account

Then made a new one

Balarka Sen

20:51

welcome back, even though i know you from my past life only it seems

Typhon

dont lie....

fpqc

I am benjalim

Typhon

no you are not

fpqc

14

A: for a $3 \times 3$ matrix A ,value of $ A^{50} $ is

You should learn BenjaLim's answer, which provides a general method for dealing with this kind of problems. However, here is a simple answer just for fun. Note that $$ A^2= \begin{pmatrix} 1&0&0\\ 1&1&0\\ 1&0&1\end{pmatrix} =I+\underbrace{\begin{pmatrix} 0&0&0\\ 1&0&0\\ 1&0&0\end{pmatrix}}_{L}...

Typhon

and I'm Donald Trump... -_-

fpqc

20:52

@BalarkaSen They mention benjalim.

Typhon

liar

fpqc

Ben Lim, Stanford, CA

659 6 21

ag.algebraic-geometry ac.commutative-algebra nt.number-theory arithmetic-geometry elliptic-curves teaching tensor-products

benjalim = ben lim

Balarka Sen

Ah, Ben Lim.

I have seen you on MO then.

fpqc

Yes duh....

I don't know why my chat name is still fpqc

it's weird

Balarka Sen

maybe because it's still linked to your deleted MSE account

you can probably associate it to your MO account

fpqc

20:53

yes

Typhon

you're not ben lim

stop lying

fpqc

In any case I feel like math.se is dominated by lots of stupid questions nowadays

Balarka Sen

homework-like stuff. i agree

fpqc

It's getting boring.

Also the questions I usually have are more appropriate for MO

Balarka Sen

MO is too hard for me

fpqc

20:55

Sure. If you're a grad student like me it's ok.

@TedShifrin Long time no see! @robjohn

@TedShifrin From memory your advisor was chern yes?

@BalarkaSen are you an undergad?

Balarka Sen

more or less pretty much almost.

Faust7

@TedShifrin i think i maybe got it lets assume the limit could converge to some constant L so $L=\lim_{n \to \infty} (1+ \frac {1}{n})^n$ next ln both sides to yield $\ln (L)=lim_{n \to \infty} \space n\space \ln (1+ \frac {1}{n})$ if we let $ h =\frac {1}{n} $ then we have $\ln (L)=lim_{h \to 0} \frac{1}{h} \ln (1+h)$

or $\ln (L)=lim_{h \to 0} \frac{\ln (1+h)}{h}$ now the FToC should let $f^{'}(c) = lim_{h \to 0} \frac{\ln (1+h)}{h}$ now we know that the original function was $f(x)=\ln(1+x)$ so $f^{'}(c) = \frac {1}{1+c}= \ln (L) $ so $L=e^{\frac{1}{1+c}} $ now $ c \in \mathbb{R} $ but more than that $c \geq 0$ i think c is bounded above by $\frac {1}{n} $as $ n\to \infty $ so $L=e$ ?

Balarka Sen

(Also, yeah, Ted's advisor is Chern)

Dis-integrating

ayy @BalarkaSen which university?

Faust7

the thing is im not sure i can ln a limit

fpqc

20:59

your question is what is $\lim (1 + 1/n)^n$?

It's just e man

Faust7

im trying to prove that it is e

fpqc

Look, take the log of that

you have to prove the limit of (1+1/n)^n is 1.

Dis-integrating

l'hopital's rule then

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$Mathematics$ Mathematics