Mathematics - 2016-09-17 (page 2 of 2)

« first day (2236 days earlier) ← previous day next day → last day (3081 days later) »

0celo7

20:00

Hopefully the prof will talk about it

It's not hard, one can show they're path connected

Just write the path explicitly.

Balarka Sen

@0celo7 By hand.

0celo7

That's not very helpful.

Balarka Sen

I know it isn't.

All you need is to show a disk minus a point is connected when the disk is of dimension > 1. You can do this by hand, by writing down an explicit path between any two points.

@Adeek The point is, if you perturb a matrix (i.e. change it's entires by a very small $\epsilon$), rank cannot go down.

Because look at a $r \times r$ submatrix, which has nonzero det ($r$ = rank of your matrix).

That's the reason why that set is open.

@0celo7 Pointwise limit?

robjohn

@JessyCat: haven't seen you here in a while. Welcome!

0celo7

@BalarkaSen I figured it out, never mind that

Balarka Sen

20:08

okie.

(I should have said "product topology" instead of "pointwise limit" by the way, since you asked for a topology)

0celo7

@BalarkaSen It converges in the product topology, yes.

But not in the box topology.

Balarka Sen

Of course not.

0celo7

I've asked you not to say that.

Balarka Sen

That's why I am saying it.

But I take it back if you haven't figured out why it doesn't converge in the box topology, and apologize.

0celo7

I did figure it out.

That's why I said "never mind"

Balarka Sen

20:12

Then there's no point taking that back.

0celo7

Correct.

Balarka Sen

What's new?

Adeek

I think there is a mistake in something that I am reading

sorry not this

@BalarkaSen this should be $\hat{u_j}$ right ?

0celo7

what are you reading?

Adeek

not $\hat{u_i}$ right ?

@0celo7 john lee

0celo7

20:15

@Adeek Check the list of errata.

Adeek

oh ok let me check

Balarka Sen

Would be better than me checking that junk of expressions.

0celo7

Which book of Lee's

I have two of them, that's not in either as Example 1.11

Adeek

smooth manifold.

0celo7

Get the 2nd edition.

Adeek

20:18

arctic tern

hey people of chat

Balarka Sen

Hi @arctictern

0celo7

hello person who was not in chat but now is

arctic tern

say $G$ is a group, $H,S\le G$ subgroups, and $g\in G$ an element. any ideas if $\{t:tHgS=HgS\}$ can contain $H(N_G(H)\cap gSg^{-1})$ strictly?

Balarka Sen

looks complicated

0celo7

20:20

eww

Adeek

@0celo7 second edition is much better

0celo7

@Adeek Yes.

It's one of the better books out there, despite what @BalarkaSen says.

Balarka Sen

I didn't say much.

It just didn't suit me at a glance.

SAWblade

20:55

wahahaha my question got answered

0celo7

@BalarkaSen $\epsilon,\delta$, is $\eta$ next? Doing a nasty metric space proof.

Balarka Sen

Maybe

0celo7

What would you use?

Balarka Sen

$\epsilon_0$, $\epsilon_1$ etc

0celo7

Oh...no thanks I'll use $\eta$.

Balarka Sen

21:00

okie

0celo7

the various letters are unrelated

$\epsilon_0,$ etc. implies a relationship

or at least that they have the same function

Balarka Sen

whatever floats your boat

lololol

"It is alleged that Timur's tomb was inscribed with the words, "When I rise from the dead, the world shall tremble." It is also said that when Gerasimov exhumed the body, an additional inscription inside the casket was found, which read, "Whomsoever opens my tomb shall unleash an invader more terrible than I."
In any case, three days after Gerasimov began the exhumation, Adolf Hitler launched Operation Barbarossa, the largest military invasion of all time, upon the Soviet Union. Timur was re-buried with full Islamic ritual in November 1942 just before the Soviet victory at the Battle of Sta…

0celo7

Huh.

Proof that ghosts exist, wow.

Balarka Sen

curses, if not ghosts, at the very least. :P

0celo7

Yeah.

Let $\underline z\in B_{\bar\rho}(\underline x,\epsilon).$ Then $\eta:=\bar\rho(\underline z,\underline x)=\sup\{\bar d(z_i,x_i)\}<\epsilon<1$ and $\eta\in U(\underline x, \frac{\epsilon +\eta}{2} )$.

This is not going to be fun lol

3 hours later…