Mathematics - 2020-04-16 (page 3 of 3)

Ted Shifrin

22:00

I'm saying he is sloppy about naming his hypotheses that he uses, at least in the edition I have.

So the proof uses $f$ continuous and $D_1 f$ continuous, even though he doesn't state that.

I quit on that source.

skullpatrol

I was surprised to find out Mary Rudin was Moore's student? @TedShifrin

Ted Shifrin

Why surprised? How many "big names" do we know in the point-set world?

Balarka Sen

1

Bing

Ted Shifrin

I would put Moore in there.

Bing was actually more geometric :P

Balarka Sen

yeah i was joking

skullpatrol

22:04

lol

Ted Shifrin

Now you're making me want cherries.

Thorgott

He only ever needs continuity in one variable at a time, which is guaranteed by differentiability in that variable, no?

Balarka Sen

I always found it funny how "R. H." in R. H. Bing doesn't stand for anything

skullpatrol

srsly?

Balarka Sen

Yeah look it up

skullpatrol

22:08

I trust you, pal

Leaky Nun

Bing's father was named Rupert Henry, but Bing's mother thought that "Rupert Henry" was too British for Texas. Thus she compromised by abbreviating it to R. H. (Singh 1986)

It is told that once Bing was applying for a visa and was requested not to use initials. He explained that his name was really "R-only H-only Bing", and ended up receiving a visa made out to "Ronly Honly Bing".[4]

Ted Shifrin

Oh, you're probably right, @Thorgott. His screwy notation confused me.

Reminds me of B.J. Honeycut on MASH. :)

They had a whole episode in which Hawkeye was obsessed with what the B.J. stood for.

Balarka Sen

lol

Thorgott

Yeah, the notation is ugly, but I believe the argument does check out with the hypotheses given.

skullpatrol

> His full name remained a mystery throughout the series. He claimed (in the Season 7 episode "Lil") - perhaps in jest - that he was named after his mother Bea and father Jay (hence Bea-Jay = B.J.).

Ted Shifrin

22:19

I have to confess that, in general, worrying about the most general statements possible doesn't interest me that much, since in most cases we have stronger hypotheses. Now somebody(s) can prove me wrong.

@skull: Yes, I know about the parents. I remember the punch-line.

skullpatrol

TIL :-)

Thorgott

It can be pretty interesting

I'm still amazed that everywhere differentiability instead of $C^1$ suffices for the Inverse Function Theorem

Balarka Sen

I worked that out once but promptly forgot about it

I don't think I have ever used these results

Mike Miller

@Thorgott Wild. Immoral

Ted Shifrin

That isn't quite right, @Thorgott. I think someone in this chat pointed us to a post by Terry Tao. But the usual counterexample shows you need to assume differentiability PLUS more (one-to-one?).

Balarka Sen

22:26

iirc you just use Brouwer fixed point theorem to find the fixed point instead of contraction mapping in the usual proof

Ted Shifrin

But something needs to be assumed. Or else the usual $f(x) = x/2 + x^2\sin(1/x)$ gives a counterexample.

Balarka Sen

You want the derivative to be invertible everywhere

By everywhere I mean on a neighborhood

Ted Shifrin

Oh. That'll do it.

Mike Miller

@BalarkaSen I hate it

Thorgott

Yeah, I meant "the usual assumptions with $C^1$ replaced by everywhere differentiable"

Ted Shifrin

22:29

I always have pedagogical issues to raise. Some general results are great, but I don't necessarily think that they're right for students seeing them the first time. That's what bothers me so much about Hubbard & Hubbard in places.

Balarka Sen

@Thorgott No, the usual inverse function theorem assumes invertibility of the derivative at a single point

Mike Miller

@Thorgott The useful assumption is that $Df$ is invertible at a specific point, though

Ted Shifrin

Right.

Mike Miller

So that one can compute less :D

Balarka Sen

@TedShifrin I have never used these things so I concur

I just forget about things I don't use

What's the point

Thorgott

22:31

Oops, I had missed that detail

Ted Shifrin

It's OK, @Thorgott. You're still ahead a point on me :P

skullpatrol

match point?

or set point

Balarka Sen

Let's just write down a concrete theory of multivariable calculus on a topos instead

Ted Shifrin

smacks Balarka

geocalc33

which arithmetic site?

Balarka Sen

22:33

the Nisnevich site

over a perfectoid space of $\ell$-adic character

skullpatrol

Smacking Balarka: A Geometric Approach

8

Balarka Sen

Geometric Geometry: An Algebraic Approach

Ted Shifrin

no "al"

You guys wouldn't have nearly so much fun without Ted upon whom to pick.

Balarka Sen

It's not really picking, it's such a good, reusable meme

We love and adore it

I wonder what happened to Hippa, he was easily the best at this

Mike Miller

He's an algebraist now

I assume, at least. He was French

skullpatrol

22:38

yeah, he was a natural

Balarka Sen

@Astyx knows Hippa I think

They're both at Polytechnique

geocalc33

oh so he good good

Ted Shifrin

We all met for lunch in Paris a few years ago.

I'm forgetting one other person.

Balarka Sen

Gabriel?

Ted Shifrin

I can't remember people who quit showing up.

Balarka Sen

22:39

Maybe I should do that

skullpatrol

Pedro?

Ted Shifrin

You did that for a year or more.

No, Pedro I met in the US.

Balarka Sen

yeah... didn't turn out well for me

Ted Shifrin

He schooled me in math and tennis, but he got some good food out of it (and met Pete Clark).

Well, I did miss you, a @Balarka.

skullpatrol

coolio

Mike Miller

22:41

I chased him off as best I could but he's persistent

Ted Shifrin

You chased you off, too, Mike, but then ....

geocalc33

what was he persistent about?

Balarka Sen

$\ell$-adic sheaves

skullpatrol

returning

Ted Shifrin

Balarka is like the Poincaré return map and ergodic flow.

skullpatrol

22:43

anon never returned

Balarka Sen

I certainly hope I'm not pseudo-Anosov

Ted Shifrin

You might be, Balarka. Geodesic flow and all.

Balarka Sen

Ergodicity is fine as long as I'm not mixing with people

If you know what I mean

Ted Shifrin

I wonder what happened to anon. Did he go to grad school? Crazy if not.

LOL, a @Balarka.

Balarka Sen

Oh btw Garbiel's other name was

Le Grand DODOM

whatever that means

Ted Shifrin

22:45

oh, right, dodo ...

geocalc33

I just realized I

Ted Shifrin

And hippa's younger brother disappeared, too.

Balarka Sen

oh right he brought his younger brother lmao

good times

geocalc33

I tried to bring my younger brother but he doesn't like math

it took me a while to adjust to this site

I asked a lot of stupid questions lol

Balarka Sen

God im hungry

its 4 am

what to eat holy shit

geocalc33

22:50

eat a tomato

Balarka Sen

thats the last thing you should eat if you're hungry

skullpatrol

\o @MonaJalal welcome

2

Mona Jalal

Hi @skul

Hi @skullpatrol

skullpatrol

hello

CaptainAmerica16

hola

skullpatrol

23:16

How's the Covid situation in Iran @MonaJalal?

Martin

Hi there, I have a problem that I think is rather simple. Consider to matrices A and B. If i know that $R(A) \subseteq R(B)$, what can I say about the matrices? Here $R(A)$ is the range/image/span of $A$.

Mike Miller

23:34

@BalarkaSen I can't tell any of the French people apart

@Martin Very little other than that the rank of $A$ is at most the rank of $B$, it seems to me. For instance, if $\det B$ is nonzero, then $A$ can be any matrix.

Balarka Sen

@MikeMiller I am going to go read what Henri Villani and Pierre de Poincare has to say about the hyperbolic plane

Martin

@MikeMiller Sure, we can't say much "new". But I was thinking about different ways to represent this. I have come to the conclusion that any column of $A$ can be written as $Bx$ for some $x$. I am not entirely sure, do you agree?

Mike Miller

$Ae_j$ is the $j$'th column of $A$, so $Ae_j \in R(A)$. We are given that $R(A) \subset R(B)$, and $R(B)$ is the set of vectors of the form $Bx$, so yes, that's right

Martin

@MikeMiller Thanks for the sanity check, I think its time to go to bed soon :)

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$Mathematics$ Mathematics