hi @Ted

hi Leaky .... back in a few

care to join us?

PayPal fee is $y = (x*0.029)+0.30$, let $x$ represent the donation

$\frac{y-0.30}{0.029} = x$

is there a continuous function f : (a,b) -> R that is not uniformly continuous on (a,b) such that it extends continuously to the endpoints of the interval [a,b]?

@famesyasd "extends to [a,b]" is equivalent to uniform continuity

Hm

Quick sanity check : if I consider the Hilbert space $\mathbb{R}$, is the projection valued measure just the Lebesgue measure

For a cayley graph i mention that Cay(G,S)= Cay(G,S U S^(-1)). Then later on for a particular group I say that we take the generator set S = {a,b}. Then is it understood that a^(-1) and b^(-1) are also belonging to S and I'm considering the undirected cayley graph eventhough I don't mention a^(-1) and b^(-1)?

Wanted to mention for a Cayley graph $Cay(G,S)$, when I say $S={a,b}$, it means that for the Cayley graph please consider $a^(-1), b^(-1)$ also as belonging to $S$. What is the proper terminology to say that?

There I wanted to mean a's inverse is not b

Thanks a lot in advance.

Any iDeas ?

Anyone feel like getting 100 rep bounty? math.stackexchange.com/q/3045860/333955

Sorry to ask another quick symbol identification question; this symbol here, wikimedia.org/api/rest_v1/media/math/render/svg/… , does that just mean any arbitrary norm or is it a norm with specific properties?

I saw it on this page, en.wikipedia.org/wiki/Matrix_norm , I've seen that symbol used to refer to vector norms, matrix norms, etc, so my guess is, it just means "some norm"

Some norm

thanks!

@mick

In Atiyah's book it's stated that "What is essential to keep in mind is the defining property of the tensor product", now the way I understand is, the defining property is that given any two $A$-modules $M$ and $N$, the tensor product is an $A$-module denoted by $M \otimes_A N$ equipped with a bilinear map $f : M \times N \to M \otimes_A N$ defined by $f(x, y) = x \otimes y$, am I correct in saying that this is the defining property of the tensor product?

you're missing the other half

Ahh that every bilinear function on $M \times N$ factors through the tensor product

is it true that det(F(V),F(W)) = det(F)det(V,W)? if so, then why?

V,W r lineary independent 2d vectors and F is 2d linear tranformation

It's a calculation

yes but with that i have problem

just dont know how it is done, that calculation

for statistics phd programs, is it worth re-taking probability and mathematical statistics if you don't have an A? like, if your grade is a little below an A?

@chandx $\det(AB) = \det(A)\det(B)$

I just bombed abstract algebra. Am I screwed for PhD programs?

How does one define the supremum of a function over a fuzzy set, i.e. $\sup {f(x) \mid x in S}$ where $S$ is fuzzy?

$\sup \{f(x) \mid x \in S\}$

What makes you think that should be defined?

hi Demonark

it's 63 freaking degrees outside!

F

You were whining when it was 37 yesterday, @CaptainAmerica.

Yeah, but at least that was natural.

Welcome to climate change and worse.

Why am I the only that finds this alarming!

My little sister just said whatever.

My dad thinks it's funny

Yup. They won't think it's so funny in a few more years.

My mom just bought 2 cans of febreeze. Isn't that stuff bad too?

I don't remember which ones it was.

Aerosol cans are all horrid.

But who needs the ozone layer?

;-;

I didn't know it was that serious. People kept saying it wasn't real.

People who watch Faux News, you mean?

That's pretty much everyone I know

Sadddd....

51 Mersenne Primes now

Since like 2 weeks ago

not that I really follow it

There isn't much we can really do if most people think it's fake

Not most, CaptainAmerica, but a depressingly large portion of our ignorant population.

@ÍgjøgnumMeg: If only $51$ were prime.

it's a pretty Grothendiecky-esque prime

wow

@user76284 researchgate.net/publication/…

I can't believe I see people walking around in track jackets

I'm just really shocked

CaptainAmerica: In San Diego, people put on winter coats when it's below 65º :P

Lol, 65 degrees is summer weather up here

Here it means we're probably all dead

?

We don't have the same unit

ah, i see

65 degrees celsius is ... kinda hot

LOL, salut @Astyx

XD

Ça va ?

You could do 65º Kelvin instead?

I want to start using kelvin

You'd be quite frozen, CaptainAmerica.

hehe

It's much funnier if you're using kelvin

It's about 290K where I am

If I did that right

I don't know how I'll be able to do that in my head every time someone asks the temp. tho.

I think I'll make a chart and put it in my pocket.

This program I'm doing for my java class isn't doing what it's supposed to. I'm tired of trying to figure it out, so I'm contemplating just sending it in and hoping my teacher doesn't notice.

Hi, from Long time haven't being learn or doing math, I can't troubleshoot a simple High school math problem, any one can help the following? With 4/5 independent probability of solving one of 15 problems correctly, what is the probability that I solved any 10 problems correctly?

Could you post the original statement? I'm having a hard time understanding this.

It makes sense, CaptainAmerica.

if you say so

You have a 4/5 probability of solving any problem correctly. What's the probability that you solved (at least?) 10 problems of 15 correctly?

@Victor: Do you mean PRECISELY 10 or at least 10?

oh, i see

@TedShifrin Precisely 10

OK, so do you know how to do this, @CaptainAmerica?

What's the probability that you do the first 10 correctly and the last 5 incorrectly?

Let me think for a minute.

2/3 I think

but that feels wrong...

it is

thank you

I suddenly realize how rusty I am at probability

I want to figure this out though.

Ignore what I'm about to type, then.

Ok

@Victor: So for the first 10 right and last 5 wrong, the probability is $(4/5)^{10}(1/5)^5$, right?

@TedShifrin Does stars and bars involoved, but I don't know how exactly it apply.

No, we don't need those for this.

@TedShifrin I understand, but for any case of 10 it sudden become much more frustrating

No, no. How many different ways can we choose a collection of 10 objects out of a total collection of 15?

Hi @Ted

Hi ssandro

15 C 10

@TedShifrin

OK. So what's the final answer, @Victor?

I'm getting used to the new phone's keyboard, I finally got a new one after mine was stolen a couple of weeks ago

What kind of phone did you get, @Alessandro?

I can't stand texting on my phone.

A xiaomi, like every other phone I owned in the last 5 or so years, I quite like them

Wow, I've never even heard of that.

I think I have an idea

on how to do it

I'm still an Apple fan, even though my stock is crashing through hell.

ew, apple

I got it, many thanks, But if we want it more rigorously, why does n C r times such number always smaller than 1

Watch out, CaptainAmerica. I've owned Macs since 1988.

@TedShifrin

Also I flew back to Italy for christmas holidays today

Great question, @Victor.

oh snap, the Shifrin bites back

Welcome home, @Alessandro. Hi to your family :P

I'm not a big apple fan either to be honest

Definitely better than oranges

Well, you folks who hate on Apple can feel free not to talk to me. I abhor Windows in all forms.

Should I type in my guess here or wait until you and Victor finish?

@Daminark What oranges are awesome?

ignores Demonark

@TedShifrin Don't worry, I use linux

@TedShifrin My parents literally refuse to buy apple

An apple a day keeps the doctor away

@Alessandro: When I started doing TeX in 1989, it ran on Macs only ... plus graphics.

However it's also quite expensive

I'm not fond. But yeah as for Apple vs Windows, I haven't used 8 and 10

@TedShifrin Is high school Algebra overkills my question

I'm going to put in my guess unless I'm stopped

It's more expensive but it lasts forever ... And Faux-News watching parents have no respect from me, regardless.

@Victor: Sorry for all this.

@TedShifrin Shoot.

guess is going into the chat...

The key point is that exponentials grow faster than polynomials, so things like $(4/5)^n$ are tiny compared to $n^5$.

No, I don't want to distract people chating otherwise, just answer mw only if you are free, Thanks You

@TedShifrin Is there more elementary way, if not, it is pretty awesome for a simple problem then

0.8^10 * (2/3) = 0.0715...

So if you look at your combinatorial coefficient, it's like $\dfrac{15\times 14\times 13\times 12\times 11}{5\times 4\times 3\times 2\times 1}$.

0.0715 * 10 = 0.715...

^ that's my guess

I have no idea what you're typing, @CaptainAmerica.

Why do you have 2/3?

because no context or because it's wrong

because I think 10 is 2/3 of 15

I should have paid more attention in pre-calc

That's irrelevant, @CaptainAmerica. You need the probability of all 15 things happening.

oh

so 0.8^10 is wrong too

Warning: abstract nonsense. The kernel presheaf is a sheaf because right adjoints commute with limits, so taking the forgetful functor $\mathsf{Sh_X}\to\mathsf{PreSh_X}$ after the kernel is the same as taking the kernel first and the forgetful functor afterward, but for the latter to even make sense the kernel must actually be a sheaf. Does this make sense?

@TedShifrin I guess it is all due to my lack of attention to these queestion, I feel very pleased, Appreciate that

Sheaves are a spook.

@Victor: So you have $(4/5)^{10}(1/5)^5$ times the numerator, so you're multiplying by 15 fractions when the numerator is a product of only 5 integers. The fractions win out.

I bought a Mac for college because I saw there were 3 brands that seemed to be associated with education: Dell, Lenovo, and Apple. And I didn't find any Dell or Lenovo laptop that was simultaneously powerful (at least 2.5GHz processor just in case), had good battery life, and wasn't a brick

so 0.8^10 is right

It's a factor of the answer, @CaptainAmerica. It's not "right."

I'm like 1/4 right

shrug

i'm going to figure out the rest

I have a lenovo laptop, it's kinda unwieldy and heavy, but has been running flawlessly for at least 5 years now and there are no signs it's going to stop anytime soon

@Alessandro Man I seriously endorse Lenovo

I'd endorse Dell or Lenovo for good laptops---the one I have now is a pretty darn decent Dell touch-screen I was able to pick up for around 500 dollars.

Our department had a lot of Dell clunkers, @Fargle.

I'm probably gonna go with a different setup for grad school. Since I'll have an apartment I might try for a desktop at home and aim less for power in a laptop

@TedShifrin Hmm. Your mileage may vary, I guess.

@Daminark Lenovo thinkpads are the dream

In 30 years I've had 5 desktop Macs or so, and in all cases but one passed on the one I replaced to family or friends. Several of those are still running fine.

And my demands of this computer aren't too great---I just need something that can do simple Mathematica programs, Internet browsing, and games from 2008.

Hmm whatever happened to @Rudi

My 500-page textbook typesets in about a half minute on my computer now (including the graphics). I love it.

Yeah if I don't go for Mac I'm probably going for Thinkpad. The main problem I had with Thinkpad at the beginning was that the powerful ones were usually bricks with 4 hours of battery. At the time I felt there was a high probability that I'd be doing something that needed a lot of power

Wow, not bad.