7:00 PM
looks like multinomial theorem after all

@Gigili I don't even have a pillow... I sleep on a pile of pants. #gradschool

You can afford pants in grad school? Must be a generous fellowship.
2

handy-downs, obviously

@HenryT.Horton OK, good for you. But don't expect to be easily forgiven for bad behavior.

They are actually hand-downs... I sleep on a pile of someone else's old pants

7:12 PM
This is interesting. Never seen someone called out in the title before.

@DylanMoreland Wonder if it produces a ping?

Doubtful :)

Happy day! My reputation has just reached exactly $6^5$.

@MarkDominus Up to $6^{6^6}$?

I'm still working on $3^{3^3}$!

7:21 PM
$5^5$ would be nice :(

user19161
@JonasTeuwen It's so hot in Netherlands now? Holy monkey!

@JasperLoy In my house.

@JasperLoy The Netherlands.

user19161
@JonasTeuwen I thought Europe would be much colder than that. It goes up to 32 degrees here often.

Ah, Jasper. You probably already have this picture framed on your bedstand but I thought I'd show it to you

7:24 PM
I think I need to vomit. BRB.
2

user19161
@HenryT.Horton What? Anyway, just to clarify, I am male and heterosexual.

Could we talk about something (anything!) quickly to make that scroll off the page?

Calm down broseph.

Like what?
Umm.

Maths?

7:28 PM
I think we should talk about ... yes math.

Or those meaty Bieber biceps.

Ugh.

I don't care what I am or what people think I am. I am... me? Not so profound, I know. 8-).

user19161
@HenryT.Horton They aren't very big. Mine are bigger.

@JonasTeuwen You are me?
I'm so confused.

user19161
7:31 PM
@JonasTeuwen Tautology! A=A.

@Gigili Yep.

I am John ... and I am nothing :)

There, it's gone. Mission accomplished.

user19161
@OldJohn No, you are Old.

@JasperLoy Thank you :)

user19161
7:33 PM
Anyway @jonas if you are not feeling well now, you should lie down in bed...

@JasperLoy I'll make some coffee.

user19161
@JonasTeuwen Hmm, then you must be lying wrongly. You need pillows of the right height and softness bro!

I have a natural Sidamo.

@BillDubuque Hi Bill, can you have a look at this please? Thanks.

user19161
@JonasTeuwen OK. Anyway I can only use a latex pillow for the head. Other materials don't provide enough support.

7:39 PM

user19161
@JonasTeuwen I don't know. But cotton pillows are not good. And I even tried the very expensive type that changes shape to fit your head. But I realized shape is not important at all.

@JasperLoy It holds too much moisture?

user19161

@JasperLoy The cotton pillow 8-)).

user19161
@JonasTeuwen No, it sinks too easily, while latex does not. It has to be high enough yet not hard.

7:43 PM
@JasperLoy Mm... I usually pass out in 2 minutes when I put my head on the bed 8-).

user19161
@JonasTeuwen That's good!

I just explained a whole question by posting over a million comments on someone else's answer and something meh happened.

user19161
@Gigili You might as well post another answer.

@JasperLoy Well, I posted but I think the OP didn't notice someone else other than the answerer was answering his questions or something weird like that.

user19161
@Gigili OK, then have a beer!

8:03 PM
@Gigili Relax!

user19161
@JonasTeuwen I have begun to parrot you by telling others to have a beer.

@JasperLoy It is a synonym for "relax". 8-).

user19161
@JonasTeuwen Though I must say, I really hate beer. I like red wine. :-)

@JasperLoy Then have some red wine... But maybe the beer there is just shit.

Is there something I'm not getting here? The math written looks awfully familiar to me, in the context of the eigenvalue approach to RH, so I'm not sure what's up.

8:07 PM
I need many beers. So many beers.

hands Ed a beer

takes beer That'll be a good start...

user19161
@anon He needs many beers.

somanibeers?
He's not here right now. Sorry.

user19161
@EdGorcenski I give you many-1 beers. So now you have many beers altogether.

8:09 PM
@EdGorcenski Plenty of beers at my place, if you are ever in the neighbourhood...

user19161
@JonasTeuwen It's neighbourhood if you use BrE.

I suppose I am technically within a neighborhood of you, for sufficiently large $\epsilon$

@EdGorcenski Yea, up to you if you think the $\epsilon$ is worth it 8-).

So, on-topic question for once.

And if the many as in your request is satisfied the question is: will the metric be the same to return?

user19161
8:15 PM
Also, many could be an infinite cardinal, in which case many=many-1.

I am taking an intro analysis class this upcoming fall, and the instructor is using Rudin's book. I have taken an analysis class before, about 5 years ago, did OK, and don't remember a damn thing.

subtraction of cardinals is well-defined?

user19161
@EdGorcenski Which Rudin book?

I guess it is when one's infinite and the other ain't.

Principles of Analysis

user19161
8:16 PM
@anon Sorry, I may be just BSing.

user19161
@EdGorcenski So what's the problem?

The class I am taking has the following course description: "The basic topology of Euclidean spaces; continuity, and differentiation of functions of a single variable; Riemann-Stieltjes integration; and convergence of sequences and series."

Do you think that the course will be sufficiently self-contained, as in won't require a whole lot of pre-requisite knowledge, other than general proof strategy?

user19161
@EdGorcenski Yes I think so.

Alright. I've read that the Rudin book is not a good introductory book, and I am beyond the introductory level, but damn if I don't remember a single thing from the class

user19161
@EdGorcenski When people say something is good or bad, that is not well-defined and must be interpreted in context.

8:19 PM
@EdGorcenski Mm, will be hard but you will probably be okay. All depends on the amount you desire to spend on it.

user19161
@EdGorcenski If you know about proofs then Rudin is an excellent book.

The book is okay. Just need some motivation (most important).

user19161
The harder the better. After all, why are you taking math if you don't crave for intellectual stuff?

Very true. I am half expecting that the class will be too simple; I am also half expecting it will be too hard. I no longer know what to expect.

user19161
@EdGorcenski That's good. It's exciting that way...

8:21 PM
The university that I am taking the course at has very strange course numbering schemes; technically, the class is coded as a graduate level class. In practice, however, it is almost exclusively taken by undergraduates.

@EdGorcenski Stop expecting and do your work. Do it well too.

user19161
Work = Force times distance. One has to put in effort and has to move in the right direction too.

Oh, there will be plenty of work to be done soon enough.

user19161
8:51 PM
@jonas Don't sleep too late, see you!

@JasperLoy Bye!

Aw man, I just wrote a detailed answer to a question thinking it was new, but then realized it was just a bumped question that will just fade into history again =(

9:07 PM
@EdGorcenski All questions fade into history :) ... as do we ...

9:47 PM
@BillDubuque Thanks for the answer to the Q about congruences, I think I have found enough evidence in Disq.Arith. to convince me that I haven't totally mis-remembered :)

Is the study of p-adic numbers a part of a branch of mathematics?
like number theory, algebra or smthing?

Mostly intersects with number theory and algebra

@ChuckFernández Also intersects with analysis - I am currently reading a book on p-adic analysis

if I wanted to buy a book that teaches me the basics of the area, what books should i be considering?

@ChuckFernández there are loads of books with a chapter or two on it - and there are some good online (free) lecture notes

9:59 PM
i want to buy one so people who go in my room think im smart

@ChuckFernández That is a stupid reason for buying a book!

Do yu know a good one?

That's a wonderful reason to buy a book!

@ChuckFernández much cheaper to just buy a couple dry-erase boards.

I dunno, do you think lawyers ever actually read all those books in their offices?

10:02 PM
certainly not. but there's a difference between read and use.

the white boards make you look like you are obsessed with math. Books make you look cool and smart at the same time

I feel really pleased with myself - I "solved" some things about p-adic numbers while I was out hill-walking today :)

I have topology without tears on paper
it takes up a lot of space
so which one of the books you mentioned can be obtained for free?

And I recently thought that the best account of p-adics from the point of view of explaining why they are useful in number theory is in this: amazon.co.uk/…

user19161
10:11 PM
@OldJohn Yes, that guy's notes are very good...

This looks good
thanks

@JasperLoy Indeed

Have any of you been to an IMO or national equivalent?

@ChuckFernández No, I entered once when I was at school (not very successfully), but I was at university with a guy who won (back in about 1970)

gold medal?
was his name grigori perelman?

10:16 PM
@ChuckFernández No - this guy: en.wikipedia.org/wiki/Bernard_Silverman

imo-official.org/participant_r.aspx?id=10185 hes really good. He scored number 4

@ChuckFernández Seriously?

nope srry it wasnt him
he id edit it however
did*
the person who wrote it was Nichola Beale
Nicholas*

@ChuckFernández He certainly picked stuff up a lot quicker than I did at Uni - but he was a good friend

Japan got a very bad result in the 2012 IMO

10:23 PM
@OldJohn When is the last time you saw him?
@ChuckFernández NL did very well!

@JonasTeuwen it was 53 of 100
I want to go the the IMO in 2013

@JonasTeuwen Several years ago - I was in email and phone contact with him until about a year or so ago - he is now a chief scientific advisor to the UK government, and I don't think he has time to talk to little people like me anymore

@OldJohn Hmm, is he someone that wouldn't want to talk to "little people"?

@JonasTeuwen oh i thought you mean new zealand

10:27 PM
@OldJohn The scientific advisor also needs friends :-).

@JonasTeuwen No - he is just so ridiculously busy, I think

Okay. Well, he will not be the scientific advisor forever.

@JonasTeuwen true!

I have a lot of trouble with the geometry questions
any tips?

@ChuckFernández what sort of geometry?

10:29 PM
can i give you an example question?

@ChuckFernández Fire away - we may or may not be able to help

Let $ABC$ be an acute triangle let $BE$ and $CF$ be heights of the triangle ($E$ is on $AC$ and $F$ is on $AB$). two circles pass through F and A and are tangent to line $BC$ in points $P$ and $Q$ such that $B$ is between $C$ and $Q$. Prove Lines $PE$ and $QF$ intersect on the circuncircle of triangle $AEF$.

@anon Hey

yo

Can I ask you something about the universal property of the union of two topological spaces?
So I want to show that $X \cup Y$ satisfies that universal property
@anon Given $f : X \rightarrow T$ and $g : Y \to T$ such that $f$ and $g$ agree on $X \cap Y$
then there exists a unique $h : X \cup Y \to T$ such that the restriction of $h$ to $X$ and $Y$ is $f$ and $g$ respectively @anon
The topology on $X \cup Y$ is as follows:
@anon For convenience we call $Z = X \cup Y$

10:43 PM
the topology on the union I imagine is generated by $\tau_1\cup\tau_2$ as a subbase

Then $W$ is open in $Z$ if $W \cap X \subset X$ is open in $X$ and $W \cap Y\subseteq Y$ is open in $Y$

My girlfriend wears a Z-\cup

@HenryT.Horton There is only upto cup E I believe :D
@anon Now I believe in this topology $X$ and $Y$ are open in $Z$

im 12 and what is this

I think it should be obvious that there is only one choice for $h$
@HenryT.Horton Because we want an appropriate diagram to commute

10:46 PM
Don't you EVER ping me without my permission

@anon So the only choice for $h(x)$ is

@HenryT.Horton @HenryT.Horton @HenryT.Horton @HenryT.Horton @HenryT.Horton

$$h(x) = \begin{cases} f(x), &x \in X \\ g(x), &x \in Y \end{cases}$$
@anon Now to prove the continuity of $h$ I wanna apply the pasting lemma

pasting lemma?

but the problem is that $X$ and $Y$ are not necessarily closed in $Z$

10:47 PM
@anon I'm cool with you homie, we ran into each other at a Dr. John's before

:-)

@HenryT.Horton Dr John - someone talking about me???

So we can't assume $X\cap Y$ closed in $X$ and $Y$.

uh yes I think

10:48 PM
@OldJohn Yeah, remember the line of sex shops you started in Omaha back in the day?

@anon Oh I forgot to say that the subspace topology of $X \cap Y \subset X$ and $X \cap Y \subset Y$ are the same

@anon Ah yes- I forget sometimes :(

@BenjaLim Are you talking about the disjoint union?

@DylanMoreland No not yet just union.

If $S\subset T$ is open, then its inverse image under $h$ is the union of its inverse image under $f$ and $g$ respectively...

10:50 PM
I don't understand, then. Are $X$ and $Y$ in some ambient topological space?

no not necessarily. @DylanMoreland
@anon yes?

well, they end up being in the ambient space $X\cup Y$..

Then how are you talking about an intersection of the two?

@DylanMoreland hmmmm
@DylanMoreland Well you can look at the intersection when you're inside $X \cup Y$, why not?

@BenjaLim the inverse images of an open set under $f$ and $g$ are open if these maps are both continuous, no?

10:52 PM
Oh crap I am stupid:
Take any $V$ open in $T$

takin a nap now

by definition of $h$
we have $h^{-1}(V) = f^{-1}(V) \cup g^{-1}(V)$
@anon wait don't I need to minus of some intersection or something like that?

@HenryT.Horton ok

user19161

10:56 PM
I'm also dead now - g'night folks

user19161
@HenryT.Horton I will ping you all I like.

user19161
@OldJohn Ding ding ding!

user19161
@HenryT.Horton I seriously doubt that.

@JasperLoy :)

Yeah, because I don't know any girls

user19161
10:58 PM
@HenryT.Horton In fact, I thought you might have a boyfriend instead.

@HenryT.Horton Actuallly my problem is trivial.......

I just have those JB posters because I think he is the perfect example of male physique and having the pictures around reminds me of what I want to be.

user19161
@HenryT.Horton OK. Though I think for the male physique you should go for Taylor Lautner.

user19161
@ben How is the first week of school?

11:02 PM
But I don't understand how some people who have never seen the definition of a topological space are taking AT
And this one guy was like
Ahh I'll borrow some notes and read up
and I'm like you don't get it
you need to internalise the ideas
@JasperLoy I have AT in one hour :D

user19161
@BenjaLim I agree with you. Slow and steady wins the race. Those people who take too advanced courses too soon will run out of ideas by the time they finish their undergrad.

Exactly.

Man this song is pretty bad

@JasperLoy I don't claim to have taken a course in topology.
@HenryT.Horton what song?

user19161
@BenjaLim Oh. What did you study general topology from?

11:05 PM

@JasperLoy munkres
@HenryT.Horton I feel extremely insulted.

user19161
@BenjaLim I dislike Munkres. I find it too long-winded.

@JasperLoy But at least I know the definition of a topological space :D

Well I hope you're joking Benja$\varprojlim$

@HenryT.Horton Hmmm

user19161
11:06 PM
@henry Besides being a JB fan, I am also a TL fan in case you dunno.

I am not sure if $h^{-1}(V) = f^{-1}(V) \cup g^{-1}(V)$

user19161
@BenjaLim One can cover all essential general topology by himself in three days I think.

@JasperLoy No impossible.

user19161
@BenjaLim Note "essential".

essential?

user19161
11:08 PM
That is to say not too much.

There's hope after all

user19161
Hey @peter!

@JasperLoy All these people I think just wanna use them as badges

@JasperLoy $\sup$?

11:10 PM
to say to other people on the outside that I'm doing all this advanced stuff
@JasperLoy Surely I would like to tell people I am studying étale cohomology
but I'm not .
@PeterTamaroff Como estas?

@BenjaLim Bien, bien. I took a day off math today.

user19161
@BenjaLim Etale? I only know cocktail!

@BenjaLim What do you mean?

What's wrong with you?

was the part about women sarcasm?

11:11 PM
What did he write? I missed it!

user19161
I only know what a jackfruit is.

@BenjaLim Whaaaa....?

@PeterTamaroff I mean you can go boast about doing advanced stuff to other people...

@BenjaLim I talked with my sister about cardinals, denumarable sets, the infinite, Cantor's set, topology.

is anyone trying to solve my problem?

11:13 PM
It was pretty dope.

@PeterTamaroff Is she a girl? I wish I knew girls

@BenjaLim She on the other hand told me to read Kant's work.

Let $ABC$ be an acute triangle let $BE$ and $CF$ be heights of the triangle ($E$ is on $AC$ and $F$ is on $AB$). two circles pass through F and A and are tangent to line $BC$ in points $P$ and $Q$ such that $B$ is between $C$ and $Q$. Prove Lines $PE$ and $QF$ intersect on the circuncircle of triangle $AEF$.

user19161
@HenryT.Horton I wish so too, but I have more important matters now.

@JasperLoy What do you even do with your life? You're a blue square

11:14 PM
@ChuckFernández I honestly hate geometry.

me too

user19161
@ChuckFernández Why don't you post on main?

@ChuckFernández Do you like machaca?
I love it so much...........

user19161
@HenryT.Horton Well, I will retain some mystery...

My friend Ricardo sneaked it in from customs

11:15 PM
You mean the food?

yes

Sure, but its not something I eat on a regular basis.

user19161
@BenjaLim Why does one have to sneak in food? It's not drugs right?

@BenjaLim You're obsessed with machaca!

australian customs
extremely strict at the airport

11:16 PM
Its like beef Jerky for men
at first i confused it with escamoles

@ChuckFernández I will go to DF one day.

tell me when you do

Why don't u study analysis at the same time as geometry?
@ChuckFernández Porque no los dos?

I understand analysis, its geometry I dont get

hey chuck norris
I have to go

11:22 PM
c ya

@HenryT.Horton Bye shawty
@PeterTamaroff BYE
Bye all
I have AT now

Stay here
I'll teach you AT

@HenryT.Horton I'm only second year I need to be a good boy and go to class.

second semester was when I stopped going to class

@HenryT.Horton Well I don't know AT and representations of lie algebras so.....

11:24 PM
Because you're always wasting time sitting in class!

ahahahahahah true
@HenryT.Horton How do you study maths?
For me I copy out every single theorem/definition/ etc line by line
the problem is that it's time consuming
and then I get stuck on small things for like hours

I waste all my time and then do it at the last minute :(

seriuosly?

But I learn best when I write expository notes on what I am studying

I try to think of as many and as varied examples as possible.

11:27 PM
@BenjaLim I do something similar. It is time worth!

I should probably do what you two do. I shoot from the hip way too much as it is.

@AlexBecker The problem is that at uni you have to cover a lot of material.
@AlexBecker what do you mean?????????????????????????????????????????????????????

For classes I don't worry about studying at all though

@HenryT.Horton ???????????????????????????????????

@BenjaLim I mean, I take a concept as far as I can before I fully understand it. And so I mess up.

11:29 PM
Classes? Do you have classes?

When I need to prepare the material on my own

Henry T Horton is lying
his real name is will

from good will hunting

I'm a janitor at a college
Sometimes I see a math problem on the board and I just solve it
My best friend is Ben Affleck

11:30 PM
@HenryT.Horton why do you like to troll ?

I don't like anything
But I'm serious about the studying thing

hahahahahaha
@HenryT.Horton your last line was a lot of bullshit

What line

@AlexBecker I need to change the way I do things to be more time efficient

Don't be like me kids
@BenjaLim Did you go to class?

11:37 PM
not yet
@HenryT.Horton you're funny.

Well don't mess up then.

I think this requirement is stupid
and a lot of people that get into the degree show off and stuff
IMHO I think it is completely trivial

Which requirement?

user19161
@jonas How was the coffee just now?

@JasperLoy Good.

user19161
11:49 PM
@JonasTeuwen OK. Still not sleeping yet?

@JasperLoy Na. Pain.

user19161
@HenryT.Horton Will Hunting was one of my usernames...