Number Theory front page... sounds fantastic

maybe if I start thinking enough, they're replace all the set theory questions

@mixedmath Neverrrrr! :-P

hello math chat ;)

Howdy.

Dammit, I'm starting to think it is time to sleep.

oh, what time is it?

5:30am

woah

I have this thing I have to finish two weeks ago.

I got several extensions, but I would really like to get it over with...

lmao

so you're wasting your time on this site instead of doing it?

Which I appreciate btw, since you've answered a few of my questions at least rofl

Well, I'm also reading the paper from which I need to take key points.

Ah, keep up the good work then

Besides, writing intro level answers is zero work after TA'ing such course even once.

If you want to see a waste of time, check the answer I gave to some questions on [axiom-of-choice]

These took quite some time. Often clearing out full days of writing and rewriting.

damn thats dedication to helping people

I can't complain, though. I'm having lots of fun writing those.

Yeah, it's the same reason while I do math at all

I'm glad it helps people, but I more often want to try and explain set theoretic issues to people. This site is a great platform for it, plus some people are genuinely interested.

that's cool.

Also, answering intro level questions is good as I will TA the introductory course in logic and set theory during the next fall semester. So once again, lots of questions similar to the ones being asked here. I consider it a good practice in having refined answers.

What college is that at?

and yeah I know the into ones are easy for a lot of people here

sometimes when I

m bored I browse and look for something I can answer

the only ones I can are already answered perfectly by the time I figure it out

Some university in Israel.

accurate enough as I wouldn

't have known it anyway

Just asked because lots of people from other countries studied in the US as well, so you never know

Well, I did say that the time here is 5:30am

If I'm right the time in California should be around 23:30 or so.

Oh look, the sun is starting to rise...

Yeah, but it is summer, so you could have been with family at home for the summer

and hm nope you

're way off

its 19:45

Well... only four hours.

That's like two decent movies.

well, I think watching two movies is a pretty good amount of time

Nah...

By the way, after some time you should accept the most helpful answer given to a question that you've asked; or edit the question to reflect what is missing from the current answers present.

Oh, alright

I've had plenty of good answers since I've figured out solutions to every question I've asked

I just never want to single one out as best because they are all helpful to me

Well, these things are up to you.

what happens when I select a best answer?

However it is considered somewhat impolite not to accept any answer to your questions. So at some point you will need to accept some answers.

(sorry I

'm pretty new here)

and I keep pressing enter instead of " ' "

lol

Yeah, I'll look the answers over right now and pick best ones

didn't realize it was impolite not to

It's fine to leave some percentage of your questions without an accepted answer.

But once you start accumulating more and more... well, then it becomes impolite.

Heh, well I'm accumulating questions pretty quickly; plus I figure I already look a bit polite for having many more questions asked than questions answered

So, I'll pick best ones now

However, I'm going to let my most recent question sit a bit even though I think I have already fixed the problem just in case I get a great late answer from someone

As I said, it's fine to let it sit for a few days.

Also, there are other ways to prove a union of two countable sets is countable.

These do not adhere to your question, so I did not answer.

Oh, hm if you get some free time I would appreciate it if you could, not show the whole other proof, but tell me the general other approaches (I might even give you a best answer ;) )

What I posted was the only line my mind was taking toward a solution

I'll give it a quick writing.

often however, I'll be somewhat short sited in my proof attempts as I haven't seen many proofs yet

never even taken a class that did any proofs yet tbh

You gotta start somewhere...

and thanks, much obliged

Yeah, I was explaining why I'd appreciate you post it

trying to convince you to do it, but I ended up sending it once you already said you would

:P

Hm.

?

Coming to write, it becomes apparent to me that this might not be a good idea. It relies on possibly more advanced theorems, which I would rather you study properly and not from a post on a website.

In time...

yeah, if it needs theorem's I haven't learned probably wasn't the type of solution intended to help me by the writer of the problem

I'm not sure which theorems you have learned and which you haven't. Either way, it's all the same trick really.

I probably haven't learned anything you would guess is more advanced

NxN is countable? Cantor-Bernstein? If X is not finite, and f:X->N is injective then X is countable?

NxN countable heh actually you could use that now that I've finished the question, it was actually a theorem pretty close after the one I asked

in the notes I'm going through

but I've never heard of Cantor-Bernstein though

nor the last one, though I suspect I could figure that one out

Cantor-Bernstein asserts that if f:X->Y and g:Y->X are both injective then there is a bijection between X and Y.

So it reduces many cases of finding bijections into finding injective functions "from both sides".

Hm, very interesting

hasn't come up in the notes yet, but I haven't read the part of the book the notes are dedicated to yet

I suspect it is probably in there

Relatively constructive as well. There are several proofs, many not very hard.

It is one of the most standard proofs in introductory texts.

Yeah, it'll probably be in there than

I'm going through baby-rudin with notes to go along with it by Terrence Tao

if it's not then I'll try going over it myself outside the text

Yuck. Analysis :-D

not an analysis fan?

Although you're gonna have to fight through a lot of text in those books. That's a good thing.

I'm a set theorist. I was one since the intro course I took in freshman year.

oh, no wonder you answer my questions

2 of them were questions about sets

Although I do not recall answering any of the three questions you have posted.

actually you're right

you were commenting in my most recent one though I believe

I did retag both of them, too.

on my possibly incorrect usage of "countable"

While you did not make an actual mistake, remember that when talking to other mathematicians it is always best to be explicit.

Yeah, I realize I should be as specific as possible in the questions anyway, to make sure I get accurate answers

However, both the text and the notes referred to what I was talking about as countable

so I had no idea

Yeah, a lot of people don't tell you at first - but there's a lot of dissonance in the mathematical lingo.

Which, once again, is a great reason to be explicit.

I wonder why that is

Because at one point someone says "I like this notation/term/definition better". If it's any good - it will catch up, and then we have two factions using two different definitions/terminology/notations.

It takes quite some time for notation to disappear.

Okay, well. It was nice talking to you. I'm going to sleep.

I'll finish this work when I wake up in a couple of hours.

Makes sense, and alright goodnight

Enjoy your studying and whatnot. I hope to answer your questions sometime.

I'll be sure to ask enough that you get to answer at least one ;)

cya

I wonder if I kill conversations or something - whenever I leave, the conversation starts to buzz

I'm back, and it's slower

I'm still here ;)

Aha!

Maybe I'm not so bad then

probably not

although these chats are far more dead than I expected them to be when I got on here

When I first joined, no one was ever on chat. Ever.

Something in the last bit has made people come on more often. I think J.M. and Asaf come on everyday now. I try

but I'm bad at hitting peak hours or something

I think they could be really cool

yeah me too

although I know nothing about math, so I probably couldn't keep up with much chat lmao

as long as theres a few people in here though rather than none

Yepyep!

and maybe you guys are making chat cool by coming in here lmao

;p

lol so whats up?

I'm ruminating over a couple of problems now, not really making much headway with any of the three.

But this has sort of been my life for a bit, so it's no big surprise. MSE is a very pleasant backdrop - or perhaps too convenient to waste time.

Hard to say.

You're at UCLA? Is that right?

yep thats right

I was about to ask if you recognized my name somehow

how is it over there?

then I realized I put it in my profile

& hard to say, I've lived my whole life in so-cal so I don't really have anything to compare it to

However, I can say the professors are nice in general

I like to study on my own a lot and a lot of the time I can just walk into someone's office who works in the field I'm looking at and ask a question

so thats nice

do you go to brown?

(guessing since it says providence in your profile)

I visited there once. I was working with a professor (from Georgia Tech), and he happened to be working on a problem with Terry (not hard, as he does so much). So I went there briefly.

Yepyep! Well, I'm starting in fall.

To be fair, I'm in the process of moving right now.

oh Yeah Terry is pretty cool

he hooked me up with some notes he wrote for an analysis class a long time ago, I've been studying through them recently ( hence my recent surge of questions)

& oh, whered you go undergrad?

Georgia Tech. It's just up the road from where I grew up.

oh should have figured since you said you were working with a professor from g.tech

you know what you wanna study in grad school?

I've been focusing on number theory so far

my undergrad thesis had its roots in number theory, and a little algebra

that's why I applied to Brown in general

oh, browns top notch in number theory?

yepyep, it has one of those reputations anyway

thats good

I don't know if it beats UCLA, to be fair, but I don't know much about rankings in genreral

Terry does have quite a reputation

well, I'm not in grad school anyway

lol :P

but I like Dr. hoffstein at Brown a lot, so there's that

you're a math major, though?

but I'd probably lean toward applying to schools with cool people over anything

& yes I am

just finished my first year of undergrad

I hope that you know more about math then than I did

I was very clueless until my 3rd year, I think

lol unlikely, I don't know much

but at least if you didn't know much, thats good hope for grad school in the future ;)

alright man, I'm outta here

cya

Good night. Nice chat.

test, anyone here?

yepyep!

lol, i thought no one uses this actually

Often, that's true.

just curious, what kind of number theory are you looking into?

I work with a lot of analytic, and my undergrad thesis was related to finding primes quickly

But I'm still learning a lot, so it's fluid

Yeah, it's only pretty recently that conversation actually picked up.

i see

hi el'endia

Hiya!

Hello Soarer.

Hello mixedmath! :P

El'endia, I remember you once asked about a variant of Pascal's triangle, made only of primes. Did you play much with that?

mixedmath, from where are you learning analytic stuff? I would like to know more about it, but not too sure what are the key questions in the field

I was tempted, but I never really came back to it.

My first text in the subject was Davenport's Multiplicative Number Theory

@mixedmath: I didn't really play much with that particular thing. I tend to wander around...find something, go "ooo...I wonder...", investigate it a bit, maybe post something about it here, and then I wander off... :P

I should probably revisit it, too, because I went off on an Additive combinatorics tangent

@El'endia I understand completely! I do the same thing very often.

I'm a mathematician that uses computers, so that was a neat thing to investigate...

You have any interest in recreational mathematics by the way?

@mixedmath, any suggestion what to do next? I went over davenport basically, though I should really reread the last 6-7 sections again

Absolutely! And it occupies a good spot in my heart.

Wait...who are you replying to? :P

@Soarer After Davenport, I took a class on it, and there was no text. So it's hard for me to say. I know that there are lots of different directions to go in.

@El'endi - sorry, that was to you - I like recreational math.

hehe

Have you ever read Martin Gardner's Colossal Book of Mathematics?

Or Godel, Escher, Bach?

I've read a lot of Gardner. That doesn't happen to be a collection of his work or anything, does it?

I have GEB, but I haven't read it yet. I'm waiting for a long period of time.

I thought that was the case - then I've likely read most of the works in it. I love Gardner. When I was interested in math but hadn't yet figured out what it consisted of, I read him all the time.

Then when I learned more, I thought he was fun.

And, given the choice, I would read more of him now.

Hah, very nice.

@Soarer I have since referred to Tenenbaun's Analytic and Probabilistic NT, and Vaughan's Hardy-Littlewood Method

Ooo! mixedmath, do you know about Project Euler?

I've heard of it. Are you a big participant in it?

They come up with a problem every week or so, right?

...define "big". :P

Yes, that is correct.

They're on "summer" break now though.

I had to take a Java-programming class at Tech, and I did some of those to entertain myself sometime

oh, that's too bad

I suppose I could have caught up a little

lol

I'm currently at 107 solved.

@mixedmath, I see. Thanks

I'll have a look. Thanks for that.

You're welcome. :)

Good night all.

night

Hello

@WillieWong: What's up?