Mathematics - 2015-01-12 (page 2 of 4)

robjohn

14:18

@Chris'ssis sure! Thanks

Chris's sis

@robjohn hehe, thank you very much! :-)

user153330

greetings

@Chris'ssis oh nice idea lol : P

Chris's sis

@user153330 Hi. I mean it's going to be like a caricature, not a part from the main proof. The reader needs a proper frame of mind before reading some stuff. :-)

When I'm happy, I laugh, I do things easier. ;)

Jasper Loy

I have nothing to be happy about.

user153330

@JasperLoy eating & sleeping can make you very happy

Jasper Loy

14:27

@user153330 They can't make me happy.

user153330

@Chris'ssis hi! glad you're happy! : ) yeah i know like in the introduction of a chapter you do a special drawing

Jasper Loy

Hi @TedShifrin

Chris's sis

@JasperLoy It's important your attitude. NEVER GIVE UP! FIGHT AND DEFEAT THE IMPOSSIBLE IF NEEDED! :-)

Jasper Loy

@Chris'ssis OK.

Ted Shifrin

@iwriteonbananas: No, not ubiquitous ... Just around enough to keep you paranoid :) ... I do not have solutions written out for the exams, sorry. If there's a particular point you want to ask about, you should ask — if I can't answer, I'm sure Mike (oh, no, he hates point-set topology) or someone else will :P

hi @Jasper!

Chris's sis

14:30

@user153330 Exactly :-)

user153330

hi @TedShifrin good morning

Ted Shifrin

hi @user153330 and hi, mr eyeglasses :D

Really cool Putnam problem for you guys from some number of years ago (I'm assigning part as an extra credit problem to my multivariable class). Suppose $f\colon\Bbb R^2\to\Bbb R$ is continuous and $\int_R fdA=0$ for every rectangle $R$ with area $1$ (and sides parallel to the axes). Prove that the average value of $f$ on the $4$ sides of each such rectangle is the same. ... Then deduce $f=0$ everywhere. :P

Jasper Loy

Putnam problems Put you on Numb mode.

Ted Shifrin

But for those of us who like multivariable analysis, this is a real cool question. It's not typical Putnam weird stuff.

Heya @Huy. You might like what I just posted above. :)

Oh, I need to clarify. The average value of $f$ on each of the $4$ sides of any such rectangle will be the same (not necessarily the same for different rectangles).

Huy

@TedShifrin: I'm a bit busy with GR currently, I'm afraid. It's so much. =_=

Ted Shifrin

14:40

Yeah, no joke :)

Jasper Loy

Is Stephen Hawking really smart, or is he famous just because he is paralysed?

Ted Shifrin

To the best of my knowledge, @Jasper, absolutely the former.

Jasper Loy

Is John Nash really smart, or is he famous just because he is crazy?

user153330

To the best of my knowledge, @Jasper, absolutely the former.

Ted Shifrin

Yes. His early work was phenomenal. I don't think he did much after the 60s ... But he's still renowned for his Nash Embedding Theorem and his thesis work on game theory [Nash equilibrium] (which I do not know personally).

@Jasper: Is this going to be an inductive list? :D

Jasper Loy

14:44

@TedShifrin Nope, my list ends. When I think about how bad my problems are, I try to think about these two fellows to give myself some consolation.

Huy

@TedShifrin: The weird thing about GR is: Usually, when going through some topic in physics, I struggle understanding the point of certain formulae but it becomes a bit more understandable as soon as I see examples. In GR, the examples somewhat confuse me even more.

user153330

@Huy work out more examples and read more papers

Ted Shifrin

I haven't learned enough GR to be of any use, @Huy, but there is are a lot of layers to it.

Huy

@user153330: I wish I had so much free time to read papers.

user153330

@Huy i hope you have enough free time

Ted Shifrin

14:46

Don't the good texts do examples reasonably well, @Huy? I have not studied the books carefully, but I looked at Misner, Thorne, Wheeler and Sachs & Wu when I was in grad school.

We don't need to be pedantic about correcting non-native speakers' English, guys.

Huy

@TedShifrin: I'm going through the lecture notes from my lecture still, because after all that will be what is tested. I'll go through Caroll's famous lecture notes after the exam.

Ted Shifrin

Although I have done so to @Pedro once or twice :D

OK, I don't know about Carroll.

Sometimes lecturers improve exposition; sometimes they don't. I hope your lecturer is a good one, @Huy.

Huy

@TedShifrin: He lectured QM last year, when I took it, and I rather liked his very mathematical approach of it. He did the same with GR, but I have a lot more trouble coping with it now, probably because the subject is so much more difficult (at this level).

@TedShifrin: I remember some professor suggesting me to take mechanics before QM, and I did because he told me so. Actually, mechanics was much more useful for GR so far, I hardly needed it in QM (just for intuition, a bit).

Samuel Yusim

the euclidean algorithm is a much more commonly used tool than I ever thought it would be when I first learned it

Huy

@SamuelYusim: I haven't used it ever since coming across it in abstract algebra. :P

Samuel Yusim

14:52

same for partial fractions, to a lesser extent

user153330

@SamuelYusim iff you're doing integrals

Ted Shifrin

You can prove or calculate partial fractions decompositions USING the Euclidean algorithm!!!

Samuel Yusim

@Huy, I'm taking a course in fields and galois theory this term so that explains that

also @user153330, they matter when you're dealing with generating functions which is what I've been using them for lately

Jasper Loy

@TedShifrin Thanks for using CAPS and triple exclamation!!!

Ted Shifrin

LOL, I didn't want it to be ignored, @Jasper. Perhaps I'll get removed for yelling :)

Huy

14:55

http://www.homegate.ch/www/ftp/hgoa/doc/201410071030515088289.pdf
Who on earth designs a flat where one has to walk THROUGH the bathroom in order to reach the shower/toilet???

Ted Shifrin

in the US that's not at all unusual, since the toilet is not a separate room the way it is in Europe :)

Huy

@TedShifrin: It is not very often seperate, at least in Switzerland. But I've never seen a floor plan where you'd have to pass the whole bathroom to get to the toilet. Toilet and shower or even toilet and bath being in the same room is rather common.

Jasper Loy

My toilet bowl and shower are in the same room.

@Huy Separate.

Ted Shifrin

OK, time for me to work ... Bubye.

Samuel Yusim

when I was in london the hotel had the shower and sink in the same room as the beds and such, and put the toilet in its own room

Huy

14:57

Have fun.

Samuel Yusim

that was messed up, honestly

Huy

@SamuelYusim: I've seen flats with the shower in the kitchen, or almost.

Jasper Loy

@SamuelYusim Cool.

Samuel Yusim

not cool if you're on a high school trip sharing a room with 3 other dudes

Jasper Loy

It's good to see one another naked.

Huy

15:02

@SamuelYusim: Maybe if you're a girl it's a problem, but I don't think as a male it should be.

Samuel Yusim

I dunno if it's different where you guys are from but that's just not something that happens here.

Jasper Loy

@Huy It should not be a problem for boys and girls sharing the same room. People should be allowed to walk naked on earth.

Huy

@SamuelYusim: It doesn't really happen here either, but I wouldn't consider it a big problem if it did in some hostel.

@SamuelYusim: Are you sure you were in a hotel though, and not in some cheap hostel?

Samuel Yusim

yeah it was a hotel

but I can guarantee that it was cheap regardless

Huy

@SamuelYusim: Do you remember its name?

Samuel Yusim

15:06

nope. I don't think I even knew the name when I was there.

Huy

@SamuelYusim: The 3 other dudes were some of your classmates or so though?

Samuel Yusim

yeah

Huy

Then it's really not that bad. I thought they were 3 complete strangers.

Samuel Yusim

honestly I might rather have strangers see me naked than friends

Jasper Loy

We should organise an MSE shower. Everyone strips and showers together.

Huy

15:08

@JasperLoy: Sorry, I charge for that.

@SamuelYusim: Is it not usual to shower after PE in your country?

Samuel Yusim

nobody took showers after gym class, no

I'm from canada, by the way

Jasper Loy

@SamuelYusim That's why school kids mostly stink, lol.

Huy

@SamuelYusim: It's very common here to do, so maybe that's why I don't find it as repelling as you do.

Samuel Yusim

yeah, that makes sense

Jasper Loy

In the army where I am we all see each other naked.

Huy

15:11

@JasperLoy: True though, when some kids don't shower after PE, the classroom stinks really bad after class. =_=

Jasper Loy

@Huy Stinks of Swiss cheese, LOL.

Huy

@JasperLoy: At least.

Jasper Loy

Sweaty men smell like cheese and sweaty women smell like onions, a study said.

Pedro Tamaroff

@TedShifrin What have you done now?

Jasper Loy

@PedroTamaroff Hello Pedro. I was not angry with you, in case you think I am.

@huy Change your pic to a recent one.

Ted Shifrin

15:16

You paged me, Sir @Pedro? :D

Jasper Loy

Hi Madam @ted.

Pedro Tamaroff

@TedShifrin You paged me first.

Huy

@JasperLoy: That is a very recent one, relatively spoken.

Jasper Loy

@Huy That's what they teach you in GR.

Ted Shifrin

Yes, @Pedro, I was telling people not to correct non-native speakers' English. But I admitted to having corrected yours :P

Huy

15:17

@JasperLoy: I've studied it well.

Ted Shifrin

How're you doing, @Pedro? Oh, you might like that problem I posed above.

Pedro Tamaroff

@TedShifrin Hehehe. But that's fine.

Ted Shifrin

Oh, Pete told me he voted for you, @Pedro :D

Pedro Tamaroff

@TedShifrin Ah! Tell him it's nice to hear from him. =)

Ted Shifrin

LOL, I did mention you guys were complaining about his problem. It was only slightly mis-stated :P

Pedro Tamaroff

15:20

@TedShifrin His problem?

@TedShifrin Reading.

Ted Shifrin

that point-set topology stuff that Kaj posted ...

Miguelgondu

@TedShifrin After reading such problems I feel dumb as hell. Perhaps it's because I'm just starting.

Mike Miller

That problem was from a year I took it I think.

Pedro Tamaroff

@Miguelgondu Hell is not dumb.

Ted Shifrin

Yes, @Mike, it should have been one of your years. It's a very cool problem.

Miguelgondu

15:21

@PedroTamaroff How'd you know?

Pedro Tamaroff

@TedShifrin Is it genuinely difficult? Doesn't feel like it.

Ted Shifrin

@Miguelgondo: Typically I can do only a few Putnam problems each year if I try hard. But this problem fits me better :)

Pedro Tamaroff

@Miguelgondu It is known.

Mike Miller

You're probably ignoring the area 1 condition, @Pedro

Ted Shifrin

No, the first part is an appropriate challenge problem for my students. The deduction that $f=0$ everywhere is a bit sneaky, and I have to rethink it ...

Jasper Loy

15:22

@TedShifrin I wonder if say Tao can do all the Putnam problems...

Ted Shifrin

I would assume so, @Jasper.

Pedro Tamaroff

@MikeMiller No, I read it alright.

Miguelgondu

@PedroTamaroff by whom?, can I see the demonstration?

Ted Shifrin

LOL @Pedro: A fine mess you've started.

Pedro Tamaroff

@Miguelgondu No. It's axiomatic.

Jasper Loy

15:23

@TedShifrin I wish that my mental illness transforms my brain, so that after I recover I can also do all Putnam problems, lol.

Miguelgondu

@PedroTamaroff In ZFC?, didn't know that.

Ted Shifrin

Well, @Jasper, you can dream :)

Jasper Loy

@Miguelgondu I just had KFC for dinner.

Ted Shifrin

smacks @Jasper

That stuff is terrible for you, BTW.

Mike Miller

If that's what you want to do, @Jasper.

Jasper Loy

15:25

@TedShifrin Anyway, although Tao can do all Putnam problems, he can't solve RH because he is not crazy. But there is hope for me because I am crazy, lol.

Huy

KFC is the only thing I miss in Switzerland, really.

Ted Shifrin

Doesn't exactly fit your obsession with Jack Lee, @Jasper :D

Mike Miller

Personally, I liked the Putnam precisely because my school threw money at me for it, and not because of the problems. I found the problems mostly uninteresting.

Jasper Loy

@MikeMiller They rewarded you with money?

Oracle

@JasperLoy Then start working on it.

Ted Shifrin

15:25

You're more combinatorially-minded than I am, @Mike, but it's never fit my strengths, what few those are.

Jasper Loy

@Oracle Hi, I am reading your blog now.

Oracle

Mission successful!

Mike Miller

@Jasper There was an award for the top scorer (or more, if there's a near tie). This wasn't hard to get as very few people at my school took it.

Pedro Tamaroff

@Miguelgondu Now you do!

Jasper Loy

You know, if you know who is reading your blog at that time, you can tell his location from your blog statistics.

Ted Shifrin

15:27

If I had known that, @Mike, I definitely would have made you pay for lunch! :D

Miguelgondu

@PedroTamaroff I'll invent my own axiomatic system, with blackjack and hookers.

Pedro Tamaroff

@Miguelgondu That sounds good.

Mike Miller

@Ted Be reasonable; I spent it all within a week!

Oracle

@JasperLoy I know where you are from. I don't require any Wordpress to know that.

Jasper Loy

@Oracle How do you know? You read the transcript from long ago?

Miguelgondu

15:28

@PedroTamaroff A bit of a personal question, how's studying in Argentina?

Ted Shifrin

I'm realizing that rent will probably take the majority of my retirement allotment, @Mike. Maybe moving to an expensive city was a dumb idea :D

Oracle

Pedro Tamaroff

@Miguelgondu Well, it's free.

Oracle

@JasperLoy An analogy.

Jasper Loy

@Oracle OK. There are a few people in the world with my name, and a few people in my location with my name.

Oracle

15:30

Come on, I'm THE Oracle.

Jasper Loy

@Oracle Are you in the same location as I am?

Oracle

Of course, no.

Ted Shifrin

I love Calvin and Hobbes.

Jasper Loy

I love math and women.

Ted Shifrin

Um, ... OK.

Jasper Loy

15:31

I am surprised nobody flagged me yet, lol.

Oracle

@JasperLoy Then why aren't you working on it?

Jasper Loy

@Oracle Well, if you have been following my news, you know why.

Oracle

Of course, I know why. But you should start working.

Mike Miller

@Ted After spending a bunch of time on handlebody diagrams, I'm sick of my 3D brain.

Ted Shifrin

LOL @Mike. You're ready to move up to 4D, of course.

Mike Miller

15:34

Yes, and that's just enough dimensions for me.

Jasper Loy

I just learnt that there is no Windows 9.

Although my condition now is not good, I have stopped feeling dizzy when I climb the stairs. Also, my hair seems to be starting to grow back a little.

Oracle

@JasperLoy That's good news.

Jasper Loy

@Oracle Well, not really.

Ted Shifrin

@Mike: Here you go.

Oracle

@JasperLoy Why?

Jasper Loy

15:40

@Oracle Good news is the day I get well and go to grad school. The other things don't matter. But I get your point, but I just wanna say my point too.

Don Larynx

Hi @Jasper @Ted

Jasper Loy

@DonLarynx Hi. Have you been playing soccer?

Ted Shifrin

hi @Don

Don Larynx

@Jasper I sprained my ankle on Saturday and I have to recover.

@Ted I dropped topology.

Oracle

@JasperLoy What prevents you from going to grad school?

Jasper Loy

15:41

@DonLarynx Just chop it off, lol.

@Oracle I need to get well first. Otherwise, I cannot function optimally.

Ted Shifrin

Ah, @Don. If you haven't already taken a serious real analysis class, topology would be inappropriate. I haven't kept a scorecard of your background :)

Pedro Tamaroff

@TedShifrin When you say the average on each side, you mean to keep the orientation?

Oracle

@JasperLoy In the meanwhile you could start studying.

Jasper Loy

@Oracle By the way, where are you from, if it is not a secret?

Ted Shifrin

No, @Pedro. Average value of $f$ on a region $\Omega$ is just $\dfrac1{\text{Vol}(\Omega)}\displaystyle\int_\Omega fdV$. (Here it's just intervals, of course.)

Oracle

15:43

@JasperLoy That's a secret. But not Singapore!

Jasper Loy

@Oracle I see. Hmm, I don't know where Singapore is...

Pedro Tamaroff

@TedShifrin But intervals have zero measure.

Oracle

@JasperLoy Sure?

Ted Shifrin

We're talking about average value on the edges of the rectangle, @Pedro, so those are $1$-dimensional integrals.

Pedro Tamaroff

@TedShifrin OK.

Oracle

15:45

@JasperLoy Look chat.stackexchange.com/…

Ted Shifrin

BTW, @Pedro, I don't remember if you were here yesterday for a question from two of my great students. Give an example of a bounded open set in $\Bbb R^2$ whose boundary does not have area $0$.

Jasper Loy

@Oracle I live in Antarctica.

Ted Shifrin

Good wifi you have there, @Jasper.

Jasper Loy

@TedShifrin Yeah, it's not many of us here.

Oracle

@JasperLoy But you lied.

Pedro Tamaroff

15:46

@TedShifrin So, it is quite clear that $f$ vanishes on every rectangle of integral area.

Ted Shifrin

It is, @Pedro?

Pedro Tamaroff

With parallel sides.

Don Larynx

@Ted I have taken Real analysis 1

Jasper Loy

@DonLarynx Then go ahead and take topology.

Ted Shifrin

Did you do well, @Don? How far did your course get?

If you're less interested in abstract math than some people, topology is not the wisest choice. It's pretty abstract, and I don't know what text your prof is using, either.

Pedro Tamaroff

15:50

@TedShifrin So, you divide the rectangle into $n$ rectangles of area $1$.

Ted Shifrin

Rectangles always have parallel sides, @Pedro. I don't see remotely how it's clear. The integral is vanishing on such, sure.

Don Larynx

@Ted I obtained a C+. We got up to sequences and series and spent a lot of time on compactness.

Ted Shifrin

@Don, with a C+ you probably should not be going on to topology.

Pedro Tamaroff

@TedShifrin I mean sides parallel (to the axis).

Ted Shifrin

Sequences and series of functions, @Don?

Don Larynx

15:51

@Ted yeah

Ted Shifrin

yeah, sure, @Pedro, but still I insist only the integral is clear!

Pedro Tamaroff

@TedShifrin What is not clear?

OH.

Yes, I meant the integral of $f$ vanishes.

Don Larynx

We were using point-set and geometric topology by wiley 2nd edition

@Ted

Ted Shifrin

OK, @Don. Generally, I would advise students that they should have at least a high B in analysis to go on to topology. So I concur with you. I would have given that advice ages ago.

By Wiley? I know no such author. Is that the author or the publisher? @Don

Pedro Tamaroff

@DonLarynx Willard?

Ted Shifrin

15:52

Well, sure, @Pedro, but not heading in a useful direction :P

Don Larynx

Shick

sorry

wiley is the publisher

Huy

Munkres, all day long. ^_^

Don Larynx

I just seem to be less interested in abstract math than algorithms for now. I was just sitting in topology trying to be interested but it wasn't clicking, so I just thought "oh well, maybe another semester".

In other news, I am looking very forward to my numerical analysis 2 class. I am already almost done with project 1, and it's not due until 3 weeks from now. There are 6 projects and no midterms/finals.

Ted Shifrin

Yeah, @Don, maybe take more applied stuff that uses analysis.

Although you said you didn't like PDE. Hmm. :(

Maybe you're really a discrete applied type or computer scientist.

Don Larynx

@Ted I liked graph theory.

and number theory isn't so bad either

Ted Shifrin

15:55

Yeah, I think you're headed down the CS/discrete math path. You should learn some cryptography if you've had some algebra.

Don Larynx

Should I take abstract algebra 2 @Ted?

Ted Shifrin

OK, time for me to go teach and ruin people's minds.

Huy

@TedShifrin: Good luck!

Ted Shifrin

It's harder than abstract algebra 1, typically, @Don. If you still are interested in proofs, sure. How'd you do in algebra 1 ?

Pedro Tamaroff

@TedShifrin For the topology problem, I am thinking joining many parallel open sticks of positive decreasing width might work.

Don Larynx

15:57

I got a C. but we had the worst book. ever. like it was abysmal. not even the teacher liked it, and I didn't show much interest (due to the book).

but I may give it a second shot if it's worth anything

Jasper Loy

@DonLarynx Which book?

Ted Shifrin

Hmm, @Don, again a C makes continuing dubious, but if you're motivated by a good teacher, you should do it. Yeah, what book, before I leave?

Jasper Loy

@TedShifrin Maybe it's yours, lol.

Don Larynx

cmon man

Ted Shifrin

So, @Pedro, you're basically doing it in one dimension?

Don't know that book, @Don. Looks like it's slanted towards future high school teachers, which is not necessarily horrible.

Jasper Loy

15:58

@DonLarynx The title itself gives me a bad impression.

Pedro Tamaroff

@TedShifrin I want to mimick taking many lines over the rationals but trying to make it open.

Don Larynx

Have fun in class @Ted

Ted Shifrin

OK, @Pedro, keep me posted :P

Pedro Tamaroff

@TedShifrin Do you know of a solution?

Perhaps it is not possible?

Jasper Loy

Nothing is impossible.

Impossible is nothing.

Don Larynx

16:03

Proofs aren't bad, I personally like them. Topology was too abstract for me, however.

The name abstract algebra should imply something....hmmmmm...what is it?

Jasper Loy

It implies the notion of abstract structures.

Abstract groups vs concrete groups.

Don Larynx

Another reason why I dropped topology is because now I only have class at 9 and 3:30 on Mondays instead of 9, 130, and 330. yay!

Jasper Loy

That's not a good reason.

Don Larynx

cries with tears my matrix solver works :)

@Jasper!

Jasper Loy

@DonLarynx Good. How many days already since that thing?

Don Larynx

16:14

I began solving it on Saturday afternoon

Now I have solved the matrix solver algorithm :O

Jasper Loy

@DonLarynx LOL, I am talking about that thing, you know...

Don Larynx

what thing

?

Jasper Loy

@DonLarynx The thing you keep telling me about, lol.

Don Larynx

I don't know what u r talking about, sorry.

Jasper Loy

Now you are just being naughty with me.

Don Larynx

16:15

wat

Jasper Loy

You must have just done it again.

Now I expect a whole bunch of flags.

cirpis

Hey, has anyone here had the problem, where you understand everything taught in class, but when faced with a test, you just dont have enough time to work everything out?

Jasper Loy

@cirpis It's not just time, it can be other factors.

cirpis

Well its time for me mostly, Im not too stressed at tests, I usually get trough 3/4 of the test and then times up. And I can easily see the idea needed to solve the rest of it too. Normaly I just accept it, but now its becoming quite an issue since my grades have started dropping significantly.

So I wonder, are there any methods for doing things more efficiently?

evinda

Hello @DanielFischer!!!
I want to show that the subsets of finite sets are finite sets.

That's what I have tried so far:

Let $A$ be a finite set.
Then $A \sim n$, for a natural number $n \in \omega$.
That means that there is a $1-1$ and surjective function $f: A \to n$.
Let $B \subset A$.
That means that $\forall x(x \in B \rightarrow x \in A)$.
What bijective function could we take in order to show that $B$ is also a finite set?

Don Larynx

16:29

@cirpis exposure.

Daniel Fischer

@evinda You can without loss of generality assume that $A = n$. Then $B$ is a subset of a well-ordered set, hence well-ordered, and you have an order-isomorphism of $B$ to an initial segment of $A$.

Don Larynx

I may make a matrix solver using Cramer's rule next.

cirpis

@DonLarynx what do you mean by that?

Don Larynx

I made a matrix solver using Gaussian elimination i.stack.imgur.com/Lh9SO.png but I may construct one using Cramer's rule

cirpis

Whats the time complexity of your solver?

Don Larynx

16:38

I don't know what that is yet.

Possibly $O(n^2)$ @cirpis

Don Larynx

16:52

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evinda

@DanielFischer Could you explain it further to me? Why can we assume that A=n?

Jasper Loy

@cirpis Practise past year papers if you really want to score in exams. But I never did that.

Don Larynx

@cirpis exposure = expose yourself to the material

not too long per day, but every day :)

Jasper Loy

@DonLarynx And what does exposing yourself to the material mean?

cirpis

Checking my notes, working out some problems at home I suppose? I do that, but maybe not enough?

Don Larynx

17:00

to surround yourself with whatever you want to study

@cirpis do interesting problems that cannot be solved in one day.

like problem 60 from a calculus book (if you are interested in calculus) or problem 20 from analysis book (if analysis is your interest)

Alex

when doing long division should i only take i digit at a time or do 2. ever time i do 2 i end up with big complex numbers

Don Larynx

@Alex example?

Alex

25/435

cirpis

@DonLarynx Oh, that kind of stuff :D Sounds nice. Thanks for the advice!

Alex

should i work out 25 into 4 first or just goto 25 into 43?

Don Larynx

17:08

25 into 43

you can't do 25 into 4

Ted Shifrin

@Pedro: Sure, I know examples.

Pedro Tamaroff

@TedShifrin Oh, OK.

I think something in the lines of what I said should work.

Jasper Loy

Hi @TedShifrin I am going to try to sleep more normal hours.

I think 2 am to 10 am would be good.

Daniel Fischer

@evinda We have a bijection $f\colon A \to n$ by assumption. Then instead of $B\subset A$ just look at $f(B) \subset n$. Since the restriction of $f$ is a bijection between $B$ and $f(B)$, you know that $B$ is finite if and only if $f(B)$ is.

2

Don Larynx

Hi @Ted. How was class?

Or are you texting :o

@Jasper that sounds good. What's your sleep schedule right now?

Jasper Loy

17:14

@DonLarynx No schedule at all, lol.

Don Larynx

@Jasper consider when most (productive) people are awake.

John Doe

@DanielFischer Hi Daniel how you doing?...quick question, possibly...Do you think my short proof in comments of this post works if you take $m$ large enough?

pourjour

Hi

user153330

@pourjour hi

Jasper Loy

I keep thinking pourjour = pourquoi

pourjour

17:23

@JasperLoy I mixed two terms of french language (pourquoi = why et jour = day)

Jasper Loy

@pourjour Aha! My knowledge of French is limited to one or two words, lol.

pourjour

it's not hard to be learned

I have a question in analysis?

is the simple limit of increasing functions is increasing?

Don Larynx

@pourjour: Your question doesn't make sense

Balarka Sen

@DonLarynx Topology is not abstract if you can see it.

evinda

@BalarkaSen Happy Birthday!!! May all your wishes come true!!! :)

Don Larynx

17:36

@Balarka I can't see it.

Particularly because I am not interested.

Balarka Sen

why are you not interested?

user153330

@BalarkaSen happy birthday!! =))

Balarka Sen

thanks @user153330 @evinda.

Don Larynx

Are you asking me to rationalize my feelings? It is unnecessary @BalarkaSen

evinda

How is your day? @BalarkaSen :)

user153330

17:38

@BalarkaSen so you're 15 i guess? or 16?

Balarka Sen

15.

very interesting number

pourjour

@DonLarynx Why?

Balarka Sen

unique number that can be written as a product of 3 and 5 in 2 ways.

:P

@evinda alright

evinda

Nice @BalarkaSen

Balarka Sen

@DonLarynx i never asked you to tensor with Q. just why you're not interested.

Don Larynx

17:41

I don't know @Balarka.

@pourjour is the simple limit of increasing functions is increasing?

Here you are asking "is **x** is increasing"? Remove the is. Next, what is a simple limit?

pourjour

@DonLarynx it's about analysis in banach space

simple is $\forall x \in \mathbb{A} \lim_{n \to \infty} f_n(x) = f(x)$

evinda

@DanielFischer We want to to show that there is a bijective function from B to f(B), right?
And we know that the function f is bijective. How do we conclude that there is a g:B->f(B) that is bijective?

Balarka Sen

@TedShifrin hello.

Ted Shifrin

Hi @Balarka: So you're a counterexample to the Fundamental Theorem of Arithmetic?

Balarka Sen

Why would I be a counterexample to FTA?

Ted Shifrin

17:47

'Cuz this

user153330

"unique number that can be written as a product of 3 and 5 in 2 ways.
:P"

Balarka Sen

15 can be written as a product of 3 and 5 in two different ways.

And no other integer is equal to 15.

Ted Shifrin

"different," eh?

I'm in my prime for just a few more weeks ...

Balarka Sen

3 * 5 = 5 * 3.

My version of FTA uses unordered sets.

Ted Shifrin

As well it should!

Balarka Sen

17:50

So i'd consider {3, 5} and {5, 3} to be different.

Ted Shifrin

Pfeh.

Balarka Sen

@TedShifrin I'm in my semiprimes. 14, 15, etc.

:P

Gosh I'm bad at making puns.

evinda

@DanielFischer If we have $A \subset B$ then do we conclude that $f(A) \subset f(B)$ since f is injective?

Ted Shifrin

More like you're in your duplicit years, @Balarka.

Mike Miller

You're still in your prime, @Ted?

Ted Shifrin

17:55

Yes, last one for a while, @Mike.

Balarka Sen

@Mike Why don't you just unignore me.

Mike Miller

Ah, we're using different notions of 'your prime'. ;)

Ted Shifrin

Well, you had to be there ...

Balarka Sen

looks like Mike and you really did switch places @Ted

Alex

when converting minute to hours multiply by 60 ?

Ted Shifrin

17:57

Try an example, Alex.

Alex

clearly wrong

i type before i think

Ted Shifrin

Well, stop that :D

robjohn

@BalarkaSen I'd use $(3,5)$ and $(5,3)$. The curly braces are usually for unordered sets.

Ted Shifrin

LOL @robjohn

robjohn

@TedShifrin just sayin'

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$Mathematics$ Mathematics