Mathematics - 2011-10-24 (page 1 of 3)

@JM: Since you're the semi-official maintainer of the Generalization thread on the meta, could please find some [elementary-set-theory] questions and add them to that thread? I think that more than a few should probably be there for easy access later on.

t.b.

One guy at the trumpets is called Gary Grant :) Oh no that was Cary...

robjohn

12:07 AM

Gotta finish getting ready. See you guys later.

t.b.

@robjohn enjoy and have fun!

t.b.

12:49 AM

@Asaf: going after the cheapos eh?

Asaf Karagila

Going after the set theory questions, even if they are elementary :-)

t.b.

ah, as I said, cheapos

Asaf Karagila

Besides, I'm gonna have to explain this in a few weeks. Better get some practice ;-)

t.b.

Are you a TA on elementary set theory?

Asaf Karagila

Yeah.

t.b.

12:51 AM

I never liked doing it (teaching) at that level. Too much pain to get people to write properly. Tremendous effort...

Asaf Karagila

Introductory course in set theory and logic. We teach naive set theory, propositional and predicate calculus (without getting into provability and models) and naive cardinal arithmetics.

t.b.

Oh, you could chase me quite far with that...

Asaf Karagila

I enjoy that, I liked this course a lot when I was a freshman, and I enjoyed very much TA'ing it last year.

So I am practicing the in-depth explanation now, so when the students ask I have them well prepared in the relatively short-term memory...

t.b.

It's exactly what you need to do, I think.

However, I find it sometimes hard to understand what people have difficulty with.

That's not to denigrate their abilities, but half a year ago I suffered a lot with linear algebra...

Asaf Karagila

I also find it hard. Unlike other TAs I don't really solve lots of exercises in my classes. I just review definitions and go over examples.

I think that this is the key to understanding and passing this course successfully. Many students dislike that, but they go away and soon I am left with a good core of folks that like it.

t.b.

12:56 AM

Oh, then it can be very enjoyble.

Asaf Karagila

I do my best to explain as clear as possible and I don't mind starting all over from a different angle. I also try to relate the explanation to something more familiar.

t.b.

Sounds like what a good teacher should do.

Asaf Karagila

I had a student that really tried to understand, but she wasn't the sharpest crayon in the box... so one time after a few short weeks she came to ask me something during the break, while two other guys were talking to me. I told her to wait just a minute for me to finish with them, in that minute she packed her things and disappeared. She never returned to my classes, but she held no grudge against me.

t.b.

Well, those things happen...

Asaf Karagila

Sometimes, I'm really not sure how this folks choose the accepted answers. :P

Yeah, I don't mind. I met one of my students from that same class later that year in the laundromat. We spoke a bit and she said she very much agrees with my approach to the course. It is not about solving problems but about understanding the definitions.

t.b.

12:59 AM

Maybe she had the impression (the moment she left) that the other guys were occupied with stuff way over her head...

Asaf Karagila

Probably.

I also kept quoting Feynman :-)

t.b.

What?

Feynman and set theory?

Asaf Karagila

I read once that he gave a speech at some graduation and explained that one should avoid scientific voodoo, in the sense that trying to do stuff just because it seems to work, and without any reason.

t.b.

Ah, voodo, that reminds me...

Asaf Karagila

I equate that to how freshmen use "buzzwords" such as "arbitrary" in a very wrong way because they think it would make their proof better.

anon

1:02 AM

lol

thats always funny

Asaf Karagila

When I was in my second year I was grading homework assignment for this course. I would pick the exercise which we grade from the paper. Me and the TA would write a 5 liner proof on the board, and the students would fill a whole page.

t.b.

A friend of mine taught a first analysis course and he explained how to integrate cos^2 by parts, he made a big fuss out of it: so he started integrating, got something and integrated again -- oh shoot, arrived again at an integral containing cos^2 -- then he said, okay, now comes "voodoo" shifted the integral over to the other side and divided by two. He forgot about that, but when correcting the exams there were about ten people writing "voodoo => ..." when they meant that trick :)

3

Asaf Karagila

lol

t.b.

one of those rare occasions when correcting exams is fun

Asaf Karagila

Wow. It's 3am

t.b.

1:07 AM

@Asaf: model theory on the main site

yeah.

late it is.

Asaf Karagila

I saw. I am way too tired for actual mathematical thinking ;-)

t.b.

I see :)

Asaf Karagila

I don't know the answer right away, and spending time on that is not a good idea. I have a long day tomorrow.

I left a comment and upvoted (it is a good question, after all)

t.b.

Me too. Lots of things to do.

Dunno, didn't read it

Asaf Karagila

Well, good night folks.

anon

1:10 AM

night

t.b.

Good night to you, too!

Srivatsan Narayanan

5:11 AM

Anyone up?

t.b.

@Srivatsan: yes, I'm up (it's early in the morning here)

Srivatsan Narayanan

Er, @t.b., I did not have anything specific in mind when I typed that. Sorry if I caught your attention for nothing.

anon

I'm cooking pasta, I'm up.

t.b.

@Srivatsan: no problem

Srivatsan Narayanan

By the way, if it's early in the morning, you must be in Europe. (It's past 1.20am here, in the US.)

t.b.

5:19 AM

Yeah, Zurich, Switzerland 7:20 AM

Srivatsan Narayanan

Yes, currently looking you up. Good.

anon

10pm whatever this time zone is

Srivatsan Narayanan

PDT, it seems :)

t.b.

Does anyone know what this symbol is? There's another user wearing it as Gravatar.

besides a \lambda with red and blue background

Srivatsan Narayanan

I had the same question.

Rajesh D

5:25 AM

try giving it as an image in google image based search

Srivatsan Narayanan

tinyurl.com/4y3a5qu

DrRacket

DrRacket (formerly DrScheme) is an open source integrated development environment for the Racket programming language which has a graphical user interface. It is widely used among introductory Computer Science courses that teach Scheme and is lauded for its simplicity and appeal to beginner programmers. The IDE was originally built for use with the TeachScheme! project (now ProgramByDesign), an outreach effort by Northeastern University and a number of affiliated universities for attracting high school students to computer science courses at the college level. DrRacket is built on top of...

anon

crap all my pasta got stuck together :(

t.b.

@Srivatsan: thanks!

Rajesh D

my internet is going down soon

Srivatsan Narayanan

Thanks must go to Google image search, of course.

@t.b.

@Rajesh Internet is going down? How come? In the middle of the day...

Rajesh D

5:32 AM

there is some repair at Univ.

after it is gone...i wont be able to tell you that its gone :-)

t.b.

@Rajesh: now that's a dilemma :)

Srivatsan Narayanan

@anon The food I cook seldom tastes too bad to me, even if I know that something went wrong. Perhaps you can still try the pasta...

anon

I'm eating it right now. and burnt my lip.

t.b.

@anon: bad day, huh :/

Srivatsan Narayanan

Ah

Srivatsan Narayanan

5:48 AM

@t.b., I and a couple of my friends are doing some self-study of some sort, and I have some question about references.

Gortaur

6:31 AM

In a dark-dark morning, in a dark-dark country, in a dark-dark city, in a dark-dark room Gortaur is sitting trying to realize if he wants some flakes on the breakfast. After he lost the ring, that became one of the most important problems

robjohn

@SrivatsanNarayanan Studying yourselves?

@Gortaur Perhaps there will be a ring at the bottom of the box of cereal.

Wow, my mean square image is getting more votes than most of my answers.

@Gortaur I see you've chosen a custom gravatar. Good choice. :-)

Orange seems the color of the day for new custom gravatars.

Gortaur

@robjohn sure, orange is the choice of Gobjohn ;)

good evening

robjohn

Indeed

Gortaur

@robjohn I hope that was just a typo ;D

robjohn

Indeed?

:-)

Gortaur

6:40 AM

if you put a cursor on such messages, you can see what they are referring to: I talk about your question to Srivatsan

I feel yellow myself. don't know if anybody can understand it

robjohn

They mentioned self-study.

Gortaur

@RamanaVenkata: how is life? when you're young and full of hopes

@robjohn и то правда )

Ramana Venkata

Fine

Gortaur

that grass was greener, the light was brighter. with friends surrounded, nights of wonder

robjohn

действительно!

@Gortaur are you quoting from something, or have you had a bit too much tonight?

2

Of course, it is morning there.

Gortaur

6:45 AM

@robjohn it's Pink Floyd, High Hopes. The last song from the last album. After I saw the clip (I was graduating that moment) I've finally decided to start listening them

to my knowledge of English, 'и то правда' does not mean 'then the trouth'

robjohn

I haven't heard that album, but I have a lot of their earlier work.

So Google Translate fails.

Gortaur

Indee )

robjohn

:-)

Gortaur

from the last album I love the first song - instrumental, [cluster one]

and [high hopes]

but the last one is one of their best I would say

robjohn

I think that Animals is the most recent album of theirs that I have.

Gortaur

6:48 AM

►

robjohn

Make that the Final Cut.

I have The Wall, too

Then more before those.

Gortaur

@robjohn sorry, didn't understand you

robjohn

Pink Floyd albums

Gortaur

that I've got )

robjohn

The most recent ones are Animals, The Wall, and The Final Cut.

that I have.

Gortaur

6:53 AM

icic

robjohn

I am currently playing the clip you posted.

Gortaur

I really like it so in the case you say contrary, I'm your enemy forever and ever )

though by Tolkien it does not bother my enemies too much

robjohn

I just have to put the secret decoder ring in the oven.

Gortaur

'I really like it so in the case you say contrary, I'm your enemy forever and ever' - perephrase of Bulgakov, btw

I'm full of quotes today

not fool of quotes I hope

robjohn

fool of quotes? is that the name of the first Joker in the deck?

Gortaur

6:58 AM

no, that is fool of spades

see ya, I need 2 catch da bus

robjohn

good luck.. off to school?

Asaf Karagila

7:32 AM

Top of the morrow, folks.

Asaf Karagila

7:53 AM

Huzzah, 16,000 reputation.

I like these round reputation numbers.

Gortaur

@robjohn yeah. imagine, I cannot login to my user in school as well - as I expected in fact. I need to kick some sysops' asses

robjohn

8:31 AM

uh oh. Poor sysop.

This question has two nice answers.

for a problem which is probably a duplicate...

lim sin(x)/x =1 has to have been asked before.

Gortaur

9:11 AM

@robjohn: the comment by Joren is somehow expected )

robjohn

@Gortaur L'Hospital! why didn't I think of that?!

:-p

Gortaur

you know, these are modern methods to find the first perfect limit

robjohn

All shiny and scientific and such.

t.b.

9:30 AM

@SrivatsanNarayanan Yes, just ask...

Gortaur

(0)

Gortaur

9:50 AM

and that wasn't what you guys thought about

Srivatsan Narayanan

10:16 AM

(@t.b. Feeling too tired to do any thinking. I'll ask my question tomorrow or so.)

t.b.

@Srivatsan: sure, just one thing: Ping me using @tb from chat, because .@t.b. doesn't seem to work, sleep well

Benjamin Lim

10:35 AM

Hello guys, I have just learned about rings and this is probably a stupid question

Say we have a ring homomorphism from R[x,y] -> C, where R and C denote the real and complex numbers respectively that takes say f(x,y) -> f(i)

I am thinking that the kernel is the ideal generated by the polynomial x - i but i is not a real number, so how can one speak of the kernel?

J. M.

10:47 AM

Now I know whose Eye was staring intently...

Jack Schmidt

@BenjaminLim: if takes two variables at first, what does f(i) mean? Where does x*x + 7*y go?

Asaf Karagila

@JM Mine?

J. M.

I don't know. Is yours jaundiced?

Asaf Karagila

Nope.

Are yours?

J. M.

Certainly not you. ;)

Maybe if I drink beer for five years straight for breakfast, lunch, and dinner...

Asaf Karagila

10:50 AM

Try a bottle of arak for each meal.

J. M.

@AsafKaragila I think I'll leave the privilege of choosing what makes the cut to you. You know I always defer to you in matters of choice... ;)

That sounds like a better recipe for jaundice... :D

Asaf Karagila

For cutting I prefer my Arcos chef knife ;-)

J. M.

@anon Insufficient mixing... ;)

Oh Jack, you're there?

J. M.

11:15 AM

"Sweet dreams, Arturo; now the rest of us get a chance to answer some questions, heh, heh."

Gortaur

@JM how do you know when does he sleep

J. M.

I don't know; I'm just quoting Gerry.

...and that's a shiny Eye you have...

Gortaur

@JM (0) that one?

J. M.

Yes.

Gortaur

it shouldn't bother you. I use it to read in the night )

J. M.

11:24 AM

It doesn't. At least, not unless I'm holding a certain ring...

Gortaur

unless I have a guess that you're holding it

robjohn

12:03 PM

@ben?

Gortaur

@robjohn ghosts again?

t.b.

@robjohn: there's the easiest part of the mean ergodic theorem to prove for the mean square :)

Hi all, btw.

robjohn

I saw him ask a question and then not respond.

Gortaur

hi @tb

robjohn

But he's not here any more.

@tb good morning

Gortaur

12:07 PM

@tb are you experienced in ergodicity theory for Markov processes? say, discrete-time?

t.b.

@Gortaur: I used to think about it a bit maybe 8 years ago, but I've forgotten everything in the meantime because I didn't use it.

Gortaur

@tb icic ) anyway, maybe you can help me to clarify some stuff. I'm working with Markov processes in metric spaces and I'm interested in attractivity properties of subsets of the state space

with attractivity I mean study of such kind of probabilities P_x( d( X_n,A ) -> 0 )

it seems that I have some interesting features to characterize such properties and show how these probabilities can be computed - but I have doubts that it was done within ergodic theory

on the other hand, I had an impression that ergodic theory is more focused on 'mixing' kind of behavior, moreover, usually provided invariant distribution

t.b.

@Gortaur: before you expand further, let me say that I don't think that I can help here. Sorry

Gortaur

Fairy nuff

thanks @tb

Rajesh D

hi all

t.b.

12:19 PM

hi Rajesh, I gather the internet's working again?

Rajesh D

yes....

how is your day goin

t.b.

Hm. Not much, so far. I'm a bit in a lazy mood.

Rajesh D

do you know about Diwali

J. M.

Oh, it's now? Happy Diwali!

Rajesh D

@Gortaur : how was your lunch ?

t.b.

12:21 PM

Same from me!

Rajesh D

thanks...it tomorrow and dayafter

gtg home town tonight....travel of 350 Km

J. M.

Shouldn't you be outside having fun instead of hanging around with us? ;)

Rajesh D

packin stuff

J. M.

No use having a festival if you're cooped up, you know.

Rajesh D

yes....i will be....i hope

Gortaur

12:23 PM

@RajeshD thanks, I can stand it ) I mean, the food

t.b.

@Gortaur: So, did you meet Jonas IRL?

Gortaur

ah, that was the question )

@tb no I didn't

t.b.

He's probably still recovering from me spamming him on Choquet's theorem :)

J. M.

He choked on Choquet...

t.b.

Apparently...

Gortaur

12:27 PM

If I were a girl, wth. I will burn this thought with fire

Gortaur

12:40 PM

@tb what are you doing when you're in a lazy mood?

it usually just bothers me since I cannot focus on any problem

t.b.

I'm too lazy to go into detail, one part of it is hanging around here...

J. M.

"I cannot focus on any problem" - usually, that means your mind has gotten strained on whatever you were thinking about. One solution that works for me is to do something completely unrelated and relaxing.

or what those Americans call "find your happy place".

Gortaur

icic

I think I will smoke a cigar, should be relaxing

J. M.

It often happens that you figure out a breakthrough while doing something completely different.

For some reason, there are thoughts that need some "fermentation time"...

Gortaur

I agree )

sometimes I'm so confused that I forget how to drive my mind in the optimal way I use ti

t.b.

12:47 PM

You're lazy just stay in bed
You're lazy just stay in bed
You don't want no money
You don't want no bread

If you're drowning you don't clutch no straw
If you're drowning you don't clutch no straw
You don't want to live you don't want to cry no more

Well my trying ain't done no good
I said my trying ain't done no good
You don't make no effort no not like you should

Lazy you just stay in bed
Lazy you just stay in bed
You don't want no money
You don't want no bread

(Deep Purple)

J. M.

Eh, I'd rather have bread than money... :)

robjohn

@JM Those Americans?

:-p

J. M.

@rob, well, it's those self-help books that popularized the "find your happy place" bit.

...and I have yet to see a self-help book coming from another country... ;)

t.b.

Oh, there was "the lol^2a principle" in the early nineties from a swiss guy...

LoLa with the second L squared

robjohn

@JM So you're saying that other countries want you to rely on others to help you...

J. M.

12:52 PM

I don't know, I'm just oberving why aren't there "gurus", from, say, Sweden...

t.b.

here we go, didn't think that was still sold...

robjohn

That's why so many want us to do their homework for them...

:-)

J. M.

...and it turns out those "Indian" gurus were based in America anyway, so they don't count. :P

Rene... another one of those names that I'm not sure if it's a man's or a woman's...

t.b.

Only one e => male

J. M.

Sometimes, the additional accent throws me off. :) Here, "Rene" is a man's name, but the pronunciation is more "re-neh" than "re-nay"...

t.b.

12:55 PM

Uriella is a Swiss "gura" (if that's the word), the spiritual leader of Fiat Lux. I like to think her name was inspired by Uri Geller.

Gortaur

yeah, a bit better now, thnk you guys for the support

J. M.

Anyway, that was one good thing I got from those self-help bits. The more important thing I got from them, though, is that it was a good way to train my bull filter... ;)

t.b.

I once got a few of those books from some friends. My conclusion was that if that crap made others feel better, then my situation can't be that bad...

robjohn

@JM Some is bull, but therer are often ideas that are worth internalizing.

Gortaur

@tb btw, I can say that in Schiphon (Amsterdam airport) Swiss Airlines' attendances are the most pretty

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$Mathematics$ Mathematics