Mathematics - 2012-07-19 (page 4 of 6)

2:00 PM

@RagibZaman that's why it's not your job to come up with a problem. find a good supervisor (in anything) and let them guide you

Ragib Zaman

I've been reading a huge pile of combinatorics journal papers/grad textbooks recently, only for about a month and I'm sick of it.

Jonas Teuwen

@BenjaLim Oh, I do know some of his papers.

@AlexanderAmenta It is best if you come up with a problem yourself.

@RagibZaman For what do you have a passion?

@RagibZaman You should then not work on a PhD in combinatorics :-). The project needs to be your (brain)child.

And you don't want to have that your children make you want to vommit.

Alexander Amenta

@JonasTeuwen i disagree - if you don't have a significantly strong grasp of a field, how can you see which problems are most suitable?

Jonas Teuwen

@AlexanderAmenta That is not a disagreement with my statement.

I am just saying, that if you would be able to come up with a problem yourself, that would be the best.

Ragib Zaman

I like most fields of analysis, but I got too far into analysis too quickly and it limited my exposure to other fields, recently I've been thinking more about algebra and its been really interesting so far.

Alexander Amenta

2:02 PM

@JonasTeuwen ah, you're right, but that won't help @RagibZaman

BenjaLim

@RagibZaman forgot to tell you that artin has a proof of the nullstellensatz

Jonas Teuwen

And of course, you are very right. Get some small problems to tackle and from there on find your own way.

BenjaLim

for $\Bbb{C}$ without a lot of machinery

Alexander Amenta

@JonasTeuwen it is best if you are able to come up with a good problem yourself. it's possible to come up with some pretty bad problems

Jonas Teuwen

@RagibZaman So, do they do master degrees in AU?

Ragib Zaman

2:03 PM

Yea at USYD and UNSW I know for sure they do.

Jonas Teuwen

I am very able to come up with good problems. The problem is solving them...

@RagibZaman So maybe you should do that. Snuff some subjects?

Alexander Amenta

we're talking about honours year problems, and they're pretty different from phd problems. you want things in which you could get reasonable progress in 9 months

but not too much progress, otherwise the problem is too easy

Gigili

@BenjaLim Yuck.

Jonas Teuwen

@AlexanderAmenta Or you are too smart.

Ragib Zaman

I have no problem with people thinking I'm too smart.

Jonas Teuwen

2:04 PM

Don't start working on a PhD in something you don't really like: you will fail.

Ragib Zaman

I'm quite fine with that actually!

Jonas Teuwen

It will be a problem if they think you are smarter than you actually are. Certainly if that guy is your advisor.

Alexander Amenta

if you're actually that smart, then it's no problem - but chances are you're not (few are)

and if you really were that smart, it would be better to work on something more difficult!

could just be my own biases, but i think it's better to not finish an honours project than to finish one

Jonas Teuwen

It needs to be something original, you are not working to get the Fields medal :-). Well, maybe that is a dream, but not the goal.

I suggested a masters degree to just do some courses in different fields and figure out what you like best. Not to solve problems.

I am pretty certain that you will fail getting a PhD if you do something you don't really like.

2

Ragib Zaman

Yea I'm giving quite a lot of consideration into a masters actually.

I want to spend at least a few more years learning lots and lots of math, rather than specializing heaps into one tiny problem.

Alexander Amenta

2:07 PM

of course nobody should do something they don't like - but they should be open to problems they hadn't considered

Ragib Zaman

The lonely runner conjecture seems like a problem that a clever enough undergrad with a good supervisor could work on.

Jonas Teuwen

@RagibZaman There are plenty of such problems.

@AlexanderAmenta Pierre will be your advisor right?

Ragib Zaman

Probably very naive of me, but it seems like one of those things that someone with a fresh mind could come and solve with relatively simple methods because they aren't clouded by all the advanced techniques.

Jonas Teuwen

@RagibZaman That can be very true...

Ragib Zaman

Somewhat inspired by those 3 undergrads in Mumbai showing PRIMES is in P.

Alexander Amenta

2:09 PM

@RagibZaman chances are you will not solve this problem, in which case it's a lot of time wasted unless you were learning pre-existing techniques

Ragib Zaman

and they were computer scientists, not mathematicians.

Alexander Amenta

@JonasTeuwen pierre and auscher

Jonas Teuwen

In any case: setting your goals too low will probably not make you reach something about that :-).

@AlexanderAmenta Wow, cool. You're lucky.

So you will go to Paris-Sud once?

Alexander Amenta

@JonasTeuwen quite lucky. but the thing is, i didn't try to work with them

i'll be there from 1.5 years into the phd until the end

Jonas Teuwen

That is pretty cool, if you are there for some time you can also visit Delft for some weeks.

Alexander Amenta

2:11 PM

i will be!

Jonas Teuwen

Can probably be arranged, but I don't have much influence on that but my advisor has (and he knows Pierre and Pascal quite well).

Alexander Amenta

pierre's told me i should (and can) visit, so i will

Ragib Zaman

Does ANU have some awesome partnership with Paris XI or something?

Jonas Teuwen

Ah, great.

Well, in Paris XI they have Pascal Auscher, and they all know each other :-).

Alexander Amenta

no, but my ANU supervisor has a Paris XI collaborator

Jonas Teuwen

2:11 PM

@AlexanderAmenta Why... are you... not at IWOTA?

Alexander Amenta

because i'm in russia!!

Jonas Teuwen

Oh, right.

Alexander Amenta

(why am i in russia rather than IWOTA? because i booked my flights before i knew about it)

Ragib Zaman

@AlexanderAmenta Because your supervisor has a collaborator there, your uni lets you spend most of your phd over there?

Jonas Teuwen

Just received an e-mail of my advisor about how cool it is there.

@RagibZaman Yea, these people like that.

They send me to ANU.

Ragib Zaman

2:13 PM

where are you atm?

BenjaLim

@JonasTeuwen cool?

Jonas Teuwen

@RagibZaman NL.

@BenjaLim Yea.

Alexander Amenta

@RagibZaman it's an ANU/Paris XI joint phd (cotutelle)

Ragib Zaman

:(

Alexander Amenta

@RagibZaman both universities have to approve

Jonas Teuwen

2:15 PM

Why is that ":("?

Ragib Zaman

I want to say something like "you are too damn lucky" but that would be an insult to how hard you have worked to get that.

BenjaLim

huh?

Alexander Amenta

you can get these deals by talking to people, not by going through the standard channels - hence my advice

BenjaLim

@JonasTeuwen why is it cool?

@RagibZaman who is lucky?

Ragib Zaman

Alex

Alexander Amenta

2:16 PM

there's luck involved, being in the right place at the right time - by not pigeonholing yourself early, you can seek out these right places

BenjaLim

@RagibZaman no university medal :D

Jonas Teuwen

@AlexanderAmenta How is your French? I can send you some mail about a French conference.

BenjaLim

@JonasTeuwen I can do the translation

@JonasTeuwen and why is anu cool?

Alexander Amenta

@JonasTeuwen i know no french, but will be taking lessons from septemberish onwards

Jonas Teuwen

@BenjaLim I can read French, maybe he can go there.

@BenjaLim Because you are there.

Ragib Zaman

2:16 PM

So at some point soon

All 3 of you will be at ANU

Jonas Teuwen

@AlexanderAmenta What do you mean? You should let yourself be known early on.

Alexander Amenta

join ussss

Ragib Zaman

I want to visit, definitely.

BenjaLim

@RagibZaman you're missing out :D

@JonasTeuwen why because i'm there????????????

Jonas Teuwen

@BenjaLim You make it totally cool, bro.

Alexander Amenta

2:17 PM

@JonasTeuwen i was talking earlier about doing a lot of broad math, not focusing on one thing to early. that way you can meet a lot of people, see what opportunities are there, and take them

Jonas Teuwen

@AlexanderAmenta Okay, agreed.

Alexander Amenta

@JonasTeuwen if i'd 'chosen a field', i wouldn't have got this offer

Jonas Teuwen

@AlexanderAmenta Mm, I wanted to go elsewhere, and then I got a way better offer from my MSc thesis advisor :-).

Alexander Amenta

@JonasTeuwen since it's not in my honours field at all, and it had never even occured to me - but i did a course with pierre and he could see that i cared about my work

Jonas Teuwen

I like Pierre's approach to math.

Alexander Amenta

2:19 PM

@JonasTeuwen but i care about math as a whole, not individual fields - which sits in with pierre's approach. hence the phd

BenjaLim

@JonasTeuwen i don't get it...

Jonas Teuwen

@AlexanderAmenta Me too :-).

@BenjaLim Haha, it is a joke. Australia seems nice to me, and it is also nice that you guys will be there, at least I will already know somebody by name.

BenjaLim

@JonasTeuwen i agree with that. That's why I decided to stab myself in the guts to do reading course in several variables

@JonasTeuwen You know two at anu now

how great is it you have friends before you even arrive :D

Alexander Amenta

and pierre. so three

BenjaLim

@JonasTeuwen if you're in sydney, ragib makes it four

Alexander Amenta

2:20 PM

there you go, he already knows half of canberra

Jonas Teuwen

@BenjaLim Yes :-).

BenjaLim

I can't believe we're witnessing live networking being done on chat right here right now all live and exclusive guys

2

Alexander Amenta

i always feel like we're clogging up m.se chat whenever this happens

BenjaLim

@AlexanderAmenta don't worry there's only one topic going on now

it's not like 3 or 4 conversations are going on

Alexander Amenta

i should ask some calculus questions

BenjaLim

2:22 PM

all the other usual guys are not here

huhu?

Jonas Teuwen

Because we suppress the others?

We are like an opportunistic infection. Once the bacteria went on a holiday we funghi infest everything 8-).

2

Alexander Amenta

yeah, like we should be on msn or something

BenjaLim

@JonasTeuwen trust me I don't think the math education at ANU is that good.....

Alexander Amenta

but then others can't join in.. i guess we're ok

Jonas Teuwen

@BenjaLim I know that it isn't.

BenjaLim

2:23 PM

it's up to you to make it good or not @JonasTeuwen @AlexanderAmenta

Alexander Amenta

yeah ANU education isn't great. it's probably not great in many places really. but the people are good

Jonas Teuwen

I'm going there for Pierre primarily.

BenjaLim

@JonasTeuwen Like I had a look at AC and loved it and decided to do a reading course on it

Jonas Teuwen

Well, right, I mean to work there, and then Pierre can help me (once in a while).

BenjaLim

I think it's the course that I've learnt the most at ANU

Jonas Teuwen

2:24 PM

@BenjaLim Axiom of Choice...?

BenjaLim

I really am missing commutative algebra right now. Especially after seeing this

Alexander Amenta

@JonasTeuwen you will have to teach me some stuff

Ragib Zaman

Algebraic Combinatorics?

BenjaLim

@JonasTeuwen AC on Arxiv is comm algebra

Jonas Teuwen

@BenjaLim Oh, right. When I am there, lecture me about that 8-). I will tell you cool stuff about functions.

@AlexanderAmenta Sure! And you teach me stuff!

BenjaLim

2:25 PM

@JonasTeuwen I know nothing about this stone - weierstrass shit or borel measures.

Zhen Lin

Algèbre Commutatif, no doubt...

Jonas Teuwen

@BenjaLim Right, I know that. It is the coolest in a general Banach algebra.

Alexander Amenta

@JonasTeuwen there should be a seminar course on harmonic analysis we'll all get involved in. should be really fun

BenjaLim

speaking about that where is lashi

Jonas Teuwen

@AlexanderAmenta Excellent.

@ZhenLin Sir Bourbaki...?

Alexander Amenta

2:26 PM

@BenjaLim probably still in missouri

BenjaLim

@ZhenLin you need the definite article in the front.

I don't get why this guy won't prove the weak nullstellensatz using noether normalisation

Jonas Teuwen

@BenjaLim Because he can?

BenjaLim

@JonasTeuwen What algebra courses did you do?

@JonasTeuwen TBH I actually quite like arzelà - ascoli

Jonas Teuwen

@BenjaLim Almost none? I just read some stuff.

BenjaLim

@JonasTeuwen I skipped almost all the analysis lectures this semester :D :D

Jonas Teuwen

2:29 PM

Some papers, some stuff. You know.

BenjaLim

@JonasTeuwen I mean surely you've taken a basic algebra course on groups/rings/fields/galois theory

Jonas Teuwen

I skipped all lectures except perhaps five in my five years of study.

2

Alexander Amenta

guys i have to go and eat

Jonas Teuwen

Oh yes, I did the exam.

Alexander Amenta

talk to you all later!

Jonas Teuwen

2:29 PM

See you!

BenjaLim

@AlexanderAmenta borsch and vodka?

Ragib Zaman

cya alex!

BenjaLim

@AlexanderAmenta bye nice talkin come on chat more

@RagibZaman what are you doing at 12.30

way past my bed time

I hope you're not in kings cross

Ragib Zaman

Reading papers on graph theory

BenjaLim

saw the guy that got punched and then died?

Ragib Zaman

2:30 PM

that exactly opposite of partying in kings cross

BenjaLim

@RagibZaman WHY????????????

man that was scary

Ragib Zaman

giving my heart and soul into these SUMS problems man

BenjaLim

AH.........

Still trying to show the whole kernel is that

Ragib Zaman

no I've stopped on that problem for now

BenjaLim

ok

Ragib Zaman

2:31 PM

I read an epic load of combinatorial stuff to solve Q9

BenjaLim

ahahahahahahahahhahahahahahahahahhahahahahah

Ragib Zaman

maths.usyd.edu.au/u/SUMS/sums2012.pdf

Chuck Fernández

guys, is algebraic geometry usefull for other parts of math?

Ragib Zaman

For number theory, quite a bit

BenjaLim

@ChuckFernández why?

@JonasTeuwen so lucky

Ragib Zaman

2:33 PM

But not so much for too many other areas I don't think.

BenjaLim

before coming to anu already you have so many friends

Jonas Teuwen

@RagibZaman You like analysis?

BenjaLim

category theory

AT

Chuck Fernández

what do you mean why?

BenjaLim

@RagibZaman complex geometry

Jonas Teuwen

2:33 PM

@RagibZaman You can combine analysis with combinatorics.

BenjaLim

@MattN. my god

If I need help for AT

Ragib Zaman

@JonasTeuwen Yea I like analysis, and yea I love that approach.

BenjaLim

I will come to you @MattN.

Ragib Zaman

Wilf's generatingfunctionology is a great mix, I love that book

BenjaLim

@RagibZaman where did you learn your hard analysis from?

Jonas Teuwen

2:34 PM

@RagibZaman What approach? Oh, right.

Ragib Zaman

Got the foundations from a mix of course notes and skimming lots of books

Matt N.

This is not an answer. I'm wanting to flag. It's clearly an advert as well, so it counts as spam, no?

Jonas Teuwen

@RagibZaman So read more about that?

Matt N.

@BenjaLim No, it's just Matt : )

@BenjaLim Sure, do that. But after my exams.

Jonas Teuwen

@MattN. No, leave it.

BenjaLim

2:35 PM

@MattN. when

Matt N.

@BenjaLim Mid-September.

BenjaLim

@MattN. AT exam?

Matt N.

@JonasTeuwen But it's annoying.

Ragib Zaman

@JonasTeuwen That is actually a great idea...

Jonas Teuwen

@MattN. For you. The notes are good.

Matt N.

2:35 PM

@BenjaLim No, CA & FA.

BenjaLim

@JonasTeuwen Can't skip lectures next sem

Jonas Teuwen

@BenjaLim Sucks.

BenjaLim

@MattN. ok

@JonasTeuwen for starters I found the first half of my analysis course dead easy

Ragib Zaman

@MattN. Do you have more exams or only those 2?

BenjaLim

@MattN. Did you die in AT?

Matt N.

2:36 PM

@RagibZaman Those two, why? It's enough.

BenjaLim

and how was your GT going in there?

Matt N.

@BenjaLim No, that was not so difficult. Why?

BenjaLim

@RagibZaman last semester I only had exams for analysis and galois theory

how was homology? @MattN.

Ragib Zaman

@MattN. Sorry, I didn't mean to sound like you don't do a lot of study, I was just wondering because normally one does 4 subjects per semester don't they?

Jonas Teuwen

@BenjaLim Yes, but you are quite good at it. Pierre told me that the results were quite... bad?

BenjaLim

2:37 PM

@JonasTeuwen results for what?

Matt N.

@RagibZaman Hm, I think the definition of "normal" probably depends on your uni. No worries : )

BenjaLim

finals?

Jonas Teuwen

@RagibZaman The Swiss system is different.

@BenjaLim Analyssi course.

BenjaLim

mid sems?

Matt N.

@BenjaLim Good, especially cellular, why?

BenjaLim

2:38 PM

@JonasTeuwen the final results?

Jonas Teuwen

Our Bro, @MattN. does pretty advanced courses...

@BenjaLim Oh, was the midterm I believe.

BenjaLim

@MattN. ok thanks. Hey did you guys learn about CW complexes right at the beginning?

@JonasTeuwen 70% of the class failed.

Jonas Teuwen

@BenjaLim 89% of my class failed.

Ragib Zaman

The swiss system sounds a hell of a lot better than what we have over here.

Matt N.

@BenjaLim I think so.

BenjaLim

2:39 PM

HOLY SHIT

Matt N.

@RagibZaman Wait a second: when did I tell you that I was Swiss?

Jonas Teuwen

@RagibZaman The place where Matt is educationally wise way better than the ANU.

BenjaLim

@MattN. did that not screw everyone up?

Jonas Teuwen

@MattN. Oops, I did... (above, nothing else).

@MattN. But that is like the coolest country on earth, Bro.

Matt N.

@JonasTeuwen Ok. I guess I'll have to kill now because you know too much and blabbed.

Ragib Zaman

2:40 PM

I remembering being impressed with how far your courses go (from the questions you post).

Matt N.

@JonasTeuwen Yeah, if you're a cow.

Ragib Zaman

remember*

Jonas Teuwen

@MattN. It was not a secret anyway here with teddy and such.

Matt N.

@RagibZaman ugh you read my questions? Yikes. They are all stupid.

Jonas Teuwen

@MattN. Well. Try another country.

@MattN. The questions are quite good. Stop whining. You act like a girl.

Matt N.

2:41 PM

@JonasTeuwen Hey, teddy is different. To me he's special. Or what did you mean?

BenjaLim

@MattN. you've met him in person?

Jonas Teuwen

@MattN. Yes, but if one reads the chat it is quite easy to decide where you live (about).

Ragib Zaman

@MattN. Not so, I took Functional Analysis last semester and was hoping I could help but many of the questions were harder than the level of questions given at my course.

Jonas Teuwen

It it taught by Einsiedler, that bro is hardcore.

We had an exchange student and he showed me the course and said he suffered.

BenjaLim

@AlexanderAmenta actually come to think of it a lot of the material in analysis I led to functional analysis

like arzelà - ascoli, equicontinuous functions

@RagibZaman you should have stuck with AT lasst sem

then a lot of avenues would have been open for you

in terms of knowing stuff about homology, cohomology, etc

Matt N.

2:45 PM

@RagibZaman Well yes. The dudes inventing these questions are not trying to make questions from which you learn something because they're juuust the right level of difficulty but rather they try to impress and amuse themselves by coming up with clever questions that are interesting to them.

@BenjaLim Well that is not relevant, is it? : ) But as you know: I know his name, his favourite crisp bread and the colour of his favourite underwear.

Jonas Teuwen

@MattN. Well, if you can solve them you are quite good actually. It does serve a purpose, but not the purpose for the average student.

Matt N.

Ok, maybe not the last one. : )

Ragib Zaman

@BenjaLim I think I made the right choice, I'm not as good at algebra as you so I think I'll be fine waiting another year to learn those. By dropping that I focussed more on my Rings/Fields/Galois Theory class and I understood that better.

BenjaLim

@MattN. I will tell you a secret. Next year @AlexanderAmenta @JonasTeuwen and I will all be in the same uni

@RagibZaman good!!

Ragib Zaman

(I got 94 in that btw, quite happy =D )

Jonas Teuwen

2:46 PM

So, MattN should come too...?

BenjaLim

@RagibZaman hahahahaha

@RagibZaman I think that is better than getting 99 in my analysis course

Matt N.

@BenjaLim Somehow it's not so secret if you post it on a site that's visible by anyone on the internet. : )

BenjaLim

@MattN. how was your GN going into AT?

Matt N.

What's GT?

Group theory?

Ragib Zaman

Geometry/Topology?

BenjaLim

2:47 PM

general topology

Matt N.

Oh, what?

Zhen Lin

@BenjaLim You should probably stop using these abbreviations...

BenjaLim

@MattN. yes

I mean how was it just before you took AT

Matt N.

I don't understand. The two have not much to do with each other. Except that I needed the definition of path-connectedness

BenjaLim

@ZhenLin arxiv.org/archive/math

@MattN. Then what is the prereq for AT at ETH?

Jonas Teuwen

2:48 PM

@BenjaLim I reject your ArXiv abbreviations.

Matt N.

@BenjaLim I'd done one semester of it.

Jonas Teuwen

Make a macro if you'd like to use them.

Zhen Lin

@BenjaLim I know what those are, that doesn't mean it's well understood!

Matt N.

@BenjaLim Nothing.

Gotta go, byee

BenjaLim

@MattN. OH CRAP

Ragib Zaman

2:49 PM

That was a quick exit!

Jonas Teuwen

@MattN. Babye.

BenjaLim

@MattN. bye

Zhen Lin

at any rate GT is geometric topology.

BenjaLim

@ZhenLin that's why I made the correction

Jonas Teuwen

I like geometric measure theory.

Zhen Lin

2:50 PM

GN is even more inscrutable!

Jonas Teuwen

I was actually wondering something today. Do non-measurable sets serve any purpose? Other than give funny paradoxes?

Ragib Zaman

They are forced

Zhen Lin

@JonasTeuwen Wasn't there a M.SE question about that just this week...?

Ragib Zaman

I wondered this for a long time too

BenjaLim

@RagibZaman nite!

Jonas Teuwen

2:50 PM

@ZhenLin I don't know...? I don't read it that often.

BenjaLim

nite all

night guys

Ragib Zaman

@BenjaLim Gnite

BenjaLim

@RagibZaman GO TO BED FOOL.

Jonas Teuwen

@ZhenLin I actually was wondering if we could not redefine "sets" to only be the measurable ones if we actually do not care about the others.

Zhen Lin

0

Q: Advantage of accepting non-measurable sets

What would be the advantage of accepting non-measurable sets? I personally feel that non-measurable sets only exist because of infamous Banach-Tarski paradox...

@JonasTeuwen Well, first of all, we should give up the axiom of choice... :p

Ragib Zaman

2:51 PM

Jonas, basically, there are 4 things we "want", 1) all sets measurable 2) countable addivity of measures 3) cant remember and 4) cant remember lol

I can look it up if you want

Jonas Teuwen

@ZhenLin Well, not necessarily, right?

That would be like a very strange way of doing things because stuff gets even stranger than.

Ragib Zaman

but basically, it turns out that we cant get all 4 desirable properties at once, we must reject one of them

Jonas Teuwen

@RagibZaman Translation invariance.

Ragib Zaman

yes!

BenjaLim

nite guys

Ragib Zaman

2:52 PM

If we keep "all sets measurable" we get the banach-tarski paradox

Jonas Teuwen

You are mentioning the Vitali set and whether it is measurable wrt the Lebesgue measure.

Zhen Lin

You don't need much set theory to go from the axiom of choice to an unmeasurable set.

Jonas Teuwen

But the condition that all sets must be measurable plus the translation invariance messes things up.

As you partition a nice set into very ugly ones using choice.

Ragib Zaman

Yup, you get things like Banach-Tarski

Jonas Teuwen

@ZhenLin Right, but perhaps we can change or add other axioms which make it impossible to construct a non-measurable set.

Zhen Lin

2:53 PM

Right. You can either give up translation invariance or countable additivity to get around this problem...

Jonas Teuwen

So we give up countable additivity.

And then use the Caratheodory construction.

Zhen Lin

Eh, how does one do analysis without countable additivity?

Ragib Zaman

Ok, but it seems like the best one to give up is that "all sets are measurable" no? The others seem far more useful.

And we don't often run into the problem "damn I wish this set was measurable but its not and this is a problem for me"

Countable additivity or translation invariance though? Invaluable.

Jonas Teuwen

@ZhenLin Subadditivity...?

That's what you do with outer measures.

Ragib Zaman

Are we talking about outer measures now?

Jonas Teuwen

2:56 PM

Then you find a restriction that improves the subadditivity to additivity.

So, I was wondering if we could actually skip all this.

Zhen Lin

hmmm

Jonas Teuwen

In the end we don't care much about $\sigma$-algebras, but only about our measurable functions.

So, they are like some technical thing to me that is there to make things work.

Zhen Lin

If every set is measurable, doesn't that mean every function is measurable...?

Jonas Teuwen

So why not take our measurable functions as primitives? But then again... the non-measurability messes it up.

@ZhenLin Yes. So that should mean that for the theory to fruitful, our "sets" should be less prevalent (in one way or another) than the ZFC sets.

It was just something I was thinking about while sitting in the coffee bar, nothing... profound.

I was wondering why we actually do all this stuff. It seems to serve no purpose other than make things work.

Ragib Zaman

I think that is indeed at the core of it all.

Henning Makholm

2:59 PM

Isn't that a noble purpose, though?

Zhen Lin

Well... that is what a lot of mathematics is about...

Jonas Teuwen

We usually restrict the set of objects on our general space. Why not restrict the space instead?

Yes, I know :-).

But that doesn't mean that I should not think about it, right? :-).

Transcript for

$Mathematics$ Mathematics