Mathematics

Martin Sleziak

8:00 AM

(It feels almost ridiculous that such a trivial question causes so much discussion.)

robjohn

@MartinSleziak No, I was being serious. I missed the discussion.

@JM haven't had the chance to read the transcript (and I don't know if I will :-)

Martin Sleziak

@JM That bug is interesting. I can't see the reason why backslahs is added to the title.

@robjohn I think the comments explain it all. (It was mentioned in the chat, but it was not discussed here so much.)

But basically: Several people did not agree with the reasons for (the first) closing and discussed at lengths whether it was correct decision and whether it should have been closed, and that it was closed prematurely. The question was closed as non-constructive first time, then reopened and closed again as exact duplicate.

This is basically the summary of the whole thing, as far as I can say.

Skullpatrol

I have a quick fun math question, first right answer wins. Question: I am four times as old as my daughter, in 20 years I will be twice as old as her. How old am I now?

robjohn

@MartinSleziak I just read the comments. I didn't see the comments when I was asked to vote to close, but I looked at the question and the proposed original, and it looked like a duplicate to me, so I voted to close as a duplicate.

40

Skullpatrol

We have a winner!!!

Asaf Karagila

8:11 AM

Top of the morrow to you folks.

robjohn

@AsafKaragila Hey Asaf!

Skullpatrol

@AsafKaragila Hello

Asaf Karagila

@robjohn: It's late out there, no?

robjohn

@Skullpatrol perhaps only someone not doing something offscreen :-)

@AsafKaragila just past midnight.

Asaf Karagila

Ah, it's fine then.

robjohn

8:13 AM

@AsafKaragila Are you imposing a curfew here? ;-p

Matt

Morning Asaf!

Asaf Karagila

@robjohn Only on teenagers.

@Matt What's up?

Matt

@AsafKaragila Nothing. Are you feeling better?

robjohn

@AsafKaragila I was a teenager once...

I am a teenager emeritus

3

Asaf Karagila

@Matt Somewhat better.

Matt

8:15 AM

@robjohn : )

Skullpatrol

@robjohn O.K. smarty here is another one: What does moving towards each other and moving away from each other have in common?

robjohn

@Skullpatrol moving?

Asaf Karagila

@Matt How's forcing?

Skullpatrol

@robjohn Too obvious ... but true

there is something else

robjohn

@Skullpatrol was there something else you were looking for?

@Skullpatrol okay... they simply differ in time, but let's see...

Skullpatrol

8:23 AM

@robjohn no need to bring in Relativity theory ... but this is also true

robjohn

The first thought that came to mind was that they are the same motion viewed before and after passing each other.

Skullpatrol

We have a winner!!!

robjohn

@Skullpatrol That's what I meant about time difference

Matt

@AsafKaragila I'm about to do some FA : )

Asaf Karagila

Forcing Axioms?

robjohn

8:24 AM

@Skullpatrol Ah, so my time difference idea was what you were looking for.

Matt

Functional Analysis

Asaf Karagila

Too bad.

robjohn

@Matt Futile Attempts

Skullpatrol

@robjohn Simply put they are both moving in opposite directions.

Matt

@robjohn : P at what?

robjohn

8:26 AM

@Skullpatrol okay. When there are so many answers, it is like a "what's the pattern" question

@Matt I'm not saying your Functional Analysis will be futile...

Daniil

Does the known Jech's book on set theory includes information I need to know about "models"?

robjohn

@Matt just figuring out the anagram.

Daniil

(not sure myself what that means, but it sounds cool)

Asaf Karagila

@Daniil Not really.

It talks about inner models and such, but I'm not sure if that's what you mean.

Matt

@robjohn I know that's why I'm asking. If FA stands for futile attempts -- then what am I attempting?

robjohn

8:28 AM

@Daniil All I know about models, I've learned from the obverse of the centerfold.

2

Matt

Futile attempts at ignoring this chat and getting focus on the homework maybe.

: )

Daniil

hi matt

robjohn

@Matt as good as any :-)

Matt

Need a coffee first though. Nothing better than the first cup of coffee of the day : )

Daniil

Addiction: confirmed.

Matt

8:29 AM

: D

Martin Sleziak

@Daniil Just to clarify: You mean models as models of ZFC or models as in model theory? (Perhaps after clarification someone will be able to give you a better answer.)

Daniil

@MartinSleziak models of ZFC

robjohn

@MartinSleziak or December 2011

Daniil

Well, can I say models of logical systems?

robjohn

@Daniil you can say whatever you want. It's a free internet...

Asaf Karagila

8:31 AM

@Daniil: The working assumption is always that ZFC is consistent, there is no real point to working with it otherwise; so it has a model. However since we want to work inside that model, it cannot be a set. So we usually just assume it exists and go forth.

Daniil

Well, does what I say make any sense whatsoever?

Skullpatrol

@robjohn It's true that there are so many answers, and it is like a "what's the pattern" question, but don't you think that the answer: "they are both moving in opposite directions," is a simple way of describing the pattern?

Daniil

@AsafKaragila I see... I really should start reading that book you recommended.

robjohn

@Skullpatrol certainly, but so were the other answers I gave, I thought.

Daniil

Btw, what about this: gowers.wordpress.com/2011/11/28/… Is this comment true?

Asaf Karagila

8:33 AM

Jech?

Daniil

@AsafKaragila yeah

Skullpatrol

@robjohn I Agree

Asaf Karagila

@Daniil Which comment?

Daniil

Tom's comment. I linked it.

I can also give a quote

> Surely most mathematicians ignore ZFC (and all other axiomatizations of set theory).

> There’s an implicitly agreed collection of “naive” rules about how sets can be manipulated, and this forms a kind of fixed framework for almost all non-set-theorists. But that collection of rules is definitely not ZFC. It’s probably more like what appears in the first year course that Tim is writing about.

Asaf Karagila

It is half true, in my opinion.

They do ignore ZFC, but almost everything they do involving sets is a subset of the rules of ZFC.

Zhen Lin

8:36 AM

Although occasionally something big is assumed like global choice.

Asaf Karagila

Saharon Shelah told me once that a good set of axioms is one that you don't "feel" when you use it. It should feel natural.

Skullpatrol

@robjohn In fact your answer: " they are the same motion" is the simplest way to describe it ;-)

Asaf Karagila

Most mathematicians, I'd imagine, are living in L which is a very thin model but it has GCH and Global Choice, etc etc.

Martin Sleziak

One of the pair of duplicate question was closed and now some people are voting to close the other one: math.stackexchange.com/questions/87907/…

robjohn

@ZhenLin is global choice like karma? ;-)

@Skullpatrol that is the first thing that came to mind...

Martin Sleziak

8:40 AM

@ZhenLin Most uses of global choice could be replaced by Scott's trick I would guess. (At least those ones I have seen - which is only a few.)

Asaf Karagila

@MartinSleziak Not always.

Martin Sleziak

@ZhenLin I guess you have seen it in category theory somewhere. (IIRC Adamek-Herrlich-Strecker mention global choice in their book.)

Zhen Lin

Indeed. For example, the "fact" that a fully faithful essentially surjective functor is an equivalence uses global choice.

The problem here is that we very much do need a member of each equivalence class.

Martin Sleziak

I also remember seeing global choice in Chang-Keisler, which I did not read but I had a brief look as it was recommended for one of the courses I take.

But that are probably all my encounters with it.

I remember reading somewhere that adding global choice is a conservative extension, so if I am only interested in proving facts about sets and not about classes, it does not really matter whether I am using it.

Skullpatrol

@robjohn Thank you for your answers.

robjohn

8:44 AM

Oh, dear! Global Choice is for sale!

Martin Sleziak

But I would guess that proof of that fact is not easy.

Matt

@robjohn Are you looking for xmas presents for Asaf?

Martin Sleziak

@ZhenLin Also the proof that each category has a skeleton would probably use global choice.

robjohn

@Matt :-D

Zhen Lin

@MartinSleziak: No, I think that one can be circumvented with Scott's trick.

Skullpatrol

8:47 AM

@robjohn How can a "A World of Opportunity" be for sale?

robjohn

@Skullpatrol Sounds like a bargain to me...

Zhen Lin

It's clear that the objects of the skeleton category can be the sets that Scott's trick gives us. What's not obvious is whether we'll be able to define the morphisms correctly.

Skullpatrol

@robjohn When opportunity knocks it's not supposed to be selling anything at a bargain price is it?

robjohn

@Skullpatrol Well, if it's selling encyclopedias, close the door.

Transcript for

$Mathematics$ Mathematics