Mathematics - 2017-06-15 (page 6 of 9)

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6:00 PM

The $a_n$ being reals

@theDoctor I just posted a link where he did.

that's geometry -- yet another domain crossover!

@SteamyRoot I actually understand that lol

@SteamyRoot Do you know why he writes - -

math people need to work out domain boundaries, because they've been VERY sloppy.

$\bb A$ is not $\bb Q$ is not $\bb R$ is not $\bb C$.

6:01 PM

Define domain?

> & [et] il suffist [suffit] de les designer par quelques lettres, chascune [chacune] par une seule.

there is no rigor to just using them across domains because different domains have different AXIOMS!

@Krijn No idea :/

domain -- an ordered arena in math defined by a set of axioms.

> Comme pour adiouster [ajouter] la ligne BD a GH, ie [je] nomme l'une a &[et] l'autre b,&[et] escris [ecris] a+b

6:02 PM

replace arena with field, if you wish.

and the relevant part:

> Et aa, ou a^2, pour multiplier a par soy mesme [soi meme]; Et a^3, pour le multiplier encore une fois par a, et ainsi a l'infini.

@theDoctor Who's been sloppy?

mathematicians.

@Krijn math people. all of them.

Define arena?

6:03 PM

@Krijn That sounds like a question for HSM.SE, tbh

@TheGreatDuck: :^)

I have not been sloppy :(

Also "field" is a well-defined mathematical notion.

Who's being sloppy with terms now?

@Krijn don't lie. We all know you are a messy eater.

^

6:03 PM

@Krijn: well can you start moderating down all these sloppy ones on SE?

What grade are you in?

let's just delete all the sloppy posts and ban the heathen that dare post it!

XD

@SteamyRoot: Probably you justa little. The world field implies more than one dimension.

@Astyx does $E[X] = 0$ and $-1 \le X \le 1$ ?

Like "corn field".

6:04 PM

Erm....

Field (mathematics)

In mathematics, a field is a set on which are defined addition, subtraction, multiplication, and division, which behave as they do when applied to rational and real numbers. A field is thus a fundamental algebraic structure, which is widely used in algebra, number theory and many other areas of mathematics. The best known fields are the field of rational numbers and the field of real numbers. The field of complex numbers is also widely used, not only in mathematics, but also in many areas of science and engineering. Many other fields, such as fields of rational functions, algebraic function fields...

Field is perfectly well-defined

A set is too sloppy too.

Troll alert

Yeah, pretty much.

@theDoctor Bravo.

6:05 PM

Is the set $\bb R^2$ the same looking as $\bb R$?

@user685272 well yeah. I know I am a troll. :-(

I'm not a troll, i'm just really miffed.

@theDoctor No.

that's why I constantly get chat banned.

:p

that I'm having to clean up the field, and I'm the one rotting in the basement.

Call me Lazlo.

Can you even enumerate the field of real numbers? I think I found a way actually.

6:07 PM

Yawn...next question troll

At least this kind of crankery makes me feel better about my students' awful exams.

@theDoctor show me your way.

Akiva Weinberger

Qué pasa

Sets are well-defined, but a field....

@SteamyRoot This is one of the reasons I TA

Also one of the reasons why I don't feel incredibly stupid all the time, just most of the time

6:09 PM

Tell me how do you order your field/set of $\bb R^2? Is it sets within a set?

What's happening here?

@AkivaWeinberger hay un hombre aqui que tiene ninguna idea de lo que esta diciendo

@theDoctor dont impersonate poor @lazlo

Akiva Weinberger

The LaTeX is \Bbb R^2

or \mathbb R^2

otherwise it doesn't render

Ew, \Bbb

6:09 PM

@theDoctor lexicographical order.

Define number @theDoctor

Akiva Weinberger

@SteamyRoot I've been using it the whole time

@Dodsy The doctor is impersonating Lazlo. Oh, and I am a troll confirmed.

Akiva Weinberger

TARDIS noises

@AkivaWeinberger One day backwards compatibility will be abandoned!

6:10 PM

@Dodsy il y a un type ici qui a aucune idea de ce que il dit

Well, I know that you're a troll.

Switch while you can!

@SteamyRoot: Come on a lot of math is awfully, shall we say.... just messy hand-waving.

2 mins ago, by theDoctor

Can you even enumerate the field of real numbers? I think I found a way actually.

@theDoctor I'm still waiting for your way.

@theDoctor Ummm, no.

6:10 PM

@LeakyNun Sorry, my french is rusty, though being Canadian.

Not if you do it properly.

@LeakyNun: oh... one moment...

Akiva Weinberger

If it's $0.00\!\dots\!1$, $0.00\!\dots\!2$, etc., it doesn't work

I found a way to order the complex numbers...

@AkivaWeinberger solo dejalo hacerlo; quiero saber lo que el diria (out of curiosity)

6:11 PM

@AkivaWeinberger Actually, given your age, I'm guessing \Bbb has been deprecated since before your birth, lol

To enumerate the field of real numbers, use the "reverse odometer":

@theDoctor is that a fancy name for the flux capacitor?

Akiva Weinberger

@TheGreatDuck There's a bunch of ways to order them... just no way that's compatible with the field operations

@AkivaWeinberger quiero saber lo que pasa en los mientes de personas como el

0.000... we'll say is the starting number since it's not easy to start at the other end (LOL)

6:12 PM

@LeakyNun
Ich denke, du meinst zu sagen, dass es in diesem Chatroom eine Düne gibt?

@AkivaWeinberger i found one that is compatible.

no listen, it's actually the only way I've ever seen suggested so shut your trap.

@TheGreatDuck sure

it is called... MODULUS!

@Dodsy was ist eine Dune?

6:12 PM

@LeakyNun Dunce* :P

I really want to know what he would say. People, please let him talk.

Does 0.999... = 1.000.. @theDoctor

@theDoctor Why... would anyone listen when we all know you cannot ever enumerate them?

Akiva Weinberger

@user685272 He's not finished

@Krijn I would listen.

Akiva Weinberger

6:13 PM

@theDoctor OK, what's the next one?

0.1, 0.2, 0.3...0.9, 0.01, 0.11, 0.21, 0.22..., 0.03. As you see..

The Doctor is a time lord. Surely he can distort the real numbers and show they are discrete?

Akiva Weinberger

Ah. And when do you get to infinite decimals such as $0.333\bar3$?

@Dodsy ich verstehe dich nicht noch

the numbers simply count the integers in a mirror image.

Akiva Weinberger

6:13 PM

Or $\pi$?

to the right of the decimal.

Hahahaha

who can say then the odometer turns over and you get to 1.0?

I needed this

Akiva Weinberger

@theDoctor That never gets any infinite decimal. In particular, it never gets to any irrational.

6:14 PM

@Semiclassical Well, anyway, I got a reply. The guy said he made a mistake, so it was wrong.

@AkivaWeinberger it doesn't even get to $0.\overline3$

If you've found an enumeration, then the how manieth number in your enumeration is $\pi$?

@AkivaWeinberger: Keep in mind I'm not the idiot who suggested the concept of a field as a SET.

Akiva Weinberger

"How manieth"? lol

@SteamyRoot Seventh

Akiva Weinberger

6:14 PM

@theDoctor Why's that idiotic?

@theDoctor:

1 min ago, by Akiva Weinberger

Ah. And when do you get to infinite decimals such as $0.333\bar3$?

1, 2, 3, 4, 5, 6, $\pi$, 7, 8, 9

lots of crackpots in here these days

@LeakyNun ein Dummkopf in das Chat.

Akiva Weinberger

I mean, it can have an underlying set easily

6:15 PM

@AkivaWeinberger: well, look at the questions lampooning the idea. If a set cannot be enumerated is it conceptually valid as a SET anymore?

Akiva Weinberger

Jesus Christ, everyone, the guy made a simple mistake, no need to mock him

(Her?)

@AkivaWeinberger ah, ja.

enumerated = iterated.

@AkivaWeinberger he's a troll. It's on purpose. He knows it doesn't work.

@theDoctor you'll never get to $0.\overline{3}$.

6:16 PM

Yeah, back to grading programming exams and reading science communication papers.

@AkivaWeinberger please forgive me.

@TheGreatDuck not really a troll to me; just a crackpot.

What number is BETWEEN 0.999... And 1.000... @theDoctor

Akiva Weinberger

@theDoctor You can't write it out as a list of things in curly braces, but there's nothing preventing you from considering it to be a set

so you get to the infinite decimals, like 0.3333... just before it slips over from 0.333.....2 lol

6:16 PM

@LeakyNun no. He is certainly a troll. He's been in here before claiming that every man on Earth was homosexual.

literally

Akiva Weinberger

A set is (roughly) just a collection of objects. What's wrong with considering the collection of real numbers?

in all seriousness, the real issue is for you to define the ellipsis symbol "..." mathematically. Go ahead.

@AkivaWeinberger it's actually counter-intuitive. It depends on AoP.

Akiva Weinberger

Axiom of... powerset?

@AkivaWeinberger yes.

6:17 PM

@@TheGreatDuck: Who was saying that?

Akiva Weinberger

Yeah, I guess it does

Goes on without end

@theDoctor you. Don't lie

what goes on?

@TheGreatDuck Sigh....

6:18 PM

Shall we go back to actual mathematics?

@thegreatduck:

@theDoctor I try to avoid the ellipsis in formal mathematics.

Akiva Weinberger

@Krijn raises hand I'm all for it

the ellipsis is an informal notation, I will admit that.

The pattern

6:18 PM

@Dodsy what? Is he the wrong guy?

I think you're getting into the confusion about whether humans on earth are homo sapiens or hetero sapiens.

:p

@AkivaWeinberger and not to mention AoI

Akiva Weinberger

@theDoctor Haha, puns

@LeakyNun ...Fair

read his profile math.stackexchange.com/users/39676/marxos rofl

6:18 PM

@theDoctor homo, Latin for man, has nothing to do with homo, Greek for same.

@theDoctor no. Homosexual... as in gay.

Akiva Weinberger

Well, that's the one Wildberger hates

(No relation! :P )

What is happening...

First of all, I don't like this.

@Dodsy trolls.

Akiva Weinberger

@Dodsy I don't even know

6:19 PM

I don't like this either

let's go back to ripping apart fields.

with a scythe

Akiva Weinberger

Why do we hate fields??

Oh, that type of field

@LeGrandDODOM sock confirmed. 1. "suicidalburg" 2. crackpot 3. pangaia.sf.net

I don't want to hear bigotry in here, please.

Akiva Weinberger

I've never seen a scythe in real life

@AkivaWeinberger we don't hate fields. We harvest them.

6:20 PM

@Dodsy not really bigotry.

@dodsy: me either

@AkivaWeinberger You are privileged

in any case, how is a field "perfectly well defined" if you define it with sets and can't enumerate the set?

Stop feeding the troll guys

@user685272 I'm really interested lol

Akiva Weinberger

6:20 PM

@theDoctor Nothing wrong with sets that can't be enumerated

Although, $\Bbb Q$ is a field and you can enumerate it

so you really just don't like $\Bbb R$ and $\Bbb C$ and the like

@Dodsy there was no bigotry. I was saying that the doctor was a troll as a while back he was in here claiming that humanity was 100% gay. That's an obvious troll seeing as how that would obviously result in the end of the human race... and we have no issues in that sense. I'm sure we'd be hearing about that.

Number fields is all you really need in life to be happy

plus,I'm not gay so... 100% is a bit extreme

@theDoctor the existence of $\Bbb R$ depends on the axiom of infinity and the axiom of powerset. If you don't accept the two axioms I just stated, then you won't believe that $\Bbb R$ exists. [cc @AkivaWeinberger]

:p

6:21 PM

Now "thegreatduck" has me confused with someone else.

Please drop the conversation on sexuality, Duck.

Shhh

@AkivaWeinberger $\Bbb Z_2$ is even a finite field.

Akiva Weinberger

Yes.

Time out

6:22 PM

hey crackpot, I know the perfect channel for you to waste time on youtube.com/channel/UCXl0Zbk8_rvjyLwAR-Xh9pQ

@Dodsy you're the one who called it bigotry? I was just telling them why i thought he was a troll...

Akiva Weinberger

@LeGrandDODOM Knew it

Guys can we all stop

2

^

I think there is something wrong with a set that can't be enumerated. The beauty of sets is like the countable numbers themselves.

bizarre behavior

@theDoctor do you accept the axiom of powerset? If so, I can demonstrate to you that uncountable sets exist.

Akiva Weinberger

6:23 PM

They might be weird, but there's nothing impossible about them. @theDoctor

I must review the term, one moment.

Akiva Weinberger

(Set of all *subsets)

@AkivaWeinberger subsets

Akiva Weinberger

@theDoctor It's a foundations thing.

@LeakyNun Derp, that's what I meant

@theDoctor Sets do not need to be countable. Stop making up silly ideas. Sets are sets. That's it. Nothing more.

6:24 PM

I think, I haven't seen a good enumeration of $\bb R$ using powerset notions, either.

Akiva Weinberger

@theDoctor What he means is,

@TheGreatDuck: a moment ago you were hurling personal accusations at me, either stick with math or leave the discussion

Akiva Weinberger

you need the axiom of powerset to construct $\Bbb R$, and in fact any uncountable set.

@theDoctor I am sticking to math.

@ManolisLyviakis hello

now the combinations of {0,1,2,3,4,5,6,7,8,9}, could potentially be conceived to create all numbers in \bb R, but I haven't seen that notionl.

6:25 PM

@theDoctor if you accept the following two facts, then uncountable sets would exist:
1. there are countably infinite sets
2. every set has a powerset

@Liad Sorry I had to go. Indeed, then it's just convexity and power series. I should learn how to read once again

"uncountable" means that you can't enumerate them.

Akiva Weinberger

@theDoctor You only need {0,1}, really

you only need {}. Just ask Von Neumann.

@Astyx :)

Manolis Lyviakis

6:26 PM

guyz

@TheGreatDuck you only need ZFC-R

user image

@LeakyNun You only need the philosophy of measuring.

@TheGreatDuck measuring?

yes

real numbers are measurements

of distance

6:27 PM

@LeakyNun: Doesn't it fail at the empty set? Because it's not anumber

@theDoctor what are you referring to?

{} = 0

{{}} = 1

Akiva Weinberger

Oh, I've seen that book

the idea of a powerset as an enumeration of \bb R

Akiva Weinberger

Give it to your grandparents

6:28 PM

{{},{{}}} = 2

Akiva Weinberger

(Not really)

etc

lmfao

Akiva Weinberger

(Though I suppose they may be the intended audience?)

(It's a really weird book)

@theDoctor I didn't mean that powerset can enumerate $\Bbb R$. I meant that I can show you that $\Bbb R$ cannot be enumerated.

6:28 PM

that'd be mildly inappropriate.

@Dodsy give that book to a crocodile.

The real question here I think is the domain \bb R really mappable onto \bb Q? And I think not.

uuuhhh

no

Akiva Weinberger

There is no injection from $\Bbb R$ to $\Bbb Q$, correct

there are more irrationals than rationals

Akiva Weinberger

6:29 PM

(An "injection" is a one-to-one map, meaning it sends each input to a unique output)

i mean the common use of numeric symbols like "1" and "2" and "1" "+" "2" vs 1.0+2.0

@theDoctor do all data relate to other data?

there are not more irrationals than rationals, STOP propagating this tripe.

@leakyNun: haha, where did you read that?

@theDoctor yes or no?

@theDoctor i am not propagating tripe...

Akiva Weinberger

6:31 PM

@theDoctor There are. ("More" means that there is no injection from the irrationals to the rationals, or equivalently, no surjection from the rationals to the irrationals)

@LeakyNun: All data but NULL and random noise.

(not pseudorandom -- which DOES relate to other data.

Wtf

Yep. Sock confirmed.

Akiva Weinberger

...What does "sock" mean?

i can prove there are more irrational solutions to polynomials than rational solutions to polynomials via induction.

6:32 PM

Either you guys are all idiots or I'm a genius. Which is it?

Akiva Weinberger

(Eso sí que es — socks)

and i mean in the sense that we look at all combinations

Case closed

wait no

@AkivaWeinberger alternative account

6:32 PM

polynomials with integer coefficients

Who care about polynomials, I already showed that there's a domain cross over there which makes it sketchy math.

Troll

Stop feeding it

@user685272 i know. I'm sorry. I'll stop. It's just that it is fun to troll people.

Akiva Weinberger

@theDoctor Uh... Some of us may be bad at explaining stuff, though

Quick question about limit point compact. My book defines $X$ as being limit point compact if every infinite subset of $X$ has a limit point. My question is, what is meant by "has a limit point"? Does this mean that it contains its limit point?

6:33 PM

@AkivaWeinberger diciendo en espanol porque no quiero que el sabia lo que digo: este hombre se llama el profeta...

@theDoctor I was trolling you. Sorry.

@AkivaWeinberger delusivo es? no pienso que el es un troll... es algo mas severo que eso

Akiva Weinberger

You know he can just use Google Translate, right...?

@AkivaWeinberger I was uncertain before you said that, but now that you said that, then it's a yes.

why are you trying to hide messages from me?

is it cause you don't trust me...?

6:35 PM

@TheGreatDuck not from you

Google translate is not always right

Anyone know the answer to the question I posed above?

well google translate cannot be all right, otherwise there would be none of it left.

Just a reminder: if there's a user you don't want to interact with, there's always the "hide posts" option

Akiva Weinberger

There's a great 3-part online series on infinite sets, by the way: artofproblemsolving.com/school/mathjams-transcripts?id=182

(That's the first one)

6:36 PM

@Semiclassical :-( Please don't ignore me.

Akiva Weinberger

@Semiclassical Hm, I should probably hide some subset of $\{\rm theDoctor,TheGreatDuck,LeakyNun\}$ for the next hour or so

Lol. I meant more in the context of ignoring trolls

Hide all posts: thedoctor

WTF? Are all you guys poseurs that don't like the rigor of math, but only the excitement of arcana terminology?

Please leave.

6:39 PM

no

okay, stop

a subset of NOW.

Could someone help me with a question on modular arithmetics?

Akiva Weinberger

@theDoctor You haven't been rigorous at all for the entirety of this

2

You've just said that "something seems wrong" with sets that can't be enumerated

Someone unbanned me. :-(

Akiva Weinberger

6:40 PM

That's not a proof of impossibility

@LeakyNun Please shut up.

@FrimeKemic go ahead

Even if you think the behavior being shown is trolling (and I do) yelling at another user to leave is not productive/civil

2

@TheGreatDuck I removed a post from a while back that was not compliant with Be Nice, but didn't feel the suspension was presently necessary or relevant.

Nor is baiting a troll

@AkivaWeinberger sorry

6:41 PM

@doppelgreener Well that's because it was a combination of flags.

from users in chat

Hence my comment earlier re: hiding posts.

@LeakyNun I'm trying to prove that a certain formula is a $3$-cocycle but something is not going well

@TheGreatDuck No, this one I removed at my own initiative. There weren't any flags on it.

oh

(There should have been, though.)

6:41 PM

@LeakyNun See math.stackexchange.com/questions/2323594/…

there were flags on others though, right?

accusing him of stuff

If you think you're interacting with a troll, then there's nothing useful to be gsined from it

@Semiclassical exactly. I'm a troll. Everyone ignore me. rolls eyes

@FrimeKemic sorry, no idea

Akiva Weinberger

@theDoctor Obviously, it's very counterintuitive that there exist sets that can't be enumerated (known as uncountable sets). But they do exist; $\Bbb R$ is one of them. It is not obvious how to show that $\Bbb R$ is uncountable; the standard argument is Cantor's diagonal argument, which you may have seen before.

6:42 PM

@TheGreatDuck I may not have seen all the flags from today, but I did see a couple of flags from you on your own posts which were not ones I could discernibly action.

@LeakyNun Thanks anyway

uuhh

Akiva Weinberger

If you do agree that $\Bbb R$ is uncountable, all that remains is to see that it's a set; this is more a matter of definition than anything. @theDoctor

i didn't realize you guys could see who was making the flag. This is awkward.

(At least, I think they were from you? Maybe I misunderstood the flag interface. I've only been a mod for a month and a week.)

6:43 PM

@AkivaWeinberger: why would you believe that $bb R is a set?

Akiva Weinberger

@theDoctor "Set" is just the word we're using

Whoa, things have escalated in the 20 minutes I was gone, it seems

Akiva Weinberger

It's really a matter of definition

The word "set," in mathematics, allows for uncountable things.

@doppelgreener I thought those were anonymous. Figured you'd guys would just take them as offensive and remove them. :p

Lmfao.

6:43 PM

popcorn.gif

@AkivaWeinberger: it's not just a word -- it means something quite precise to me.

@theDoctor for the construction of the real numbers, go read up on dedekind cut or cauchy sequence.

Duck, you know people can see who is flagging.

Dedekind cuts

the word set or the concept of set?

6:44 PM

$\mathbb R$ is constructible, why wouldn't you believe it's a set

@Dodsy I was using the custom flag.

@Semiclassical sure, sorry

I miss ted.

Akiva Weinberger

@theDoctor Of course.

ted isnt here anymore? :(

6:44 PM

The way I tend to think of power sets is in terms of binary sequences

@TheGreatDuck Like I said, there wasn't any actionable request in the flag message.

I just gave a partial construction for R, what is yours?

Ted is in Italy

oh

How do you create a room?

Akiva Weinberger

6:45 PM

@theDoctor But the way the word "set" is used in English is not necessarily the same (precise) way it's used in mathematics.

If I have n binary digits, I can represent 2^n different objects

Akiva Weinberger

That's true for lots of mathematical terms.

@AkivaWeinberger like the prefix "co" in certain fields of mathematics.

@doppelgreener by any chance, was there supposed to be a chat ban on me? A few days ago a mod messaged me saying I was banned from chat for a month. Yet... no ban.

Akiva Weinberger

@Dodsy Not quite what I mean

6:46 PM

@AkivaWeinberger like the word "real"

Akiva Weinberger

I mean things that have precise meanings, but don't necessarily match up with what you think the word should mean

O o o

the word root

2 is an odd prime!

no.

Akiva Weinberger

@theDoctor In any case, what's your precise meaning of set?

6:47 PM

@SteamyRoot Thanks for backing me up on that!

If I then use these 2^n sequences as labels of binary digits, I can represent 2^(2^n) different objects

@AkivaWeinberger Well, the prefix 'co" in english means to be one with, or part of something. But in (i think it's linear algebra?) math co means in the opposite category of. Or, the opposite of.

Akiva Weinberger

Oh, I see

a coconut is just a nut

right.

6:48 PM

To get to something uncountable one should start with a binary digit for each natural number

@TheGreatDuck I am not sure. That must be quite a weird limbo for you to be in. :l

@doppelgreener yeah. Probably should just follow through on the ban? Might be better that way so nobody accuses me of ban dodging?

ideally I should say something re the diagonal argument but uh

i mean, what's the worst that would happen?

I'd rather not :p

6:50 PM

@TheGreatDuck Safe to say "someone forgot to give you the suspension at all" won't be counted against you as any sort of ban dodge on your part.

Don't ban our ducky

@user685272 you must not know him well..

@user685272 but I'm a troll. :-(

:/

all i do is spam all day.

6:51 PM

Okay I'm gonna go do homework, when I come back everything will be back to normal.

just look at my message count

Go find skull patrol and ban him for life.

@dodsy Riiight (idontbelieveyou)

Akiva Weinberger

So, I have a puzzle

@doppelgreener true, but if it intended to happen then it should happen, right? :/

Akiva Weinberger

6:52 PM

to which I do not know the answer

Are you all familiar with the Kuratowski definition of ordered pair? $(a,b):=\{\{a\},\{a,b\}\}$ IIRC

(Well, 'definition,' 'construction,' same thing)

I am now

Akiva Weinberger

This isn't what's known as flat.

oh lord, thedoctor is infecting hbar now

Akiva Weinberger

The rank of $(a,b)$ is two more than the maximum of the ranks of $a$ and $b$.

Supplementary info done for now, awaiting my supervisors review. Tmr might be able to do some ordinal collapsing before continue on the literature review

6:54 PM

Oh lawd

@TheGreatDuck I can't find any records about that, and I'd prefer to leave it up to whatever moderator mentioned doing that.

Akiva Weinberger

($\{a\}$ has a rank one higher than $a$, for example)

hehe

fair enough

Akiva Weinberger

So, the question is, is there a construction of ordered pair such that its rank is the same as the maximum rank of $a$ and $b$? So it doesn't unnecessarily increase the rank

This would be called a flat ordered pair

:-(

Akiva Weinberger

6:55 PM

We still want $(x_1,x_2)=(y_1,y_2)\iff\forall i,x_i=y_i$

@doppelgreener Fair enough. i suppose that would make sense. I think the mods post got deleted later.

Are there any Martin Hardener article on polynomials (not polynomino) ?

@AkivaWeinberger what is the rank of $\{a,\{a\}\}$?

Hmm. maybe it would be a good idea to start with a finite collection of rank-one objects

Akiva Weinberger

@LeakyNun Two more than the rank of $a$

It goes by the maximum

And $\{\{^n\}^n:n\in\Bbb N\}$ has rank $\omega$ :P

6:58 PM

@TheGreatDuck consider yourself off the hook. you might've misunderstood something; maybe no suspension was intended for you to begin with.

2

Akiva Weinberger

(Using that notation trick thing again)

Any idea on my question ?

@doppelgreener ok thanks.

Akiva Weinberger

Ordinals all equal their rank.

@AkivaWeinberger I don't really think it's possible, although I don't have a proof.

6:59 PM

What I have in mind is: if I take an ordered pair of two rank-one objects

Where should I ask it to get yes/no answer ?

You'd want that ordered pair to also be rank-one, yes?

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$Mathematics$

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