This is the Realm of Simply Beautiful Art

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Simply Beautiful Art

01:15

https://www.mersenne.org/
If your computer finds a prime with 100,000,000 digits, you could win $50,000, and its not hard on your computer

10 hours later…

Simply Beautiful Art

10:57

C(α, ß, 0) = {0, 1}
C(α, ß, n+1) = C(α, ß, n) U {σ+µ, σµ, σ^µ, Ω_σ, psi(σ, Θ), sup(C(0, Θ)) | σ, µ, Θ in C(α, ß, n), Θ < ß}
C(α, ß) = U C(α, ß, n) for n < ω
psi(α, ß) = sup{δ | δ in C(α, ß), δ < Ω_(ß+1)}

@user21820

Mithrandir

It's all Greek to me

user21820

@Mithrandir: Literally, you're right!

αβδσμθψω are all letters of the Greek alphabet.

Mithrandir

I know, that's why I said that ;)

user21820

@SimplyBeautifulArt: I just noticed that you wrote it in unicode! So easy to read lol! But actually, why don't you just learn the little bit of set theory that you need so that you know exactly how transfinite induction works, and then you can check yourself whether it works out?

SBM

11:50

hello

shredalert

Hello @SBM

SBM

hello @shredalert

shredalert

What's up? @SBM

SBM

looks up, ceiling.

Have chemistry exam tomorrow

preparing

shredalert

12:06

@SBM Hope it goes well.

SBM

thank you

Simply Beautiful Art

12:21

@user21820 Unicode on mobile is horrible

To type I mean

user21820

What browser are you using?

SBM

but you can use ChatJax

Simply Beautiful Art

13:16

Hey @LearnHowToBeTransparent

@user21820 chrome

@SBM meh, Unicode doesn't look so bad

user21820

13:32

@SimplyBeautifulArt I use Transliterator on Firefox that allows me to easily type Greek letters in any textbox. The advantage of Unicode is that it can be copied into an email, and I use that quite often

Simply Beautiful Art

Mhm...

@user21820 you missed one

user21820

Well I've the whole lot but I only typed those I thought you used.

Aha μ.

Simply Beautiful Art

And capital Omega

user21820

By the way, θ is the small letter and Θ is the big letter.

Simply Beautiful Art

Yeah

user21820

13:37

Ya.. Ω. At least ο,Ο,ω,Ω,Θ are very useful for asymptotic expansions.

Simply Beautiful Art

o.O

(^ω^)

ψ(｀∇´)ψ

Lol, phone emotes are where most of my greek letters are

user21820

Aren't they? I use them all the time, and it was one reason I went to the trouble of getting a Firefox extension for that purpose...

Plus δ,ε for real analysis of course.

Simply Beautiful Art

Mhm...I'll look into it

(σˋ▽ˊ)σ

::wonders how large of an ordinal I can make without getting too complicated::

user21820

Haha..

Simply Beautiful Art

That last one isn't too complicated and goes up to psi(psi_I(I))

I is first weakly inaccessible ordinal

I think

user21820

13:46

Uh how do you get to that point without essentially diagonalizing against provably total functions in ZFC? Which would be far easier too.

Simply Beautiful Art

I think it was the axiom of inaccessible cardinals

user21820

The existence of an inaccessible cardinal is equivalent to Con(ZFC) over ZFC.

Simply Beautiful Art

Mate, do you think I know what you're saying?

::probably should::

user21820

Well if you don't then I can quite safely assume that you didn't actually get to such a point. =)

Simply Beautiful Art

I can only describe how it diagonalizes

But no more than that

user21820

13:50

I guess you don't get my point; almost any ordinary reasoning that any professional mathematicians (who are not set theorists) use can be formalized in ZFC, so it cannot possibly prove Con(ZFC) and hence cannot prove totality of a fast-growing function that reaches anything to do with inaccessible cardinals.

Simply Beautiful Art

Hm, well, I made the thing above, so I sorta know what I'm doing I suppose

@user21820 yeah I know

user21820

As always, you can ask Deedlit. =)

Simply Beautiful Art

I know

He's not online often recently though

user21820

Yea.

shredalert

I think I saw him on yesterday, briefly. Memory might be playing tricks on me though.

Simply Beautiful Art

13:53

@shredalert yes, memory is difficult for the insane

;)

user21820

Anyway I'm going off for now. See you all next time!

Simply Beautiful Art

@user21820 see you!

shredalert

define sane @SimplyBeautifulArt lol

user21820

@shredalert Sane ≡ Rational ∧ Positive. =D

shredalert

what does it mean to be rational? And why positive? Much aribitrary. lol

user21820

14:00

Rational ≡ Equals to the ratio of two integers. Negative people have higher tendency to go insane. Just a joke.

Simply Beautiful Art

shredalert

Much joke, such funny @user21820 :P

Simply Beautiful Art

14:17

lol

The somewhat decent ordinal collapsing function :-)

Mithrandir

→ 72 messages moved to Sandbox

Riker

i have no clue wat that means ;P

Simply Beautiful Art

@user21820 I don't think inaccessible cardinals are truly necessary to describe the supremum of this one, right?

@Riker 'tis okay, just return to whence you've been

Riker

kek ok

I SHALL BEGONE

Simply Beautiful Art

what a strange place my realm is

shredalert

14:40

a strange realm is a good realm

Simply Beautiful Art

yup

user21820

@SimplyBeautifulArt It's the same as the unicode one right? I looked at it but didn't have any immediate clue whether it was well-defined or not.

Which is what prompted my response advising you to learn the theory of ordinals so that you can prove it yourself. =D But I am 99.99% sure that if it is well-defined then it can be proven in ZFC and hence won't need an inaccessible.

shredalert

nap time

user21820

@shredalert: Good nap!

shredalert

ty @user21820!

Learn How To Be Transparent

14:55

me too, nap time.

Simply Beautiful Art

@user21820 okay

5 mins ago, by user21820

@shredalert: Good nap!

user21820

Haha. If you click on the little arrow next to your last message to me, what happens? On my computer the yellow box causes the content to increase in number of lines.. looks like a GUI bug to me.

Simply Beautiful Art

Hm...

It works fine for me on mobile

user21820

Well I guess it's just that the yellow box is smaller so depending on the screen width it may be just overflowed.

Simply Beautiful Art

Yeah true

2 hours later…

amWhy

16:56

Get up, nappers! Splash cold water on your faces!

Simply Beautiful Art

@amWhy :-(

amWhy

17:17

:p You're lucky; I was going to include a link to an audio file of an alarm clock!

shredalert

17:30

I had to wake up and go out for a bit

Simply Beautiful Art

@amWhy xD God no thank you

2 hours later…

shredalert

19:39

So my mathematics reading list for the summer: Logic, combinatorics, graph theory, theoretical computer science.

amWhy

20:19

I've just added my another book to my current list of 1,273,999 books to read over the summer....hmmmmm, am I setting myself up for failure, or what?! :D

@shredalert Ambitious, but if you're like me, I like to have goals, and to reach them within a time frame! (My comment above is not to be taken tooooo literally, though!)

shredalert

Goals and I don't go well together.

amWhy

@shredalert Do you like the term "aims", "intentions", or "commitments", or some other alternative to "goals" (I'm not terribly fond of the term "goal(s)" myself).

shredalert

I just give myself a rough reading plan

I split it between fiction and study as well

Mithrandir

@amWhy I guess we're tied in the number of books we have to read...

shredalert

anyway off to read some more LOTR

amWhy

20:26

@shredalert Good Reading to you!

shredalert

will finish off my assignment tomorrow (deadline midnight tomorrow) lol

tyty

Mithrandir

Good.

AlwAlways readread LotR.

shredalert

my first time reading it

Mithrandir

O_o

shredalert

I read The Hobbit recently, and am on the last chapter of the fellowship (I have the single volume edition of LOTR)

Mithrandir

20:27

My username is from LotR.

shredalert

I know lol

Mithrandir

And avatar, but the movie

WhiWhich I havehaven't seseen

shredalert

The films I've watched when they were released. So I'm late to reading the books. But got around to it eventually.

LOTR is different in quite a few places from the films but The Hobbit is absolutely changed and unrecognisable. The film is nothing like the book. Hell, the ending is not even the same.

3 hours later…

Simply Beautiful Art

23:24

A: How far do known ordinal notations span?

As far as computable ordinals go, the ordinal collapsing function goes pretty far. Here is one, for example: $$C(\alpha)_0=\{0,1\}\\C(\alpha)_{n+1}=C(\alpha)_n\cup\{\gamma+\delta,\gamma\delta,\gamma^\delta,\omega_\gamma,\sup(C(\eta)),\psi_\gamma(\eta)|\gamma,\delta,\eta\in C(\alpha)_n,\eta<\alp...