@Ramanujan Hey man

@Ovi Hey

@Deedlit math.stackexchange.com/questions/1745275/…

@SimplyBeautifulArt Hi

@SimplyBeautifulArt So sadly my report for today is only 1.5 hours :(

I will try to do much better tomorrow

@SimplyBeautifulArt heh, sorry you are dying outside from collapsing functions. :D

I find them a lot of fun... very mind-stretching.

About the upper bound to TREE(3), see here: math.stackexchange.com/questions/1811602/…

According to Anreas Weiermann's answer, there is in fact a method to compute a reasonable upper bound to TREE(3), it's just that it would take a lot of work and no one seems to be interested in it (and would probably not be publishable).

But, I think we can be confident that it is on the order of f_{theta(Omega^omega * omega, 0)}(n) for reasonably small n.

@Ovi I spent at least four hours learning more about ordinals

What did you learn so far?

@user21820 a lot of veblen ordinals and ordinal collapsing functions

And then shoving it back into fast growing hierarchy

Haha so I see you're going to become a serious googologist.

XD

I actually feel on the verge of giving up

Oh why?

The stuff is too big for my own understanding

XD

Hmm do you know the standard construction of the ordinals and cardinals?

Sort of familiar

Some of those fast-growing hierarchies do require some set theory background, which can be tricky.

Can we put uncountable ordinals into FGH?

If you're referring to this FGH, then of course not because we need to be able to diagonalize.

Ah, ok

So there is no diagnolization to countable ordinals (thank God)

Specifically, since we want functions on N, when we define f[a] where a is a limit ordinal we need to find a countable sequence of ordinals below a whose limit is a.

This already forces us to be stuck at the countable ordinals.

For it to be computable we need this sequence to furthermore be computable.

That actually forces us to be stuck below ω[1]^CK.

Lol

Thanks man

You don't like uncountable stuff?

(I don't but I'm surprised when others don't because the current foundational system is ZFC.)

Haha..

No no, I just don't like putting more things into FGH at this point XD

I like my functions to stay theoretically computable

Ah I see.

I myself have trouble coming up with computable functions too far beyond the kind I have constructed.

I managed to get way past my super-tree function, but have trouble analyzing it...

when we are getting so close to things like the TREE sequence, there comes a point we should stop... Which of course not what the googologist does

😵

I actually don't know what it's like beyond ATR.

In reverse mathematics there are systems from PA to ACA to ATR, which I more or less understand conceptually, but beyond that all I understand is the axioms.

TREE is beyond ATR, with impredicative set comprehension.

So I don't understand it.

Perhaps one day I would.

Same

Perhaps when I lose my mind in these numbers, then I'll have the blind courage to understand the TREE

Um maybe you're going crazy already. =P

Better go back to some concrete mathematics. =)

=)

(∩＿∩)

Haha..

@SimplyBeautifulArt: Here's an amusing problem that I made up that ate up my time trying to find the optimal solution.

This problem only involves ratios of finite integers; very concrete! =D

Nice

Hey can anyone here help to confirm that this post is irreparably logically flawed, and help me to delete it? You can check that he's of the Fermat's Last Crank type, but unfortunately none of the experts care to remove the nonsense (I've tried the CRUDE room before). I just had the idea to ask people here. =)

@amWhy math.stackexchange.com/questions/2176715/…