In set theory, sets containing an infinite number things are relatively easy to describe. For example, "All the counting numbers" is a set with an infinite number of things in it.

Many sets with an infinite number of things have a one to one correspondence to each other, meaning that we can describe a function that takes elements of one set as an input, gives elements of the other set as an output, and spans both sets - no element is skipped on either side.

"All the even counting numbers" has a one to one correspondence with "All the counting numbers". You can look into Hilbert's Hotel for a good demonstration of how this works.

Not all sets with an infinite number of things correspond with the set of all counting numbers, because some are fundamentally bigger. This difference in size doesn't happen just once (e.g. there are countably infinite sets, and uncountably infinite sets, and that's all we need to know), there are actually an infinite number of sets of progressively bigger infinite numbers of elements.

Because this is a confusing mess, we needed a way to keep track of how infinitely big each infinitely big set is, and the aleph cardinalities are the preferred way to do that. Any set with cardinality of aleph zero (aka "aleph null") has a one to one correspondence with any other set with cardinality aleph zero. The same is true for every other aleph cardinality. Two sets of cardinality aleph thirty seven have a one to one correspondence with each other.

Anyways, busy beaver(tree(aleph omega)) is the biggest number.

-ant! Finish your words, it's not that hard!

This is the AI I want. Like pure early day chaos where Will Smith couldn't eat spaghetti, that Forever Seinfeld on twitch, the weird recipes like 80lbs of salt.

It's pretty easy to fake one using the developer tools in your browser.

They aren’t deterministic. There are a few common ones that are cached, but if you get bad (or good?) RNG in the response generation you’ll never manage to get the same result as someone else.

ahem.

Brazillian?

Best I can do is 3.50.

I always liked Graham's Number. I didn't like that it was TREE(1)=1, TREE(2)=3, and TREE(3) dwarfs even Graham's Number. At least G=g_64 which is built up from g_1.

You just sent me down a rabbit hole learning about TREE(3), thank you

How big?

Tbf, some infinities are bigger than others.

I always knew I could count on you

Could still be real. Ai will give different answers to the same question.

It's quite plausibly real. Gemini can def get in shitposty basins and has historically had a fairly inconsistent coherence across samples.

TREE(3) + 1

#gottem 😎