>>16557966
name one practical application of all the cardinal wankery. And by practical I mean anything relating to other areas of math.

>>16557966
>TREE of an ordinal

It's so crazy, it just might work

>>16558055
Calculus with infinitesimals rather than limits.

>>16558188
kek
so something nobody gives a shit about?

>>16558210
It satisfies the provided definition.

>>16558237
>some marginal branch of math helps some other marginal branch of math
bravo. I’d stick to algebraic geometry.

>>16558177
Like, what would the output be, because ordinals dont really work there, or do they?

>>16558752
Aleph null is a cardinal, so you'd really only have to care about ordinals with omega

A straightforward way to extend TREE to limit ordinals would be just to take the limit of TREE(n) for n < the ordinal. For TREE(𝛚) you would just get 𝛚 but maybe it's possible other values would give you something more interesting?

>>16558762
What would Aleph output, as Aleph is technically an infite cardinal? What would Aleph1 output?

>>16558769
I only addressed ordinals

>>16558770
I know, I just wanted to ask you, because I am too dumb to figure the answer out myself.

>>16558803
I don't know either

>>16558055
>name one practical application

Annoying people who ask for practical applications for everything

>>16558804
Oh, I'm gonna try to figure this shit out. I will write a frickin dissertation on this shit, when i figure it out. (if i ever find out)

>>16557966
hypothetically, couldn't a function have an acceleration such that its delta exceeds infinity?
I am thinking of plotting on a 2d graph. When you take something out to infinity, there is no way to present changes beyond straight line up and down. And then if you choose a middle reference, say zero, any approaches that drop from infinity would be displays as no distance from zero.
The blue line is impossible right?

>>16557966
yeah people do stuff like that, it’s obscure to me but your answer might be one of the named ordinals [math]\gamma_0[/math] or [math]\Gamma_0[/math] or some other ordinal you can write with the Veblen function

>>16558871
It probably should be impossible?

>>16558808
There's a difference between an enginigger going "bro but like how can I build McGuffins with this" and a fellow mathematician going "how does all this garbage relate to other areas of math so that I can understand both areas better by making connections between them". That's why I couldn't care less about number theory. It has been the driving vehicle for many areas of mathematics, but those areas have never ever benefited from number theory itself. With muh cardinals, there isn't even any incentive to drive other areas forward to prove that aleph bull's BBC can fit into beth's house.

>>16559092
>but those areas have never ever benefited from number theory itself
they don't deserve to

>>16559371
stop worshipping numbers, bro

>>16559092
>>16559092
Uh huh...
How does bro want to do maths without number theory? Numbers theory defines basically everything else...

>>16559092
If you dont understand the relationships between numbers and different kinds of numbers, then what are you doing all the time?

>>16559092
Btw, the OP's question is more about googology and about set theory, than it was about number theory, but yeah...

>>16559999
>relationships between different kinds of numbers
You mean different kinds of natural numbers? I don’t give a shit about some random equivalence relation someone pulled out of his ass (canonical example: Fermat’s last theorem). It tells me nothing about the structure of the object itself. Natural numbers are a semiring, so the only important thing about them are prime numbers. That’s the only actual property that has relevance to other areas of math. For example, a cyclic group of order p is simple if and only if p is prime. In fact a cyclic group of order p forms a Galois field. And so on.

>>16558055
See https://math.stackexchange.com/questions/1754985/what-are-some-applications-of-large-cardinals

But the "large cardinals" referred to above are about large cardinal axioms, axioms that imply very "big" cardinals. If you are talking about the googology stuff (like the TREE() or Rayo's number stuff), then no.