I’m fast as fΓ0(n) boi
What on Earth is fΓ0(n)?
Remember the last post, Fast as (insert word here) boi, where I talked about the fast-growing hierarchy? These are just extensions on it.
Let’s take a step down.
Do you remember ω? The ordinal that used the diagonal of the hierarchy table? (I’ll be completely honest, that sounds like a good book title) You can use ω in different ways, like ω + 1, ω2 (ω times two, or ω + ω), ωω and much more. Eventually, we will run out of numbers to do those operations with, so we have to move to the next step:
ωωωωω… until you run out of ω, in which it becomes epsilon-zero, or ε0. There also exists a f function for it, fε0 that grows so fast. Don’t think about thinking about it. You can do weird things to ε0, like ε1, εε0, ε0ε0, εω, εεε0, and more.
Surely that’s it?
ζ0 exists! You can also do “normal” things like powers, epsilon-ζ0 (I was too lazy to copy and paste), and stuff.
That’s it. Right?
Feferman-Schütte ordinal, named after Solomon Feferman and Kurt Schütte. That’s the one that was in the beginning of this post.
Yet that wasn’t enough to stop a beast.
We have to go one more step further. ϑ.
fϑ(Ωω, ω, 0)(n) is the approximation for the TREE function.
If you ask me, I’ll say, “I don’t know.”