The Slow-growing Hierarchy
SEE ALSO: The Fast-growing Hierarchy
I'll be using a(n) to represent g_a(n) in this page. usually you will see g_a(n) for ordinal a.
w+1(n) = n+1
w2(n) = 2n
w^2(n) = n^2
w^w(n) = n^n
w^w^w(n) = n^n^n
e0(n) = n^^n
until epsilon-zero (also called epsilon-naught) this is trivial. problem comes after that.
HOW WOULD WE DEFINE n^^^n, n^^2n, n^^n^2, and so on...?
The most common system is the Climbing system. it says that n^^^n should be associated with gamma0.
There's also a Non-climbing system that says that it should be zeta0.
I'll compare both in a google sheetsbi
tbc