The Fast-Growing Hierarchy: The Basics

The Fast-Growing Hierarchy is a definition of functions that continually grow larger and larger, faster and faster for each function (there are more than one!).

It works like this:

f0(n)=n+1

then, for each function, fm(n),

we take fm-1(fm-1(...fm-1(n))) where the fm-1 is repeated n times.

So, f1(n) = n+1+1+1+...n times...+1. This is just n+n = 2n.

f2(n) = 2*2*2*2...n times*2 * n = n*2^n.

f3(n) is harder to calculate, so I’ll leave that up to you, but f3(3) is about 10^120000000, or A(12A7) using my letter notation. Anyways...

Hope you enjoyed this blog post! I’m MatthewNotebook, find me on Wikia, and hopefully we’ll meet again.