User blog comment:Eners49/The secret 0th hyper-operator?/@comment-35470197-20180726231426/@comment-30754445-20180727085533

If you're interested in breaking operators to the smallest possible steps, you might want to learn about the slow growing hierarchy.

The rules are:

g0(n) = 0

ga+1(n) = ga(n)+1

and for a limit ordinal a:

ga(n) = ga[n](n)

You might wonder why I'm mentioning this, given that the second line already uses "+1" (the successor function)... But if you actually follow the above rules, you'll see that gm(n) = n. In other words, for any (finite) m, the function gm(n) is constant! It doesn't grow at all!

To actually create the successor function with this system, you'll need to use infinite ordinals:

gω(n) = n (note how this function is no longer constant. It doesn't grow any faster than n itself, but at least it grows).

gω+1(n) = n+1 (voila! the successor function!)

It should also be noted that using this hierarchy to create even moderately big googolisms, would require insanely large ordinals. To reach tetration, we already need to use gε₀(n). That's the price we're paying, for wanting to dissect the proccess into the smallest conceivable pieces.