First, I will write the definition of S map.
(Quote from Japanese Googology Wiki, translated by me)
 S map, a map between pairs of a natural number and a function, is defined like this.
And here's the definition of \(g(x)\).
You can also write like this focusing on the function: \[Sf(x) = g(x)\]
And the definition of SS map is this, using S map:
(A is a map. Many people use S, but I used A for disambiguation.)
Now it's getting crazy. Here's some definition:
A (non-meta)map is a map between sets of a natural number and a function. (e.g. S map)
A meta-map is a map between sets of a natural number, a function, and a map. (e.g. SS map)
A meta-meta-map is a map between sets of a natural number, a function, a map, and a meta-map.
A meta-meta-meta-map is a map between sets of a natural number, a function, a map, a meta-map, and a meta-meta-map.
Get the point? This pattern continues forever.
Now it's getting crazier.
Sn map is a metan-1map that is defined like this:
,where A_m is a metammap.
Now it's getting craziest.