G function

A G function is a type of pseudo-function used by Jonathan Bowers in his Array Notation. If a G function has base b, we say that:


 * $$G = b$$
 * $$G(a) = b\underbrace{\uparrow\ldots\uparrow}_ab$$, using Arrow Notation

The G function is not strictly a function since it can take either 0 or 1 arguments.

When a G function is iterated over itself, Bowers omits the parentheses. For example, G(G(G(4))) could be written GGG4. If G was in base 4, then this could also be written GGGG, since G = 4.

If, using this new notation, we treat iterated G functions as multiplication, we can extend them to exponentiation, tetration, etc. Thus GGGG could also be written as G4, which is G "multiplied" by itself 4 times. An extended example would be GG = G tetrated to G in base 4, which is equal to GG G G.