User blog comment:B1mb0w/The S Function Version 2/@comment-27513631-20160617114926/@comment-10262436-20160628033139

Hi. The S function returns string patterns that can be ordered. The number of string patterns that it can generate is huge.

The string patterns are not numbers, but because they can be ordered, they can be assigned ordinal values, e.g.:

S(2,0,0) ordinal value of 1

S(2,0,1) ordinal value of 2

S(2,1,1) ordinal value of 3

S(S(2,1,1),0,1) ordinal value of 4

S(S(2,1,1),0,S(2,0,0)) ordinal value of 5

S(S,2,1,1),0,S(2,0,1)) ordinal value of 6

S(2,T(0),1) ordinal value of 7

I calculate that the number of string patterns that can be generated up to

S(2,S(T(2),0,1),1) is beyond f_Gamma_0(3)

and the number of string patterns that can be generated up to

S(2,S(T(T(0)),0,1),1) is beyond f_svo(3)