GFR

This is a great attempt to generalized "operations" space that in my opinion is complementary to structure (number, function etc.) spaces. Only after that their interactions will become understandable, and, may be, number/function/structure spaces will need to be redefined.

Have You considered "+" zeration and "-" zeration?

The idea comes as follows:

If we imagine, there might be fractional operations (halfation, etc), also negative (not saying explicitly yet what a negative operation rank might mean)- then they would tend to "converge" to zeration from both positive (1/n) and negative (-1/n) sides as they get more fractional with n-> infinity.

Ivars

This is a great attempt to generalized "operations" space that in my opinion is complementary to structure (number, function etc.) spaces. Only after that their interactions will become understandable, and, may be, number/function/structure spaces will need to be redefined.

Have You considered "+" zeration and "-" zeration?

The idea comes as follows:

If we imagine, there might be fractional operations (halfation, etc), also negative (not saying explicitly yet what a negative operation rank might mean)- then they would tend to "converge" to zeration from both positive (1/n) and negative (-1/n) sides as they get more fractional with n-> infinity.

Ivars