03/24/2015, 11:29 AM

(03/21/2015, 11:11 PM)tommy1729 Wrote: f and g are some function :

f^[a - N_q](N_q[q]b) = g^[b - N_q](N_q[q]a)

(03/23/2015, 02:31 PM)MphLee Wrote:maybe this one is clearer?Quote:General case

I added a subindex to the neutral, because many operations have a different neutral for each number.

For example, right bracket tetration:

, where

...looks non intuitive. Unnecessarily complicated.

But each "a" has a neutral , which simplifies the notation:

(03/21/2015, 11:11 PM)tommy1729 Wrote: f^[a - oo](...) does not make sense as a nonconstant function.a+b = b+a

"add+1"^[a](0) = "add+1"^[b ](0)