User blog:Fejfo/Commutatieve ackermann function

This idea came from wikipedia where I read something about commutative hyperopperations, but they didn't even reach tetration so I made this.

The goal is to define a commutative hyper operation function, \( A(a,b)=A(b,a) \)

This is the definition: For \( a\ge b \) we get:
 * 1) \( A(a,b)=A(b,a) \), from now on the first argument is assumed to be larger without loss of generality.
 * 2) \( A(a,0)=a+1 \)
 * 3) \( A(a+1,b+1)=A(A(a,b+1),b) \)
 * \( A(a,0)=a+1 \)
 * \( A(a,1)=a+2 \)
 * \( A(a,2)=2a+2\)
 * \( A(a,3)>2^{a+1} \)
 * \( A(a,4)>2↑↑a\)
 * in general \( A(n,n) \) hase the same growth rate as \( f_\omega \)