Zeration

[KAR]

But see Gianfranco, the postulate
aob = max{a,b}+1 for a!=b
aob = a+2=b+2 for a=b
does not follow from your initial rule
aoa=a+2

It not a postulate!
Definition Zeration follows from similar:
a+a=a*2
a+a+a=a+3
a+a+a+a=a+4
......
a+...+a=a*n (n>1)

a*a=a^2
a*a*a=a^3
...................
If calculations to start at the left:
aoa=a+2
aoaoa=a+3=(aoa)oa=(a+2)oa, a+2>a
aoaoaoa=a+4=((aoa)oa)oa=(a+3)oa, a+3>a
......
ao...oa=a+n, a+(n-1)>a if n>1.
From definition Zeration for "a" it is possible to write for b>a:
boa=b+1 and boa=a+2=b+2 if a=b.
This base definition

The rule of evaluation Zeration is a corollary from extended base definition, but not a postulate!

KAR