User blog comment:Nayuta Ito/An attempt to well-define OCF as a number notation/@comment-35470197-20190616120315

I think that you do not need to assume the condition that + is communitive, because the equality A+B + C = A + B+C as strings always holds. (I do not know the word "communitive", though.)

> Else, Cmp(A,D) must be 0: Cmp(A,B)=Cmp(0,E)

Cmp(0,E) is always -1.

> If D=0: Cmp(A,B)=0

Maybe it should be "If E = 0".

> Else, A=Ω_C and B must be D+E: Cmp(A,B)=Cmp(A,D)

The indent seems to be deeper than intended.

> Kurd(A) is supposed to mean the "cardinality" of A is non-zero but finite.

What do you mean?

> If Cough(A)=1, A must be B+ψ(0):

Maybe ψ(0) should be ψ_Ω_1(0).