Dan Christensen <Dan_Christensen@sympatico.ca> wrote in news:email@example.com:
> Clearly, it bothers some readers here that there is not just one, but > infinitely many functions on N that fit all our requirements for > exponentiation
No, what bothers us is that you _say_ this, when we know for a fact that there are only two ways, not infinitely many. You propose inifinity-minus-two functions which fail miserably to "fit all our requirements ofr exponentiation." For instance, all of us sane people require that 3 and 9 not be equal.