On Friday, October 18, 2013 3:32:55 AM UTC-4, Robin wrote: > On 17/10/2013 21:18, Bart Goddard wrote: > > > Dan Christensen <Dan_Christensen@sympatico.ca> wrote in > > > news:firstname.lastname@example.org: > > > > > >> There is no logically compelling reason to assume that 0^0=1. > > > > > > Some people are not compelled by logic. But mathematicians > > > are. Defining 0^0=1 preserves the exponent rules. That's > > > a compelling reason and it's logical. It's logical because > > > it extends the definition of exponents in such a way that > > > the exponent rules still work, even if you put in zeros. > > > > I wonder what DC's position on 0! is. >
It is possible construct a unary function f on N (your factorial function) such that:
1. f(0) = 1 2. f(x+1) = f(x)*(x+1)
Nothing controversial here. I think I have even posted the proof at sci.math some years ago.