0^0

[Jud McCranie]

At 04:24 PM 5/4/2005, Jon Awbrey wrote:
>o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
>
>but logic says that 0^O = 1,
>as x^y is analogous to x<=y,
>and 0<=0 is true.


It is often most convenient in combinatorics to have 0^0 = 1.  See 
"Concrete Mathematics", (Graham, Knuth, and Patashnik) section 5.1, page 
162 in my first edition: "We must define x^0=1 for all x if the binomial 
theorem is to be valid when x=0, y=0, and/or x=-y.  The theorem is too 
important to be arbitrarily restricted!"