Apurdue.168
net.general
utzoo!decvax!pur-ee!purdue!mab
Sat Jan 23 10:57:24 1982
Re: Factorial Query

The idea is this:

3! = 2! x 3
2! = 1! x 2
and in general,  n! = (n-1)! x n

So, if n = 1, then 1! = 0! x 1
But 1! is 1 from the definition, so 0! HAS to be 1 for this relation to hold.

Note that this formula breaks down at n=0, because 0! = 1 != (-1)! x 0
regardless of how you define (-1)!, because 0 x anything = 0.  But 0! = 1
makes the formula consistant everywhere else.

(Oh, yes ... for any other mathematical types, that 0! = 1 is also
derivale from the relationship n! = GAMMA(n+1), where GAMMA is the gamma
function... but the formula I mentioned above is so much more elegant!!!)

					Matt Bishop (purdue!mab)