Could you then modify the definition to "for all n >= 0, n! is the product of natural numbers <= n"? That sounds kind of like the definition "f(0) = 1; f(n) = (

Could you then modify the definition to "for all n >= 0, n! is the product of natural numbers <= n"? That sounds kind of like the definition "f(0) = 1; f(n) = (n-1)! * n, n > 0".