"Alan Beban" wrote...
Once 0! is defined as being equal to 1, then n! =n((n - 1)!) for n a
positive integer.

It's not mere convention or just a definition. In Set Theory approach, n! is
the cardinality of the set of permutations of n items (similar to Excel's
PERMUT(n,n)). 1! = 1 because there's only permutation, {{a}}. 0! = 1 because
the the empty set counts as such a set, {{}}.