Let n be a whole number
n! is defined as the product of n and all whole numbers less than n
n! = n x (n-1) x (n-2) x (n-3) x ... x 3 x 2 x 1
or in a partially expanded form,
n! = n (n-1)!
We know for certain 1! = 1
Let us obtain an exapnsion for 1!
1! = 1 x (1-1)!
1! = 1 x 0! --------------------------------------eqn (*)
Since we know that 1! is 1,
Substituting 1 in place of 1!
1 = 1 x 0!
0! = 1/1
0! = 1 --------------------proved