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To Prove:- 0! =1.

Known:y! = y x (y-1)!

So, 1! = 1 x (1-1)!1! = 0!

or

0! = 1! -(a)

Proof:As We know,n! = n x n-1 x n-2 x n-3 x n-4 x .......... 2 x 1

So,4! = (3+1)!

= 4 x 3!

= 4 x 3 x 2 x 13!

= (2+1)!

= 3 x 2!

= 3 x 2 x 1 2!

= (1+1)!

= 2 x 1!

= 2 x 11!

= (0+1)!

= 1 x 0! = 1 -(b)

Hence, from (a) and (b)We get, 0! = 1

Known:y! = y x (y-1)!

So, 1! = 1 x (1-1)!1! = 0!

or

0! = 1! -(a)

Proof:As We know,n! = n x n-1 x n-2 x n-3 x n-4 x .......... 2 x 1

So,4! = (3+1)!

= 4 x 3!

= 4 x 3 x 2 x 13!

= (2+1)!

= 3 x 2!

= 3 x 2 x 1 2!

= (1+1)!

= 2 x 1!

= 2 x 11!

= (0+1)!

= 1 x 0! = 1 -(b)

Hence, from (a) and (b)We get, 0! = 1