Why 0! is equal to 1 ..??

Why 0! is equal to 1 ..??

We Know ,

n! = n x (n-1)!

Dividing both sides by n , We get

n!/n = n x (n-1)!/n 

Or, n!/n = (n-1)!

Or, (n-1)! = n!/n

Now , Putting n=1 , We get

(1-1)! = 1!/1

i.e. 0! = 1