It is defined that way. It makes possible the definition that
n! = n(n-1)! for all integer n>0
Prove that 0! = 1
3 answers
Suppose we have n objects.
In how many ways can I take all of them
of course the answer to that is 1 way.
but from the theory of combinations it would be
n!/( (n-n)(n!) )
= n!/(0!n!)
= 1/0!
but we know that has to be 1
1/0! = 1, this can only be true if we define 0! = 1
That is , we are forced to accept 0! = 1 if our theory of combinations and permutations is accepted.
In how many ways can I take all of them
of course the answer to that is 1 way.
but from the theory of combinations it would be
n!/( (n-n)(n!) )
= n!/(0!n!)
= 1/0!
but we know that has to be 1
1/0! = 1, this can only be true if we define 0! = 1
That is , we are forced to accept 0! = 1 if our theory of combinations and permutations is accepted.
Thanks for the help !