how-0-1-

how-0-1-

Question Number 1740 by tabrez8590@gmail last updated on 11/Sep/15

h o w 0! = 1

Commented by 123456 last updated on 11/Sep/15

1! = 1 \cdot 0!

so for it work to 1 them 0! = 1

Answered by Rasheed Ahmad last updated on 12/Sep/15

P e r m u t a t i o n o f r e l e m e n t s f r o m

a s e t o f n e l e m e n t s c a n b e p r o v e d

e q u a l t o :

P (n, r) = n (n - 1) (n - 2) \dots . (n - r + 1) .

F o r r < n t h i s i s e q u i v a l e n t t o :

P (n, r) = \frac{n!}{(n - r)!}

A s s a i d a b o v e f o r r < n t h e a b o v e

t w o f o r m u l a e a r e c o n s i s t e n t .

B u t a t r = n t h e a b o v e f o r m u l a e

g i v e t h e f o l l o w i n g t w o r e s u l t s

r e s p e c t i v e l y :

P (n, n) = n!

P (n, n) = \frac{n!}{(n - n)!} = \frac{n!}{0!}

T o c o n t i n u e c o n s i s t e n c y a t n = r

w e a r e f o r c e d t o d e f i n e :

0! = 1

Rasheed Soomro