Factorial Factory!!

Number Theory Level 1

0!=?

What is 0 factorial?

NOTE:
10!=10x9x8x7x6x5x4x3x2x1
9!=9x8x7x6x5x4x3x2x1
8!=8x7x6x5x4x3x2x1
...


The answer is 1.

Pablo Ruiz by Pablo Ruiz , 21, Mexico

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2 solutions

n ! = n ( n − 1 ) ! P u t n = 1 o n b o t h s i d e s . . . n!\quad =\quad n(n-1)!\\ Put\quad n=1\quad on\quad both\quad sides...

1 ! = 1 ( 0 ) ! 0 ! = 1 1!\quad =\quad 1(0)!\\ 0!\quad =\quad 1

Cheers!!!!

7 Helpful 0 Interesting 0 Brilliant 0 Confused

That is not a proof of the answer, however. It only shows some consistency. If it were a proof, then ( − 1 ) ! = − 1 ⋅ 0 ! = − 1 (-1)!=-1\cdot0!=-1 , which is not true. Even if factorials are generalized, the resulting Gamma function is not defined for negative integers.

Marta Reece - 3 years ago
William Isoroku
Aug 20, 2014

Just use the Gamma function

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