Negative Factorial

Number Theory Level 1

$\large (-1) ! = \ ?$

-1 Undefined 0 1

2 solutions

Akhil Bansal
Aug 4, 2015

Using property $\large n! = n(n-1)!$

$\Rightarrow$ Put $n = 0$ ,

$\Rightarrow 0! = 0(-1)!$

$\Rightarrow \dfrac{1}{0} = (-1)!$

Hence, $\large (-1)!$ is undefined

How do you know that this property holds for $n = 0$ ?

if we can not put 0 here..... then can you please give me the proof for 0!=1.... for the challenge master note

Ayanava Sarkar - 5 years, 10 months ago

Arulx Z - 5 years, 9 months ago

Arulx Z
Aug 9, 2015

Although it's factorial of negative integers are considered undefined, they can be found using gamma function.

Only negative rational factorial can be finded out using gamma function,not the integer one..

Akhil Bansal - 5 years, 7 months ago