+ 3

# Factorial of 0 is 1 and not 0 why???

7 Answers

+ 14

From the links provided:
n! is defined as the product of all positive integers from 1 to n, i.e.
n! = 1*2*3*...*(n-1)*(n)
which can be logically defined as:
n! = n*(n-1)!
By substituting n = 1, you get
1! = 1 * (1-1)!
1! = 1 * 0!
1! = 0!
and hence
0! = 1

+ 10

https://www.khanacademy.org/math/precalculus/prob-comb/combinatorics-precalc/v/zero-factorial-or-0

+ 4

1 x 1 = 1

+ 2

can u explain it more!@sd

0

also some mathematic fields involve 0!
e.g. Taylor's formula: f(x)=sum from n=0 to infinity: (d^nf/dx^n)*x^n/n!
When n=0 n! has to be 1.
also an extension of the factorial function, Gamma function denoted as Î“(z)
where Î“(z)= integration from 0 to infinity: x^(z-1)e^(-x)dx
proves that Î“(0)= integration from 0 to infinity: x^(0-1)e^(-x)dx =1