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

Answer 1

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

Answer 2

https://zero-factorial.com/whatis.html

Answer 3

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

Answer 4

https://en.wikipedia.org/wiki/Factorial

Answer 5

1 x 1 = 1

Answer 6

can u explain it more!@sd

Answer 7

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 Γ(z)
where Γ(z)= integration from 0 to infinity: x^(z-1)e^(-x)dx
proves that Γ(0)= integration from 0 to infinity: x^(0-1)e^(-x)dx =1