Zero Factorial

What is Zero-Factorial?

Simple answer: 0! (read "Zero Factorial") is defined to equal 1.
Involved answer(s):
There are several proofs that have been offered to support this common definition.
Example (1)
If n! is defined as the product of all positive integers from 1 to n, then:
1! = 1*1 = 1
2! = 1*2 = 2
3! = 1*2*3 = 6
4! = 1*2*3*4 = 24
...
n! = 1*2*3*...*(n-2)*(n-1)*n
and so on.
Logically, n! can also be expressed n*(n-1)! .

Therefore, at n=1, using n! = n*(n-1)!
1! = 1*0!
which simplifies to 1 = 0!

Example (2)
The idea of the factorial (in simple terms) is used to compute the number of permutations (combinations) of arranging a set of n numbers.
n: Number of Permutations (n!): Visual example:
1 1 {1}
2 2 {1,2}, {2,1}
3 6 {1,2,3}, {1,3,2}, {2,1,3}, {2,3,1}, {3,1,2}, {3,2,1}
10 3,628,800 ummm, you get the idea...

Therefore,

0 1 { }
It can be said that an empty set can only be ordered one way, so 0! = 1.

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