# an explanation, by Austin Lowder, of why zero factorial equals unity

(that is, why 0! = 1)
His explanation is given in a comment by him for the article by Merriam-Webster on ‘factorial’.
Here is his explanation:
Note that 5! = 6!/6, because 6!/6 = 1 x 2 x 3 x 4 x 5 x 6 / 6 = 1 x 2 x 3 x 4 x 5 = 5!
Continuing with this process:
4! = 5!/5 = 24
3! = 4!/4 = 6
2! = 3!/3 = 2
1! = 2!/2 = 1
0! = 1!/1 = 1
That’s his explanation.
Here is the link to the article in Merriam-Webster where his comment appears.
For factorials, the fact that 0! = 1 is merely a definition, a definition made for convenience (such as making reference to binomial coefficients). What Austin Lowder provides, therefore, cannot be a PROOF, but it IS a brilliant EXPLANATION, that is a brilliant HEURISTIC, that shows why we would want to define it so. However, by ‘going to the next level’, namely, by considering the gamma function (shifted by one unit to the left), for which factorials can be defined in a way consistent with the elementary manner, it is then a THEOREM that 0! = 1.
Here is the link to the Wikipedia article on the gamma function.