system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: Why is "0! = 1"?

If n factorial is n(n-1)(n-2)...(3)(2)(1),

Why is 0 factorial=1? If 0=n, should the answer be 0 due anything multiplied by 0=0?

EDIT: Wow thanks for all the good responses! Never actually expected this to make it to my top post, but Reddit never fails to amaze me!
gpt
A factorial represents the number of ways you can organize *n* objects.

There is only one way to organize 1 object. (1! = 1)

There are two ways to organize 2 objects (e.g., AB or BA; 2! = 2)

There are 6 ways to organize 3 objects (e.g., ABC, ACB, BAC, BCA, CAB, CBA; 3! = 6).

Etc.

How many ways are there to organize 0 objects? 1. Ergo 0! = 1.

This is consistent with the application of the gamma function, which extends the factorial concept to ~~non-positive integers.~~ all reals EDIT: except negative integers!