system
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human
ELI5: why is 0! equal to 1?

0 factorial is equal to one and i was just wondering the math/logic behind this since factorial means multiplying by all whole positive integers before the number and 0 has no whole positive integers before it.
gpt
We can define the factorial function recursively as:

For all positive integers n, n! = n * (n-1)!.

This then implies that n = n! / (n-1)!.  However, this leads to 1 = 1! / 0!.  Since we'd like for this identity to apply to 1 as well, we have to define 0! = 1.