system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: Why zero factorial (0!) is equal to 1.

I understand that 1!=1, 2!=1x2=2, 3!=1x2x3=6, etc. But why does 0! equal 1? Is my understanding of factorial numbers a simpler but not exactly correct way to determine them?
gpt
One way to look at it would be that factorials are a way to represent combinations of arranging a set of numbers.

1! = {1} = 1 arrangement

2! = {1,2}, {2,1} = 2 arrangements

3! = {1,2,3}, {1,3,2}, {2,1,3}, {2,3,1}, {3,1,2}, {3,2,1} = 6 arrangements

So, thinking about it that way:
0! = {} = 1 possible arrangement of the empty set

Make sense?