system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: Why is 0! 1 and not 0?

3! is 6 as it is 3x2x1. 2! is 2 as it is 2x1. 1! is 1 as it is just 1. Shouldn't 0! be 0 as there are no numbers to multiply?
gpt
Because a factorial is how many ways you can arrange a bunch of items in a set. You can arrange 1 item in one way {1}, 2 items in 2 ways {1,2} and {2.1}, 3 items in 6 ways etc. You can arrange 0 items in one way, it is an empty set. You can make one combination with it {} so 0! is equal to 1.