why 0! = 1. Idk it seems counterintuitive.

Question

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In: Mathematics

Answer 1

0 is what you get when you don’t add any numbers together. 0 is the “I didn’t add anything” number. Anything plus 0 is still itself.

1 is what you get when you don’t *multiply* any numbers together. 1 is the “I didn’t multiply anything” number. Anything times 1 is still itself.

Factorials are about multiplication, so if you do the factorial of nothing, you get the “I didn’t multiply anything” number: 1.