3! = 6
2! = 3! / 3 = (6) / 3 = 2
1! = 2! / 2 = (2) / 2 = 1
0! = 1! / 1 = (1) / 1 = 1
∴ 0! = 1
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0! is the number of bijections from an empty set to itself which is 1 😤
it's just a direct definition that works in all cases and doesn't require an argument that it would be a good convention or would continue a pattern. in fact you can use this definition to prove that the pattern continues all the way down to zero
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