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Possible Duplicate: Prove 0! = 1 0! = 1 from first principles Why does 0! = 1 0! = 1? All I know of factorial is that x! x! is equal to the product of all the numbers that come before it. The product. Aug 24, 2016 · 1 Indeed what you are proving is that in the complex numbers you don't have (in general) $$\sqrt {xy}=\sqrt {x}\sqrt {y}$$ Because you find a counterexample. @coffeemath Debatable: you can write Hn = S2 n + 1 n! Where S denotes Stirling numbers of the first kind. But it may not be considered a "closed form", since Stirling numbers are not much.
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