From a philosophical standpoint, $0!=1$ as it is possible to arrange nothing in one way--there isn't.
Are there any rigorous proofs showing this concept?
2026-03-29 10:47:56.1774781276
Rigorous Proof of $0!=1$
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The factorial function is defined to count the number of bijections between finite element sets, namely $n!=$ # $ f: \{1,..,n\} \to \{1,..,n\}$ that are bijective. There is precisely one bijective map $f : \emptyset \to \emptyset$, namely f is the empty map.
I recognize this is a very odd concept. Hope this helps.