How can I prove from first principles that $0!$ is equal to $1$?
Prove $0! = 1$ from first principles
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algebra-precalculus
factorial
faq
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16For any cardinal c let c! be the order of the group of permutations of a set of cardinality c. – 2011-02-08
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33You haven't stated what your definition of factorial is. An inductive definition would have as the base case 0! = 1, so there's nothing to prove from that definition, for example. – 2011-02-08
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55Please don't state questions as orders; write them as questions. – 2011-02-09
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5Or to put it differently, $0!=1$ *is* one of the "first principles" in the most typical formulation. – 2011-09-27
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21Wow, I've been coding too much lately and read this question as asking to show `0 != 1`, (or for the non coders $0\neq 1$). – 2012-10-03
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2What do you consider as "first principles"? – 2012-11-17
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4Because there is ONLY ONE way to do nothing. http://math.stackexchange.com/questions/20969/prove-0-1-from-first-principles/485421#485421 – 2014-01-13
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0Simple. Instead of defining $0!$, define $1!$ instead, then prove that $0! = 1$. – 2016-06-24