**Why does 0! = 1?**

0! = 1 is a definition so that

holds true for n = k. From the “Fundamental Principle of Counting” we know that is n!

As,

0! must equal 1 so that:

Although there is no proof, this video helps to understand why 0! = 1.

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See: https://math.stackexchange.com/questions/20969/prove-0-1-from-first-principles

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