Factorial/Examples/0

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Example of Factorial

The factorial of $0$ is $1$:

$0! = 1$


Proof

From the definition of factorial:

$n! = \displaystyle \prod_{k \mathop = 1}^n k$

where $\prod$ denotes product notation.

When $n = 0$ we have:

$0! = \displaystyle \prod_{k \mathop = 1}^0 k$

Hence the result, by definition of vacuous product.

$\blacksquare$


Sources