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as

If this product formula is changed to keep all but the last term, it would define a product of the same form, for a smaller factorial. This leads to a recurrence relation, according to which each value of the factorial function can be obtained by multiplying the previous value by $n$:

For example, $5!\; =\; 5\backslash cdot\; 4!=5\backslash cdot\; 24=120$.

Factorial of zero

The factorial of $0$ is $1$, or in symbols, $0!=1$.

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