Solution to show that factorial function is promitive recursive - Sikademy
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show that factorial function is promitive recursive

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The factorial function defined as fac:\N\to \N

Such that fac(n)=n!

From the definition of the factorial, we have that:

fac(n)= n!=\begin{cases} 1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \text{if } n=0\\ mult(n,fac(n-1))~~~\text{if } n>0\end{cases}

Thus fac is obtained by primitive recursion from the constant 1 and the primitive recursive function mult.


Hence fac is primitive recursive.

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