# Questions tagged [primitive-recursion]

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### The evolution of the term “recursive” from Goedel to Church to present day

I'm currently studying some of the history of computation / computability, in the early days known as recursion theory. I see Goedel's definition of recursive functions seems significant in his paper,...
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### Is there a name for the class of functions whose totality can be proved using “Ackermann-like” reasoning?

Primitive recursion is recursion where totality can be proved because there is a single natural number parameter that strictly decreases in every recursive call. Put another way, the recursion ...
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### Prove that variable projection is recursive

Let $\varphi:\mathbb{N}\to\mathbb{N}^*$ be an arbitrary recursive enumeration of finite strings and $\mathcal{I}^n_i(x_1,...,x_n) = x_i$ be the $i$-th projection over $n$ variables. I would like to ...
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### Showing that the quotient function is primitive recursive

I'm asked to show that the quotient function is primitive recursive. I know that the operation of integer division $div$ is not total, as it is not defined when the denominator is zero, and a ...