\begin{definition}[Definition:Basic Primitive Recursive Function/Projection Function]
The '''projection functions''' $\pr_j^k: \N^k \to \N$ are basic primitive recursive functions, defined as:
:$\forall \tuple {n_1, n_2, \ldots, n_k} \in \N^k: \map {\pr_j^k} {n_1, n_2, \ldots, n_k} = n_j$<ref>The usual notation for the projection function omits the superscript that defines the arity of the particular instance of the projection in question at the time, for example: $\pr_j$. However, in the context of computability theory, it is a ''very good idea'' to be ''completely certain'' of ''exactly'' which projection function is under discussion.</ref>
where $j \in \closedint 1 k$.
They are each URM computable by a single-instruction URM program.
\end{definition}