\begin{definition}[Definition:Identity Arithmetic Function]
The '''identity arithmetic function''' $\iota: S \to \Z$ is defined for $n \geq 1$ by:
:$\forall n \in S: \map \iota n = \delta_{n 1}$
where:
:$S$ is (in theory) any set, but in this context is usually one of the standard number sets $\Z, \Q, \R, \C$.
:$\delta$ is the Kronecker delta.
That is:
:$\forall n \in S: \map \iota n = \begin {cases}
1 & : n = 1\\
0 & : n \ne 1
\end {cases}$
\end{definition}