# Symbols:Greek/Iota/Identity Arithmetic Function

## 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:

$\forall n \in S: \map \iota n = \begin {cases} 1 & : n = 1\\ 0 & : n \ne 1 \end {cases}$

The $\LaTeX$ code for $\map \iota n$ is \map \iota n .