# Symbols:Greek/Iota

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## Iota

The $9$th letter of the Greek alphabet.

Minuscule: $\iota$
Majuscule: $\Iota$

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

The $\LaTeX$ code for $\Iota$ is \Iota .

It is pronounced yot-ta, not the incorrect but often-heard eye-oh-ta.

### Inclusion Mapping

Used by some sources to denote the mapping on $S$ to $T$ where $S \subseteq T$:

$\iota_S: S \to T: \forall x \in S: \iota_S \left({x}\right) = x$

The $\LaTeX$ code for $\iota_S$ is \iota_S .

### Identity Arithmetic Function

The identity arithmetic function $\iota: S \to \Z$ is defined for $n \geq 1$ by:

$\forall n \in S: \iota \left({n}\right) = \delta_{n1}$

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:

$\forall n \in S: \iota \left({n}\right) = \begin{cases} 1 & : n = 1\\ 0 & : n \ne 1 \end{cases}$

The $\LaTeX$ code for $\iota \left({n}\right)$ is \iota \left({n}\right) .