# 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 .

### Inclusion Mapping

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

$\iota_S: S \to T: \forall x \in S: \map {\iota_S} x = x$

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:

$\forall n \in S: \map \iota n = \delta_{n 1}$

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 .

## Linguistic Note

From the same linguistic root as the Greek letter $\Iota$, $\iota$ (iota) comes the word jot, which derives from the concept of the smallest letter or linguistic mark that can be made.

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