Symbols:Greek/Iota

From ProofWiki
Jump to: navigation, search

Previous  ... Next

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) .