# Symbols:Greek/Chi

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## Chi

The $22$nd letter of the Greek alphabet.

Minuscule: $\chi$
Majuscule: $\Chi$

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

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

### Mapping

$\chi \left({x}\right)$

The Greek letter $\chi$, along with $\psi$ and $\phi$ and others, is often used to denote a general mapping.

In the context of abstract algebra, it often denotes a homomorphism.

The $\LaTeX$ code for $\chi \left({x}\right)$ is \chi \left({x}\right) .

### Characteristic Function

$\chi_E$

Let $E \subseteq S$.

The characteristic function of $E$ is the function $\chi_E: S \to \left\{{0, 1}\right\}$ defined as:

$\chi_E \left({x}\right) = \begin{cases} 1 & : x \in E \\ 0 & : x \notin E \end{cases}$

That is:

$\chi_E \left({x}\right) = \begin{cases} 1 & : x \in E \\ 0 & : x \in \complement_S \left({E}\right) \end{cases}$

where $\complement_S \left({E}\right)$ denotes the complement of $E$ relative to $S$.

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