# Symbols:Greek/Chi

## Chi

The $22$nd letter of the Greek alphabet.

- Minuscule: $\chi$

- Majuscule: $\Chi$

The $\LaTeX$ code for \(\chi\) is `\chi`

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The $\LaTeX$ code for \(\Chi\) is `\Chi`

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### Mapping

- $\map \chi x$

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 \(\map \chi x\) is `\map \chi x`

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### Characteristic Function

- $\chi_E$

Let $E \subseteq S$.

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

- $\map {\chi_E} x = \begin {cases} 1 & : x \in E \\ 0 & : x \notin E \end {cases}$

That is:

- $\map {\chi_E} x = \begin {cases} 1 & : x \in E \\ 0 & : x \in \relcomp S E \end {cases}$

where $\relcomp S E$ denotes the complement of $E$ relative to $S$.

The $\LaTeX$ code for \(\map {\chi_E} x\) is `\map {\chi_E} x`

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## Linguistic Note

The name of the Greek letter $\chi$ (chi) is pronounced **khi**, where:

- the
**kh**sound is as the**ch**in the German**ich**, or in the Scots word**loch** - the word rhymes with
**by**.

If this causes difficulties, the pronunciation **ki** or **hi** are sometimes considered acceptable alternatives.

Under no circumstances is it correct to pronounce it **tshi** or **shi**.