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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 .


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

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


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 .