Symbols:Chi

Chi

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:

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

Alternatively, and equivalently, it can be written as:

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

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