Symbols:Greek/Chi/Characteristic Function

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Characteristic Function


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 .

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.