Item 1 (005Z) — The Clowder Project

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Style	Class	Font	Theorem Environments
Style 1	`book`	Alegreya Sans	`tcbthm`
Style 2	`book`	Alegreya Sans	`amsthm`
Style 3	`book`	Arno*	`amsthm`
Style 4	`book`	Computer Modern	`amsthm`

*To be replaced with Linus Romer's Elemaints when it is released.

The characteristic function of $U$^[1] is the function ^[2]
\[ \chi _{U}\colon X\to \{ \mathsf{t},\mathsf{f}\} \]

defined by

\[ \chi _{U}\webleft (x\webright ) \mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\begin{cases} \mathsf{true}& \text{if $x\in U$,}\\ \mathsf{false}& \text{if $x\not\in U$} \end{cases} \]

for each $x\in X$.

Footnotes

[1] Further Terminology: Also called the indicator function of $U$.

[2] Further Notation: Also written $\chi _{X}\webleft (U,-\webright )$ or $\chi _{X}\webleft (-,U\webright )$.

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