Definition:Characteristic Function (Set Theory)

Let $$E \subset S$$.

The characteristic function of $$E \ $$ is the function $$\chi_E:S \to [0,1]$$ defined

$$\chi_E(x) = \begin{cases} 1, & \mbox{if } x\in E  \\ 0,  & \mbox{if } x \notin E \end{cases}$$