Let $X$ be a D11: Set and let $I_E$ be an D41: Indicator function on $X$ with basis set $E = \{ x \in X : P(x) \} \subseteq X$. By definition of $E$, the predicate statement (or D1090: Basic boolean property) $P(x)$ is true precisely when $x \in E$. Thus, we may denote the Boolean number $I_E(x)$ briefly by $I_{P(x)}$.

As an example, consider the case where $X = \mathbb{R}$ and $E = [0, \infty) = \{ x \in \mathbb{R} : x \geq 0 \}$. In this case, we may denote $I_{[0, \infty)}(x)$ by $I_{x \geq 0}$.