Indicator Function

Definition

Indicator Function

Indicator functions are functions to simplify boolean case blocks:

$$\begin{array}{rl}{1}_{\text{cond}}& =\{\begin{array}{ll}1& \text{if cond is true}\\ 0& \text{else}\end{array}\\ 0_{\text{cond}}& =\{\begin{array}{ll}0& \text{if cond is true}\\ 1& \text{else}\end{array}\end{array}$$

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Examples

$$\sum _{i=0}^{\infty }{1}_{i=0}=1$$ $$\sum _{i=0}^{\infty }{1}_{0\le i\le 1}\cdot f(x)=2\cdot f(x)$$