Definition:Rectangle Function

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The rectangle function is the real function $\Pi: \R \to \R$ defined as:

$\forall x \in \R: \map \Pi x := \begin {cases} 1 : & \size x \le \dfrac 1 2 \\ 0 : & \size x > \dfrac 1 2 \end {cases}$

Graph of Rectangle Function

The graph of the rectangle function is illustrated below:


Also known as

The rectangle function is also known as the gate function, especially in the context of electronics.

The rectangle function of $x$ can be voiced rect $x$, and so written when the Greek alphabet is not conveniently to be used.