# How to denote a “boolean” (on/off, 1/0) variable in mathematics?

Is there any conventional notation for variables that can only take the value 0 or 1? (I'm looking for something of the nature of an overbar, a caret, etc.)

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To denote a boolean variable $b$, I would simply state the following before use: $b\in\mathbb{Z}:b\in[0,1]$. –  Shaktal Jun 24 '12 at 10:54
@Shaktal: That looks convoluted. Why not just $b\in\{0,1\}$? –  Henning Makholm Jun 24 '12 at 15:37

I don't know of such notation. You can always define that $\dot x$ means that $x$ is a Boolean variable with values in $\{0,1\}$.
What you call a boolean variable in CS, is essentially an element of the finite field or order 2. you could write: $$x \in F_2$$