# 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.)

• To denote a boolean variable $b$, I would simply state the following before use: $b\in\mathbb{Z}:b\in[0,1]$. – Thomas Russell 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

## 2 Answers

I don't know of such notation. You can always define that $\dot x$ means that $x$ is a Boolean variable with values in $\{0,1\}$.

Of course the dot can be replaced by other symbol. Be forewarned, though, that there are many many different contexts in which these symbols already have meaning. If you specify what you are going to use this notation for (logic, comp. sci., etc.) maybe some better suggestion will be given.

Until then, I think my first suggestion should probably fit.

What you call a boolean variable in CS, is essentially an element of the finite field or order 2. you could write: $$x \in F_2$$