Definition:Boolean Function

Definition
A (finitary) boolean function is a function of the form $$f : \mathbb{B}^k \to \mathbb{B}$$, where:
 * $$\mathbb{B} = \left\{{0, 1}\right\}$$ is a boolean domain;
 * $$k\!$$ is a nonnegative integer.

In the case where $$k = 0\!$$, then $$f$$ is the constant function, and its value is simply a constant element of $$\mathbb{B}$$.

The boolean domain most often seen in the field of logic is $$\mathbb{B} = \left\{{T, F}\right\}$$, where $$T$$ stands for true and $$F$$ for false.

From Count of Boolean Functions, there are $$2^{\left({2^k}\right)}$$ boolean functions on $$k\!$$ variables.

Linguistic Note
The word boolean has entered the field of computer science as a noun meaning "a variable which can take one of two values".

Note that although the modern usage renders it without a capital B, you will find that older texts use Boolean.