Definition:Boolean-Valued Function

Definition

A boolean-valued function is a mapping of type $f : X \to \mathbb B$, where $X$ is an arbitrary set and where $\mathbb B$ is a boolean domain.

Binary Sequence

A binary sequence is a boolean-valued function $f: \N^* \to \mathbb B$, where $\N^* = \left\{{1, 2, 3, \ldots}\right\}$. In other words, $f$ is an infinite sequence of $0$'s and $1$'s.

A binary sequence of length $k$ is a boolean-valued function $f : \N^*_k \to \mathbb B$, where $\N^*_k = \left\{{1, 2, \ldots k}\right\}$.

Also see

• Propositional function, which can be considered to be a boolean-valued function:
  • whose domain is a set of objects in a particular universe of discourse, and
  • whose codomain is the set $\left\{{\text{True}, \text{False}}\right\}$.

Source of Name

This entry was named for George Boole.