Binary Numbers

Standard Definition

A binary number is a number written in base 2.

Classifying Boolean Algebras

See Classification of Boolean Algebras

As an element of a boolean algebra (Esoteric Definition)

A binary number, $b$, is an element from a Boolean Algebra.

A binary number system is a set, $S$, for some boolean algebra, $\mathbb{B}$ such that $S={\bigcup }_{i\in \mathbb{N}}{\mathbb{B}}^i$ Members of this set are called bits of $S$