Definition:Boolean Algebra/Definition 1

Definition
A Boolean algebra is an algebraic system $\left({S, \vee, \wedge, \neg}\right)$, where $\vee$ and $\wedge$ are binary, and $\neg$ is a unary operation.

Furthermore, these operations are required to satisfy the following axioms:

The operations $\vee$ and $\wedge$ are called join and meet, respectively.

The identities $\bot$ and $\top$ are called bottom and top, respectively.

The operation $\neg$ is called complementation.

Also defined as
Some sources define a Boolean algebra to be what on ProofWiki is called a Boolean lattice.

Others refer to a Boolean algebra as a Boolean ring or a Huntington algebra, both of which terms already have a different definition on ProofWiki.

Also known as
Common other notations include: $0$ and $1$ for $\bot$ and $\top$, respectively, and $a'$ for $\neg a$.

In this convention, $0$ is called zero, and $1$ is called one or unit.

Also see

 * Huntington Algebra
 * Robbins Algebra