Definition:Boolean Algebra

Definition 3
The operations $\vee$ and $\wedge$ are called join and meet, respectively.

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

Also, $\neg a$ is called the complement of $a$.

The operation $\neg$ is called complementation.

Equivalence of Definitions
These definitions are shown to be equivalent in Equivalence of Definitions of Boolean Algebra.

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

 * Definition:Huntington Algebra
 * Definition:Robbins Algebra


 * Duality Principle (Boolean Algebras)