Of a set S on which some dyadic operation ° is defined. An element e with the property that a ° e = e ° a = a for all elements a in S. It can be shown that e is unique. In normal arithmetic, 0 and 1 are the identity elements associated with addition and multiplication respectively. In a Boolean algebra, 0 and 1 are the identities associated with the OR and the AND operations respectively.
a ° e = e ° a = a