## identity element

identity element of a set S on which some dyadic operation ◦ is defined. An element e with the property that ae = ea = 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.

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