Most recent change of Identity
Edit made on February 23, 2009 by derekcouzens at 18:35:27
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HEADERS_END
The Identity or Identity element is a special element of a set under a binary operation which when combined with any element of a set results in the same element.
Normally denoted by e.
If in a set A under a binary operation * there exists an element e such that for all a EQN:\in\ A then a * e = a then e is called the identity element.
Some care has to be taken if the operation is non-commutative when the definition above specifically defines what is called the right-identity.
The left identity is defined as that element such that for all a EQN:\in\ A then e * a = a.
The identity element of the set of integers under the binary operation of addition is the number zero.
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Enrichment Task
What is the identity element of the set of integers under the binary operation of multiplication?