Identity
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Normally denoted by e.
If in a set A under a binary operation * there exists an element e such that for all a $\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 $\in\$ A then e * a = a.
The identity element of the set of integers under the binary operation of addition is the number zero.
Enrichment Task
What is the identity element of the set of integers under the binary operation of multiplication?