Identity element

Written by Joe Zeng last updated

An identity element in a set with a binary operation is an element that leaves any element unchanged when combined with it in that operation.

Formally, we can define an element to be an identity element if the following two statements are true:

  1. For all , . If only this statement is true then is said to be a left identity.
  2. For all , . If only this statement is true then is said to be a right identity.

The existence of an identity element is a property of many algebraic structures, such as groups, rings, and fields.

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