identity element


: an element (such as 0 in the set of all integers under addition or 1 in the set of positive integers under multiplication) that leaves any element of the set to which it belongs unchanged when combined with it by a specified operation

Example Sentences

Recent Examples on the Web Individually examining each identity element alone when onboarding a new customer is often ineffective, as all the pieces of information provided may be technically valid. Robert Mckay, Forbes, 18 May 2021 For example, the identity element in the group must be assigned the identity matrix. Quanta Magazine, 9 June 2020 The real numbers have an identity element — the number 1. Quanta Magazine, 9 June 2020

These example sentences are selected automatically from various online news sources to reflect current usage of the word 'identity element.' Views expressed in the examples do not represent the opinion of Merriam-Webster or its editors. Send us feedback.

Word History

First Known Use

1902, in the meaning defined above

Time Traveler
The first known use of identity element was in 1902

Dictionary Entries Near identity element

Cite this Entry

“Identity element.” Dictionary, Merriam-Webster, Accessed 4 Feb. 2023.

Kids Definition

identity element

: an element of a set that leaves any other element of the set unchanged when combined with it using a given mathematical operation
0 is the identity element of the set of whole numbers under addition

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