identity element
noun
: 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
Examples of identity element in a Sentence
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The identity element always forms a subgroup by itself, called the trivial subgroup.
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Leila Sloman, WIRED, 6 Oct. 2024
The third rule is that the group must contain an element that leaves other group elements unchanged, called an identity element.
—Leila Sloman, WIRED, 6 Oct. 2024
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
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Leila Sloman, WIRED, 6 Oct. 2024
The third rule is that the group must contain an element that leaves other group elements unchanged, called an identity element.
—Leila Sloman, WIRED, 6 Oct. 2024
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
Cite this Entry
“Identity element.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/identity%20element. Accessed 21 Jul. 2025.
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