The difference between Identity and Identity element
When used as nouns, identity means sameness, identicalness, whereas identity element means an element of an algebraic structure which when applied, in either order, to any other element via a binary operation yields the other element.
check bellow for the other definitions of Identity and Identity element
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Identity as a noun:
Sameness, identicalness; the quality or fact of (several specified things) being the same.
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Identity as a noun:
The difference or character that marks off an individual from the rest of the same kind, selfhood.
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Identity as a noun:
A name or persona—the mask or appearance one presents to the world—by which one is known.
Examples:
"This criminal has taken on several identities."
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Identity as a noun:
Sense of who one is.
Examples:
"I've been through so many changes, I have no sense of identity."
"This nation has a strong identity."
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Identity as a noun (algebra, computing):
Any function which maps all elements of its domain to themselves.
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Identity as a noun (algebra):
An element of an algebraic structure which, when applied to another element under an operation in that structure, yields this second element.
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Identity as a noun (Australia, NZ):
A well-known or famous person.
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Identity element as a noun (algebra):
An element of an algebraic structure which when applied, in either order, to any other element via a binary operation yields the other element.