The difference between Identity and Identity function
When used as nouns, identity means sameness, identicalness, whereas identity function means a function whose value is always the same as its independent variable, and for which the codomain equals the domain.
check bellow for the other definitions of Identity and Identity function
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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 function as a noun (mathematics):
A function whose value is always the same as its independent variable, and for which the codomain equals the domain.