# Identity Property

When a set possesses an **identity element** for a given operation, the mathematical system of the set and operation is said to possess the identity property for that operation. For example, the set of all functions of a **variable** over the **real numbers** has the identity element, or identity function, I(x) = x. In other words, if f(x) is any function over the real numbers, then f(I(x)) = I(f(x)) = f(x).

See also Function.

## Additional topics

- Identity of Persons - Seventeenth Century, Eighteenth Century, Twentieth And Twenty-first Centuries, Bibliography
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Science EncyclopediaScience & Philosophy: *Hydrazones* to *Incompatibility*