# Transcendence (mathematics)

- Transcendence (mathematics)
In mathematics, **transcendence** refers to the property of not being algebraic. The main examples of objects with this property are:

* **transcendental numbers**, which are complex numbers that are not a root of any non-zero polynomial with rational coefficients;

* **transcendental functions**, functions that are not a root of any non-zero polynomial whose coefficients are themselves polynomials;

* **transcendental elements** generalise the idea of transcendental numbers to abstract algebra, in particular to general field extensions rather than just considering complex numbers as transcendental over the rational numbers.

**ee Also**

* Algebraic numbers, those complex numbers that are not transcendental.

* Algebraic functions, functions that are not transcendental.

* Algebraic elements, elements of a field extension that are not transcendental.

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