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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