- 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.
* 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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