Transcendence (mathematics)

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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.

[edit] See 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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