# Transcendental

## Transcendental in philosophical contexts

In philosophy, **transcendental** experiences are experiences of an exclusively human nature that are other-worldly or beyond the human realm of understanding.

Things sometimes considered transcendental are religion, parts of philosophy (especially metaphysics and ontology), humour, death and more.

See also metaphysics.

## Transcendental field elements in mathematics

A **transcendental** function in Mathematics includes all the trigonometric functionss and logarithmic functions.

A **transcendental** element ξ of a field extension *K* over the field *F* is an element that is not the solution of a polynomial equation with coefficients in *F*, i.e., if there exists no polynomial

*P*(*x*) =*a*_{n}*x*^{n}+ ... +*a*_{1}*x*+*a*_{0},

*a*

_{i}∈

*F*, such that

*P*(ξ) = 0.

In the case of the field **C** of complex numbers or the field **R** of real numbers, a transcendental number is a number which is transcendental over the field **Q** of rational numbers.

*See also: (spiritual) transcendentalism, (technological) transhumanism*