# Transcendental

## Transcendental in philosophical contexts

The philosophical term **transcendental** refers to experiences of an exclusively human nature, "other-worldly" or "beyond the human realm of understanding".

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

See also metaphysics.

An element ξ of a field extension `K` over the field `F` is called **transcendental** if it 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},

with all

`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*