## 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.

## Transcendental field elements in mathematics

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},

`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*