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.

Transcendental numbers 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, i.e. if there exists no polynomial

P(x) = a_n xⁿ + ... + a₁ x + a₀,

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 ξ is an element of the field which is transcendental over the field, Q, of rational numbers.