Main Page | See live article | Alphabetical index 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) = an xn + ... + a1 x + a0, with all ai∈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 This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.