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High Quality Content by WIKIPEDIA articles! In mathematics, a transcendental number is a number (possibly a complex number) that is not algebraic, that is, not a solution of a non-constant polynomial equation with rational coefficients. The most prominent examples of transcendental numbers are ? and e. Only a few classes of transcendental numbers are known. This is partly because it can be extremely difficult to show that a given number is transcendental. However, transcendental numbers are not rare: indeed, almost all real and complex numbers are transcendental, since the algebraic numbers are countable, but the sets of real and complex numbers are uncountable. All transcendental numbers are irrational, since all rational numbers are algebraic. The converse is not true: not all irrational numbers are transcendental (however, most are).