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Search Transcendental number Language Watch Edit Pi ( π ) is a well known transcendental number In mathematics , a transcendental number is a complex number that is not algebraic —that is, not a root (i.e., solution) of a nonzero polynomial equation with integer or equivalently rational coefficients . The most popular transcendental numbers are π and e . [1] [2] Though only a few classes of transcendental numbers are known, in part because it can be extremely difficult to show that a given number is transcendental, transcendental numbers are not rare. Indeed, almost all real and complex numbers are transcendental, since the algebraic numbers compose a countable set , while the set of real numbers and the set of complex numbers are both uncountable sets , and therefore larger than any countable set. All real transcendental numbers are irrational numbers , since all rational numbers are algebraic. The converse is not true: not all irrational numbers ar