transcendental number
number that cannot be found as a result of an algebraic equation with integer coefficients
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A transcendental number is a type of number that cannot be obtained by solving any algebraic equation made up of whole numbers and basic mathematical operations. These numbers matter because they reveal fundamental limits to what kinds of solutions equations can have, and famous examples like pi and e show up everywhere in mathematics and science.
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In mathematics, a transcendental number is a real or complex number that is not algebraic: that is, not the root of a non-zero polynomial with integer (or, equivalently, rational) coefficients. The best-known transcendental numbers are π and e. The quality of a number being transcendental is called transcendence.
Though only a few classes of transcendental numbers are known, because it can be difficult to show that a number is transcendental, transcendental numbers are not rare: indeed, almost all real and complex numbers are transcendental, since the algebraic numbers are countable, while the real numbers