Transcendental number

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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. Only a few classes of transcendental numbers are known, because it can be difficult to show that a number is transcendental, but transcendental numbers are not rare. Indeed, almost all real and complex numbers are transcendental, since the algebraic numbers are countable, while the real numbers ⁠ R {\displaystyle \mathbb {R} } ⁠ and complex numbers ⁠ C {\displaystyle \mathbb {C} } ⁠ are both uncountable, and therefore larger than any countable set. All transcendental real numbers (also known as real transcendental numbers or transcendental irrational numbers...

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