Transcendental Numbers

A number is algebraic if it satisfies a rational polynomial equation. If a number x satisfies the equation

a_nxⁿ + a_n-1x^n-1 + … + a₁x¹ + a₀ = 0,

then x is said to be algebraic.

A number that is not algebraic is transcendental. If there is no equation of the form

a_nxⁿ + a_n-1x^n-1 + … + a₁x¹ + a₀ = 0

which holds for x = y, then y is said to be transcendental.