algebraic number | |
—n | |
Compare transcendental number any number that is a root of a polynomial equation having rational coefficients such as √2 but not π |
algebraic number
realreal number for which there exists a polynomial equation with integer coefficients such that the given real number is a solution. Algebraic numbers include all of the natural numbers, all rational numbers, some irrational numbers, and complex numbers of the form pi+q, where p and q are rational, and i is the square root of 1. For example, i is a root of the polynomial x2+1=0. Numbers, such as that symbolized by the Greek letter pi, that are not algebraic are called transcendental numbers. The mathematician Georg Cantor proved that, in a sense that can be made precise, there are many more transcendental numbers than there are algebraic numbers, even though there are infinitely many of these latter.
Learn more about algebraic number with a free trial on Britannica.com.