| 1. | a root of an algebraic equation with integral coefficients. |
| 2. | root 1 (def. 10b). |
| algebraic number n. A number that is a root of a polynomial equation with rational coefficients. |
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.
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