Cantor's List of Real Algebraic Numbers of Heights 1 to 7

Abstract

Cantor gave in his fundamental article an elegant proof of the countability of real algebraic numbers based on a positive integer height, denoted by him as N, of integer and irreducible polynomials of given degree (denoted by him as n) with relative prime coefficients. The finite number of real algebraic numbers with given height he called phi(N), and gave the first three instances.\pn Here we give a systematic list for the real algebraic numbers of height, which we denote by n, for n from 1 to 7 and polynomials of degree k.