  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.

Number Theory