Idea for Problem 5 submitted by Simon Elimelakh

Problem 5

Denote by M the set of numbers of the type A + B 21/2, where A and B are integers. Prove that any neighborhood of a real number contains an infinite number of elements of the set M.


M is closed under addition and multiplication. sqrt(2) - 1 < 1/2, so its powers yield arbitrarily small elements of M. Therefore, M is dense.

Last revised August 2003