Denote by M the set of numbers of the type A + B 2^{1/2},
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.

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Last revised August 2003