It is a challenge to define an uncountable set of real numbers that is dense in the real line and whose complement is also uncountable and dense. In this article we specify, for any positive integer k ...

For more information about countable and uncountable sets, see books about "Analysis" (as advanced calculus is called). For example, Introductory Real Analysis, by A.N. Kolmogorov and S.V. Fomin (see ...