Answer to Question #4829 in Real Analysis for John

Question

Consider the set of natural numbers N.Is it possible to build a family of subsets of N such that it's cardinality is continuum and for arbitrary two subsets A and B - A includes B or B includes A?

Answer 1

yes, it is possible. {A, B, C, ...} are needed subsets, and for every of them
equation A=N is true: A=N, B=N, ...