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Answer to Question #4829 in Real Analysis for John

Question #4829
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?
Expert's answer
yes, it is possible. {A, B, C, ...} are needed subsets, and for every of them
equation A=N is true: A=N, B=N, ...

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