Recently I heard two related problems about countability. They should be good exercises for mathematial analysis amateur.
Below N denotes the set of natural numbers.
The first question is, is there exists an uncountable collection of finite subsets of N, such that for any two subsets A and B in the collection, one is the subset of another?
The second question is, is there exists an uncountable collection of subsets of N, such that for any two subsets A and B in the collection, one is the subset of another?
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The first question is very easy. The second question is a bit tricky.
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