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Chashokreddy18@gmail.com posted an Question
March 24, 2020 • 02:32 am 30 points
  • CSIR NET
  • Mathematical Sciences

Real analysis - cantor's theorem can you explain one by one ?

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  • Chashokreddy18@gmail.com Tiwari

    what is the general (minimum )cardinality of a power set?

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    Ujjawal vishal best-answer

    1. If sets are countable ,then it is not necessary that they are equivalent. Let, A={1,2} & B={3,4,5} here,both A & B are countable (infact finite) but they have different cardinality.So, they are not equivalent. Similarly, N is countable but it is not equivalent to any finite set. But, if your question is about countably infinite sets, then yes they are equivalent. N,Z,Q are equivalent sets. 2. Yes, every open interval is uncountable. 3. Yes ,we can define Cartesian product of uncountable sets. The resultant set is also uncountable. See attached image to understand Cartesian product of intervals 4.No, B is a set here. So, for P(1) we have to take every subset of A. Here, P(1) is defined in set builder method which is stating a property that it is set of subsets of A.

    cropped5234471794687822392.jpg
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