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Math Help - help to prove

  1. #1
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    help to prove

    prove if a A is uncountable and A is a subset of B, then B is uncountable
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  2. #2
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    Quote Originally Posted by dbhakta View Post
    prove if a A is uncountable and A is a subset of B, then B is uncountable
    Since A is uncountable it means |A| > \aleph_0. Since A\subseteq B it means |A|\leq |B| because the identity map on A will be an injective function. Thus, \aleph_0 < |A| \leq |B|.
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