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Math Help - infinite sets problem

  1. #1
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    infinite sets problem

    Is it possible to find infinite countable set that is subset of
    infinite uncountable set
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  2. #2
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    Quote Originally Posted by joker40 View Post
    Is it possible to find infinite countable set that is subset of
    infinite uncountable set
    You mean like \mathbb{Z}\subset\mathbb{R}?
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  3. #3
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    Z

    What is Z
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  4. #4
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    for example

    for example infinite countable set of set (0,1) . I need to find infinite countable set of that is subset of (0,1) and also uncountable set that is proper subset of (0,1)
    every text book have example of proving set (0,1) is infinite uncountable. But I am lost how to find these 2 things. I think it trows me of because (0,1) is uncountable
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    Quote Originally Posted by joker40 View Post
    for example infinite countable set of set (0,1) . I need to find infinite countable set of that is subset of (0,1) and also uncountable set that is proper subset of (0,1) every text book have example of proving set (0,1) is infinite uncountable. But I am lost how to find these 2 things. I think it trows me of because (0,1) is uncountable
    It is difficult to read and understand that question.
    It is the case that the set (0,1) in indeed uncountable.
    The set of rational numbers, \mathbb{Q}, is countable.
    Any subset of a countable set is countable.
    So  \mathbb{Q} \cap (0,1) is a countable subset of (0,1).
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  6. #6
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    And the set of irrational numbers in (0, 1) is an uncountable proper subset.
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