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Math Help - Real Analysis

  1. #1
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    Real Analysis

    1. Prove that if A is an uncountable set and B is a countable set then A-B is uncountable.



    2. Show that [0,1] is equivalent to (0,1).

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  2. #2
    Super Member Failure's Avatar
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    Quote Originally Posted by mathgirl1188 View Post
    1. Prove that if A is an uncountable set and B is a countable set then A-B is uncountable.
    If \scriptstyle A\backslash B were countable, then \scriptstyle (A\backslash B)\cup B, being the union of two countable sets and a superset of A, would also be countable: a contradiction to the assumption that A is uncountable.


    2. Show that [0,1] is equivalent to (0,1).
    [0,1] is a superset of (0,1), and is also equivalent to the subset [0.5,0.75] of (0,1), hence...
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