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Math Help - Proof: infinite set minus a fintie set is infinite

  1. #1
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    Proof: infinite set minus a fintie set is infinite

    Suppose B is infinite and A is a finite subset of B. Then B - A is infinite.

    I am supposed to prove this...

    Any advice?
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  2. #2
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    Quote Originally Posted by jzellt View Post
    Suppose B is infinite and A is a finite subset of B. Then B - A is infinite.

    I am supposed to prove this...

    Any advice?
    Greetings jzellt.

    The definition of the difference of B and A (B - A) could be written as:
    B - A = \{x \, | \; x \; {\epsilon} {B} \;  and \; x \, {\not \epsilon} \; A\}

    Hopefully this will help make it more apparent why B - A is infinite.
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