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Math Help - Compact Set proof

  1. #1
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    Compact Set proof

    If S1 and S2 are compact subsets of R, prove that S1 U S2 is compact.

    how can i prove this?

    I know that s1 and s2 are compact which would mean that s1 and s2 are both closed and bounded, and im not sure how to continue this.
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  2. #2
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    Quote Originally Posted by p00ndawg View Post
    If S1 and S2 are compact subsets of R, prove that S1 U S2 is compact.
    how can i prove this?
    The unioin of two finite collections is a finite collection.
    Any open cover for S_1\cup S_2 is a cover for each.
    So there is a subcover for each. Their union covers S_1\cup S_2.
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  3. #3
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    Quote Originally Posted by Plato View Post
    The unioin of two finite collections is a finite collection.
    Any open cover for S_1\cup S_2 is a cover for each.
    So there is a subcover for each. Their union covers S_1\cup S_2.
    ohh i was way over-thinking this.


    thanks
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