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Math Help - inverse mapping simple question

  1. #1
    Member mabruka's Avatar
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    inverse mapping simple question

    hi!

    Does the property
    <br />
f^{-1}(A\cup B)=f^{-1}(A) \cup f^{-1}(B)<br />
    hold for an infinite union of sets??
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  2. #2
    Super Member
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    Quote Originally Posted by mabruka View Post
    hi!

    Does the property
    <br />
f^{-1}(A\cup B)=f^{-1}(A) \cup f^{-1}(B)<br />
    hold for an infinite union of sets??
    Why wouldn't it? It's easy to check that \{ x : f(x) \in \cup_{\alpha \in A} A_{\alpha } \} =\cup_{\alpha \in A} \{ x: f(x) \in A_{\alpha } \} which is equivalent to your statement.
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  3. #3
    Member mabruka's Avatar
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    sh*t! you are right, it is so simple to check it!
    gracias!
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