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Math Help - Bijection between Sets

  1. #1
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    Bijection between Sets

    Suppose m<n. Prove that the intervals (0,1) and (m,n) are equinumerious by finding a specific bijection between them.


    I used the line formula to get f(x) = \frac{1}{n-m}(x-m), where m<n.

    I got this question wrong, and im wondering why? is it because it asked for a specific bijection? if so, how would I find one from what is given?
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  2. #2
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    Quote Originally Posted by p00ndawg View Post
    Suppose m<n. Prove that the intervals (0,1) and (m,n) are equinumerious by finding a specific bijection between them.
    I used the line formula to get f(x) = \frac{1}{n-m}(x-m), where m<n. I got this question wrong, and im wondering why? is it because it asked for a specific bijection? if so, how would I find one from what is given?
    You need the line determined by (0,m)~\&~(1,n).
    f(x)=(n-m)x+m.

    The function you gave does not biject (0,1) \leftrightarrow <br />
 (m,n).
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  3. #3
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    Quote Originally Posted by Plato View Post
    You need the line determined by (0,m)~\&~(1,n).
    f(x)=(n-m)x+m.

    The function you gave does not biject (0,1) \leftrightarrow <br />
 (m,n).
    ahh thank you.

    man this bijection stuff, is confusing the heck out of me.
    Last edited by Plato; October 19th 2009 at 03:52 PM. Reason: language
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