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Math Help - Bijection Example

  1. #1
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    Bijection Example

    I am working on a proof to show that two open intervals (a, b) such that a<b and (c,d) such that c<d are equinumerous. To do so I know that I need to show a bijection between the two, but am having difficulty coming up with a function that I can prove is a bijection.

    The first part of the problem asks to come up with a bijection mapping (0,1) onto (m,n) where m<n. Maybe if someone would be kind enough to give that example I could then find a general case.

    Thanks in advance.
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  2. #2
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    Hi Mom

    How about m -> 0, n -> 1, x -> (x-m)/(n-m) for all x between m and n?
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  3. #3
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    Try f(x) = \frac{{d - c}}{{b - a}}\left( {x - a} \right) + c.
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