In my homework in set theory i was asked to find a bijective function between (a,b) and (c,d) that are subsets of R. d>c and b>a.

I'm having problems thinking of a function that is surjective and injective. i thought of the function for example f(x) = x+d-b, where x is an element in (a,b) and it is indeed injective, but not surjective...

I can use some advice please



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Hint: $$(b-a)\cdot\dfrac{d-c}{b-a} = d-c.$$

  • $\begingroup$ I don't understand how this helps. I mean, yeah it's true what you wrote but I don't know how to use this to solve the question $\endgroup$ Oct 29 '13 at 19:52
  • $\begingroup$ The problem with your proposed "solution" was that the lengths of the intervals were not equal. Hence you must use this proportionality factor. $\endgroup$
    – njguliyev
    Oct 29 '13 at 21:12

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