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panderse
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Homework Statement
Let w,x,y,z be real #'s with w<x and y<z
Construct bijections
[w,x] <-> [y,z]
(w,x] <-> [y,z)
Homework Equations
The Attempt at a Solution
So for the closed interval bijection, I was trying to work with the following:
(z-y)/(x-w) * (f-w) + y where w,x,y,z are the #'s and f is the function variable.
If I'm not mistaken, this is injective and surjective, thus bijective.
One thing I was wondering is simply what it means to "construct" the bijection?? Does it just mean presenting the equation above and showing that it is 1-1 and onto? Or is there something more complex at work?
And for the (...] <-> [...) portion, I am at a loss. Can this be done in a regular function type format, or do I need to do it piecewise?
Thanks
Pete