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    I need to find a function h:[0,1) \rightarrow \mathbb{R} which is bounded but attains neither of its bounds.

    For a function in general I would say maybe tanh(x) but I don't know if I can as my domain is restricted.
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    Whilst that doesn't obtain it's maximum, it does attain it's minimum.

    Think about what's going on at the "1" end of your interval, and how openness helps...
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    (Original post by SimonM)
    Whilst that doesn't obtain it's maximum, it does attain it's minimum.

    Think about what's going on at the "1" end of your interval, and how openness helps...
    I'm still a little confused.

    This function I'm supposed to have I imagine would look similar ish to a tanh(x) graph, its got to tail off to two separate values. I'm struggling to think of a function which does this at 0 and 1.
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    (Original post by The Muon)
    I'm still a little confused.

    This function I'm supposed to have I imagine would look similar ish to a tanh(x) graph, its got to tail off to two separate values. I'm struggling to think of a function which does this at 0 and 1.
    It's a matter of compactness. Continuity forces the function to behave nicely near 0, since it is defined at 0. At 1, however, the function need not exist, so it can be as messy as you like
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    There's another thread on this: http://www.thestudentroom.co.uk/show....php?t=1168855
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    my bad.

    And thanks simon (and dave for your constant help)
 
 
 
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