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Thread: Order/Relation Question

  1. November 15th 2006, 07:05 AM #1
    action259
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    Order/Relation Question

    show that the sets A={0}U(1,2) and B=[0,1) are order isomorphic?

    not really how to do this question, can anyone give me a hand? Thanks
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  2. November 15th 2006, 09:51 AM #2
    Plato
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    \begin{array}{l}<br /> A = \left\{ 0 \right\} \cup \left( {1,2} \right)\quad \& \quad B = [0,1) \\ <br /> f:A \mapsto B,\quad f(x) = \left\{ {\begin{array}{lr}<br /> 0 & {x = 0} \\<br /> {x - 1} & {x \in (1,2)} \\<br /> \end{array}} \right. \\ <br /> \end{array}

    You must show that the function is bijective and order preserving.
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