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Math Help - Order/Relation Question

  1. #1
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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. #2
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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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