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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- Nov 15th 2006, 07:05 AMaction259Order/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 - Nov 15th 2006, 09:51 AMPlato
$\displaystyle \begin{array}{l}

A = \left\{ 0 \right\} \cup \left( {1,2} \right)\quad \& \quad B = [0,1) \\

f:A \mapsto B,\quad f(x) = \left\{ {\begin{array}{lr}

0 & {x = 0} \\

{x - 1} & {x \in (1,2)} \\

\end{array}} \right. \\

\end{array}$

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