Order/Relation Question

• Nov 15th 2006, 08:05 AM
action259
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
• Nov 15th 2006, 10:51 AM
Plato
$\begin{array}{l}
A = \left\{ 0 \right\} \cup \left( {1,2} \right)\quad \& \quad B = [0,1) \\
f:A \mapsto B,\quad f(x) = \left\{ {\begin{array}{lr}
0 & {x = 0} \\
{x - 1} & {x \in (1,2)} \\
\end{array}} \right. \\
\end{array}$

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