Possible Duplicate:
Order types of positive reals
The title is self-explanatory.
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closed as exact duplicate by François G. Dorais♦ Oct 29 2010 at 11:04 |
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The answer is yes. Choose an enumeration $\alpha_1,\alpha_2,\dots$ of your well-ordering and define a map by setting: $$\alpha_n \mapsto \sum_{k : \alpha_k < \alpha_n} \frac1{2^k} \in \mathbb R.$$ |
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