MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Possible Duplicate:
Order types of positive reals

The title is self-explanatory.

share|cite|improve this question

marked as duplicate by François G. Dorais Oct 29 '10 at 11:04

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

Yes. See the answers to this identical question - – François G. Dorais Oct 29 '10 at 11:05
Thank you, and sorry for the duplicate. – Charlie Oct 29 '10 at 11:09
up vote 5 down vote accepted

The answer is yes. Choose an enumeration $\alpha_1,\alpha_2,\dots$ of your well-ordering and define a map by setting:

$$\alpha_n \mapsto \sum_{k : \alpha_k < \alpha_n} \frac1{2^k} \in \mathbb R.$$

share|cite|improve this answer

Not the answer you're looking for? Browse other questions tagged or ask your own question.