The order type of the rationals. Herewith another mind-numbingly naive question from a reader of philosophy. My question concerns the order type of the rational numbers. Omega squared seems a natural first choice, but obviously this does not look anything like the natural ordering of the rationals. Is it known where the order type of Q occurs in the hierarchy of ordinal numbers? Is there a known ordinal-arithmetic expression describing it a function of omega? Finally, I really must buy a textbook on the subject of Set Theory. Wiki is a fantastic resource and the maths pages are of exceptionally high quality, but I don't want to get into bed at night with my laptop. Is there a standard, undergraduate text that could be recommended.

The ordinals are order types of **well-ordered partial orders**. The rational numbers are not well-ordered, therefore their order type does not occur within the ordinal hierarchy.