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I have the following problem:

Show by induction that every countable ordinal is isomorphic to a subset of rationals

I have read several posts on the site, among them [1],[2] and I have taken the answers from there to try to solve this problem by induction, but I have not achieved anything, I would appreciate any help, this topic of ordinals is new to me. Thank you.

Haus
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    You don't need the axiom of choice here, at all. You can do this either by induction, very much in the spirit of "Every countable linear order embeds into the rationals", or by transfinite induction, one ordinal at a time. – Asaf Karagila Dec 08 '20 at 12:22
  • @Asaf Yes, the axiom of choice had asked me another person. Just the problem I have is to test it by induction, I don't know how to use it for this – Haus Dec 08 '20 at 15:51

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