Every countable ordinal is isomorphic to a set of rationals

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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.