1. The problem statement, all variables and given/known data show that if q is any countable ordinal, then there is a countable set A ⊆ R (in fact we can require A ⊆ Q), so that (A, <) ∼= (q, ∈). 3. The attempt at a solution since q is a countable ordinal this implies that it has a mapping to the naturals. to me this seems strong enough. and its also well ordered.