I’m looking for suggestions and recommendations for books that focus on constructions in mathematics, or at least have exercises which focus on construction-based proofs.
In particular, I seem to struggle with formulating proofs that entail a construction, so I’m looking for a resource which discusses approaching this feat, or at least has several such problems for practice.
For example, the proof of the iteration theorem involves constructing n-admissible functions, which seemed very left-field to me (at least, to conjure up on my own as a proof attempt before checking the published proof). Thanks in advance! Any other recommendations outside of resource recommendations will also be well-taken!
Edit: I should add this based on the first couple responses. I am familiar with proofs and proof-writing, it’s simply that the books that are being mentioned don’t seem to provide adequate preparation for encountering any of the substantial proofs that entail constructions (it may be an extreme example, but consider the proof of constructing the reals from the rationals, for instance). I’d just like a resource that would help me perhaps sketch out such a proof on my own- or even a bit- before seeing it.