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[Merged by Bors] - feat(number_theory/diophantine_approximation): add Legendre's thm on rat'l approximations #18460
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This is great! Thanks for taking the time to get this proof into a mathlib-ready form -- I remember ploughing through this when I was supervising a project on it and it was pretty fiddly.
maintainer merge |
🚀 Pull request has been placed on the maintainer queue by kbuzzard. |
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Thanks! It's a nice result and well documented.
bors d+
✌️ MichaelStollBayreuth can now approve this pull request. To approve and merge a pull request, simply reply with |
Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
bors r+ |
…rat'l approximations (#18460) This adds *Legendre's Theorem* on rational approximations: ```lean lemma ex_continued_fraction_convergent_eq_rat {ξ : ℝ} {q : ℚ} (h : |ξ - q| < 1 / (2 * q.denom ^ 2)) : ∃ n, (generalized_continued_fraction.of ξ).convergents n = q ``` See this [Zulip thread](https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/Diophantine.20approximation/near/323758115). Co-authored-by: Michael Stoll <99838730+MichaelStollBayreuth@users.noreply.github.com>
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This adds Legendre's Theorem on rational approximations:
See this Zulip thread.