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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 adds Legendre's Theorem on rational approximations:

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.


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@MichaelStollBayreuth MichaelStollBayreuth added awaiting-review The author would like community review of the PR awaiting-CI The author would like to see what CI has to say before doing more work. t-algebra Algebra (groups, rings, fields etc) t-number-theory Number theory (also use t-algebra or t-analysis to specialize) labels Feb 17, 2023
@github-actions github-actions bot removed the awaiting-CI The author would like to see what CI has to say before doing more work. label Feb 17, 2023
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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.

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kbuzzard commented May 9, 2023

maintainer merge

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github-actions bot commented May 9, 2023

🚀 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+

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bors bot commented May 10, 2023

✌️ MichaelStollBayreuth can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

@leanprover-community-bot-assistant leanprover-community-bot-assistant added delegated The PR author may merge after reviewing final suggestions. and removed awaiting-review The author would like community review of the PR labels May 10, 2023
Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
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bors r+

bors bot pushed a commit that referenced this pull request May 10, 2023
…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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@bors bors bot changed the title feat(number_theory/diophantine_approximation): add Legendre's thm on rat'l approximations [Merged by Bors] - feat(number_theory/diophantine_approximation): add Legendre's thm on rat'l approximations May 10, 2023
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@bors bors bot deleted the contfrac_legendre branch May 10, 2023 16:20
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