Theorems · Theorem · number theory
AddCircle.exists_norm_nsmul_le
- 1000+ list: Dirichlet's approximation theorem
∀ {T : ℝ} [hT : Fact (0 < T)] (ξ : AddCircle T) {n : ℕ}, 0 < n → ∃ j ∈ Set.Icc 1 n, ‖j • ξ‖ ≤ T / ↑(n + 1)Dirichlet's approximation theorem
See also Real.exists_rat_abs_sub_le_and_den_le.
- Defined in
- Mathlib.NumberTheory.WellApproximable
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 249 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fact
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- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- ENNRealproof · cited by 9,879
- Norm.normstatement · cited by 5,413
- Factstatement and proof · cited by 2,726
- Nat.cast_oneproof · cited by 2,501
- LT.lt.leproof · cited by 2,189
- le_reflproof · cited by 2,061
- Set.Iccstatement · cited by 1,702
- MeasureTheory.MeasureSpace.volumeproof · cited by 1,323
- ENNReal.ofRealproof · cited by 863
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