Theorems · Theorem · general topology
Irrational.eventually_forall_le_dist_cast_div
∀ {x : ℝ}, Irrational x → ∀ (n : ℕ), ∀ᶠ (ε : ℝ) in nhds 0, ∀ (m : ℤ), ε ≤ dist x (↑m / ↑n)- Defined in
- Mathlib.Topology.Instances.Irrational
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- nhdsstatement · cited by 5,554
- Set.rangeproof · cited by 4,705
- Filter.Eventuallystatement · cited by 3,134
- Compl.complproof · cited by 2,925
- IsClosedproof · cited by 1,639
- Dist.diststatement and proof · cited by 1,539
- Metric.ballproof · cited by 735
- Filter.Eventually.monoproof · cited by 646
- IsOpen.mem_nhdsproof · cited by 470
- not_ltproof · cited by 306
- dist_commproof · cited by 188
Cited by2
Results whose statement or proof uses this declaration.
- Liouville.frequently_exists_numproof · cited by 1
- Irrational.eventually_forall_le_dist_cast_div_of_denom_leproof · cited by 1