Theorems · Theorem · general topology
Filter.frequently_high_scores
∀ {β : Type u_4} [inst : LinearOrder β] [NoMaxOrder β] {u : ℕ → β},
Filter.Tendsto u Filter.atTop Filter.atTop → ∃ᶠ (n : ℕ) in Filter.atTop, ∀ k < n, u k < u nIf u is a sequence which is unbounded above,
then it Frequently reaches a value strictly greater than all previous values.
- Defined in
- Mathlib.Order.Filter.AtTopBot.Finite
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderNoMaxOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- Filter.Frequentlystatement · cited by 414
- NoMaxOrderstatement and proof · cited by 340
- Filter.high_scoresproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Filter.strictMono_subseq_of_tendsto_atTopproof · cited by 2
- Filter.frequently_low_scoresproof · cited by 0