Theorems · Theorem · sequences and series
not_summable_of_ratio_norm_eventually_ge
∀ {α : Type u_4} [inst : SeminormedAddCommGroup α] {f : ℕ → α} {r : ℝ},
1 < r → (∃ᶠ (n : ℕ) in Filter.atTop, ‖f n‖ ≠ 0) → (∀ᶠ (n : ℕ) in Filter.atTop, r * ‖f n‖ ≤ ‖f (n + 1)‖) → ¬Summable f- Defined in
- Mathlib.Analysis.SpecificLimits.Normed
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- nhdsproof · cited by 5,554
- Norm.normstatement and proof · cited by 5,413
- Filter.Tendstoproof · cited by 3,814
- Filter.Eventuallystatement and proof · cited by 3,134
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Filter.atTopstatement and proof · cited by 2,405
- zero_addproof · cited by 2,366
- SummationFilter.unconditionalstatement · cited by 2,068
- Summablestatement · cited by 778
- norm_nonnegproof · cited by 725
- Filter.Tendsto.compproof · cited by 560
Cited by2
Results whose statement or proof uses this declaration.
- not_summable_of_ratio_test_tendsto_gt_oneproof · cited by 1
- FormalMultilinearSeries.ofScalars_radius_eq_zero_of_tendstoproof · cited by 1