Theorems · Theorem · number theory
not_summable_of_antitone_of_neg
∀ {f : ℕ → ℝ}, Antitone f → ∀ {n : ℕ}, f n < 0 → ¬Summable fIf f : ℕ → ℝ is decreasing and has a negative term, then f is not summable.
- Defined in
- Mathlib.Analysis.SumOverResidueClass
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Filter.Tendstoproof · cited by 3,814
- Filter.atTopproof · cited by 2,405
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- absproof · cited by 1,814
- LE.le.trans_ltproof · cited by 795
- Summablestatement and proof · cited by 778
- Antitonestatement and proof · cited by 563
- dist_zero_rightproof · cited by 172
- neg_le_neg_iffproof · cited by 57
- abs_of_negproof · cited by 39
Cited by1
Results whose statement or proof uses this declaration.
- not_summable_indicator_mod_of_antitone_of_negproof · cited by 1