Theorems · Theorem · sequences and series
alternating_series_error_bound
∀ {E : Type u_5} [inst : Ring E] [inst_1 : LinearOrder E] [IsOrderedRing E] [inst_3 : UniformSpace E]
[IsUniformAddGroup E] [CompleteSpace E] [OrderClosedTopology E] (f : ℕ → E),
Antitone f → Summable f → ∀ (n : ℕ), |∑' (i : ℕ), (-1) ^ i * f i - ∑ i ∈ Finset.range n, (-1) ^ i * f i| ≤ f n- Defined in
- Mathlib.Analysis.SpecificLimits.Normed
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites42
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
- Ringstatement and proof · cited by 7,463
- Finset.sumstatement and proof · cited by 5,195
- mul_oneproof · cited by 3,885
- LE.le.transproof · cited by 3,151
- one_mulproof · cited by 2,841
- CompleteSpacestatement and proof · cited by 2,532
- Finset.sum_congrproof · cited by 2,323
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- UniformSpacestatement and proof · cited by 2,040
- absstatement · cited by 1,814
- Filter.univ_mem'proof · cited by 1,672
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