Theorems · Theorem · sequences and series
cauchySeq_of_le_geometric_two
∀ {α : Type u_1} [inst : PseudoMetricSpace α] {C : ℝ} {f : ℕ → α},
(∀ (n : ℕ), dist (f n) (f (n + 1)) ≤ C / 2 / 2 ^ n) → CauchySeq fIf dist (f n) (f (n+1)) is bounded by (C / 2) / 2^n, then f is a Cauchy sequence.
- Defined in
- Mathlib.Analysis.SpecificLimits.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
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.
- Realstatement and proof · cited by 25,697
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- CauchySeqstatement · cited by 131
- hasSum_geometric_two'proof · cited by 4
- cauchySeq_of_dist_le_of_summableproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- CircleDeg1Lift.tendsto_translationNumber_auxproof · cited by 3