Theorems · Theorem · sequences and series
cauchySeq_of_edist_le_geometric_two
∀ {α : Type u_1} [inst : PseudoEMetricSpace α] (C : ENNReal),
C ≠ ⊤ → ∀ {f : ℕ → α}, (∀ (n : ℕ), edist (f n) (f (n + 1)) ≤ C / 2 ^ n) → CauchySeq fIf edist (f n) (f (n+1)) is bounded by C * 2^-n, then f is a Cauchy sequence.
- Defined in
- Mathlib.Analysis.SpecificLimits.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- PseudoEMetricSpacestatement and proof · cited by 1,536
- EDist.ediststatement and proof · cited by 735
- div_eq_mul_invproof · cited by 715
- CauchySeqstatement · cited by 131
- ENNReal.inv_powproof · cited by 9
- cauchySeq_of_edist_le_geometricproof · cited by 2
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