Theorems · Theorem · sequences and series

summable_iff_cauchySeq_finset

∀ {α : Type u_1} {β : Type u_2} [inst : UniformSpace α] [inst_1 : AddCommMonoid α] [CompleteSpace α] {f : β → α},
  Summable f ↔ CauchySeq fun s => ∑ b ∈ s, f b

The Cauchy criterion for infinite sums, also known as the Cauchy convergence test

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Group

Cited by

9 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceAddCommMonoidCompleteSpace