Theorems · Definition · commutative algebra

CauSeq.lim

{α : Type u_1} →
  [inst : Field α] →
    [inst_1 : LinearOrder α] →
      [inst_2 : IsStrictOrderedRing α] →
        {β : Type u_2} →
          [inst_3 : Ring β] →
            {abv : β → α} → [inst_4 : IsAbsoluteValue abv] → [CauSeq.IsComplete β abv] → CauSeq β abv → β

The limit of a Cauchy sequence in a complete ring. Chosen non-computably.

Defined in

Mathlib.Algebra.Order.CauSeq.Completion

Cited by

35 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRingRingIsAbsoluteValueCauSeq.IsComplete