EDB — 0N8

Exercises

1. [0N8] If \((x_ n)⊂ X\) is a Cauchy sequence and there exists \(x\) and a subsequence \(n_ m\) such that \(\lim _{m→∞} x_{n_ m}=x\) then \(\lim _{n→∞} x_{n}=x\).

   Solution 1

   [0N9]↺↻

   This ”lemma” is used in some important proofs, e.g. to show that a compact metric space is also complete.