- #1
melknin
- 10
- 0
We recently discussed completion in my analysis class and I have a brief question on the subject. The completion X* of the metric space X is defined to be the set of Cauchy sequences of X with a defined equivalence relation ({xn}~{yn} if lim d(xn,yn)=0) and metric (D([xn],[yn])=lim d(xn,yn)). I understand the proof of this being a well-defined metric space, but how is it known that X* itself is complete?
Thanks in advance.
Thanks in advance.