To be honest we haven't talked about Cauchy sequences so I'm not sure how to connect all these.

However, I will do my best with what I have gathered form Wikipedia...

Since

is a limit point in

then for

there must be a sequence of points that are contained in

that converge to

.

Therefore, we have a sequence of points that are converging to a point

. Thus,(from what I gather about Cauchy Sequences), this sequence is a Cauchy sequence since the points are converging to

.

Then, (I got the following from Wikipedia) M is said to be complete (or Cauchy) if every Cauchy sequence of points in M has a limit that is also in M or alternatively if every Cauchy sequence in M converges in M.

Here, our Cauchy sequences is converging to

where

. So,

is complete?

Sorry this is might be kinda weak but I did what I could for never have learning about Cauchy Sequences or completeness....