Solution
= Solution
A <metric space> is \b[<complete>] when every <Cauchy sequence> in it converges to a point of that space. A <sequence> is Cauchy when, for each $\epsilon>0$, there is $N$ such that $d(x_m,x_n)<\epsilon$ whenever $m,n\geq N$. The requirement that the limit lie in the space distinguishes completeness from having limits only in a larger ambient space.