Solution
= Solution
In a <metric space>, a <Cauchy sequence> has arbitrarily small distances between all sufficiently late terms:
$$
\boxed{\forall\varepsilon>0\;\exists N\;\forall m,n\geq N:\ d(x_m,x_n)<\varepsilon}.
$$
This condition compares terms to each other and does not assume that a limit exists in the space.