Cauchy Sequence that Does Not Converge What are some good examples of sequences which are Cauchy, but do not converge?
I want an example of such a sequence in the metric space $X = \mathbb{Q}$, with $d(x, y) = |x - y|$.  And preferably, no use of series.

You take any irrational number, say $\sqrt2$, and you consider its decimal expansion,
$$
\sqrt2=1.4142\ldots
$$
Then you define $x_1=1$, $x_2=1.4$, $x_3=1.41$, $x_4=1.414$, etc.
