Cauchy sequence

Lets U = {un} a sequence of points in a normed space M. It is said thatU is Cachy-Sequence if

∀ ε gt;0, ∃ n0 >0 : si n, m>n0 => || un - um|| < ε

That is, the points of the sequence are close from an0

Note 1: Every Cauchy sequence is bounded.

Note2: Every convergent sequence is Cauchy (the converse is not true, but if the metric space is complete then every Cauchy sequence has a convergent subsequence).