Definition:Cauchy Sequence

Rational Numbers
The concept can also be defined for the set of rational numbers $\Q$:

Also see

 * Convergent Sequence is Cauchy Sequence


 * Definition:Complete Metric Space: a metric space in which the converse holds, that is a Cauchy sequence is convergent.


 * Real Number Line is Complete Metric Space


 * Complex Plane is Complete Metric Space

Thus in $\R$ and $\C$ a Cauchy sequence and a convergent sequence are equivalent concepts.