**In Real Numbers**

A sequence

of real numbers is called *Cauchy*, if for every positive real number *ε*, there is a positive integer *N* such that for all natural numbers *m*, *n* > *N*

where the vertical bars denote the absolute value. In a similar way one can define Cauchy sequences of rational or complex numbers. Cauchy formulated such a condition by requiring to be infinitesimal for every pair of infinite *m, n*.

Read more about this topic: Cauchy Sequence

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