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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