| Cauchy Sequence |
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| CATEGORIES ABOUT CAUCHY SEQUENCE | |
| metric geometry | |
| mathematical analysis | |
| topology | |
| abstract algebra | |
| sequences | |
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Cauchy sequences require the notion of distance so they can only be defined in a Metric Space . Generalizations to more abstract Uniform Spaces exist in the form of Cauchy Filter and Cauchy Net . They are of interest because in a Complete Space , all such sequences Converge To A Limit , and one can test for "Cauchiness" without knowing the value of the limit (if it exists), in contrast to the Definition Of Convergence . CAUCHY SEQUENCE OF REAL NUMBERS A sequence : of Real Number s is called Cauchy, if for every Positive real number ''r'' > 0 there is a positive Integer ''N'' such that for all integers ''m'',''n'' > ''N'' one has |
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