What does cauchy sequence mean?
Definitions for cauchy sequence
cauchy se·quence
This dictionary definitions page includes all the possible meanings, example usage and translations of the word cauchy sequence.
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Wiktionary
Cauchy sequencenoun
A sequence in a normed vector space such that the difference between any two entries can be made arbitrarily small by stipulating that the two entries be sufficiently far out in the sequence.
Cauchy sequencenoun
A sequence in a metric space with metric d such that for every there exists a natural number N so that for every : .
Wikipedia
Cauchy sequence
In mathematics, a Cauchy sequence (French pronunciation: [koʃi]; English: KOH-shee), named after Augustin-Louis Cauchy, is a sequence whose elements become arbitrarily close to each other as the sequence progresses. More precisely, given any small positive distance, all but a finite number of elements of the sequence are less than that given distance from each other.
Wikidata
Cauchy sequence
In mathematics, a Cauchy sequence, named after Augustin-Louis Cauchy, is a sequence whose elements become arbitrarily close to each other as the sequence progresses. More precisely, given any small positive distance, all but a finite number of elements of the sequence are less than that given distance from each other. The utility of Cauchy sequences lies in the fact that in a complete metric space, the criterion for convergence depends only on the terms of the sequence itself. This is often exploited in algorithms, both theoretical and applied, where an iterative process can be shown relatively easily to produce a Cauchy sequence, consisting of the iterates, thus fulfilling a logical condition, such as termination. The notions above are not as unfamiliar as they might at first appear. The customary acceptance of the fact that any real number x has a decimal expansion is an implicit acknowledgment that a particular Cauchy sequence of rational numbers has the real limit x. In some cases it may be difficult to describe x independently of such a limiting process involving rational numbers.
Numerology
Chaldean Numerology
The numerical value of cauchy sequence in Chaldean Numerology is: 7
Pythagorean Numerology
The numerical value of cauchy sequence in Pythagorean Numerology is: 6
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"cauchy sequence." Definitions.net. STANDS4 LLC, 2024. Web. 26 Apr. 2024. <https://www.definitions.net/definition/cauchy+sequence>.
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