Cauchy sequence and Logic programming: Difference between pages

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'''Logic programming''' is using [[mathematical logic]] to write [[computer program]]s. There are specialized [[programming language]]s where the user can directly enter logical statements. Probably the best-known of these languages is called [[Prolog]]. [[Alonzo Church]] used a form of logic programming in what is known as [[lambda calculus]] today. Logic programming has also been used in [[LISP]].
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Programs consist of a set of rules and facts. In most cases, logic programming uses what is called [[negation as failure]] or ''weak negation:'' This means that if it is not possible to derive some clause <math>p</math> from the facts and rules, the system will assume that its negation is true.
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[[Category:Logic]]
| image1    = Cauchy sequence illustration.svg
| caption1  = (a) The plot of a Cauchy [[sequence]] <math>(x_n),</math> shown in blue, as <math>x_n</math> versus <math>n</math> If the space containing the sequence is complete, the "ultimate destination" of this sequence (that is, the limit) exists.
| image2    = Cauchy sequence illustration2.svg
| caption2  = (b) A sequence that is not Cauchy. The [[Element (mathematics)|elements]] of the sequence fail to get arbitrarily close to each other as the sequence progresses.
}}In [[mathematics]], a '''Cauchy sequence''' is a [[sequence]] where the distance between any two elements of the sequence decreases as the sequence progresses. Cauchy sequences are named after [[Augustin-Louis Cauchy]].
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Latest revision as of 11:12, 7 October 2014

Logic programming is using mathematical logic to write computer programs. There are specialized programming languages where the user can directly enter logical statements. Probably the best-known of these languages is called Prolog. Alonzo Church used a form of logic programming in what is known as lambda calculus today. Logic programming has also been used in LISP.

Programs consist of a set of rules and facts. In most cases, logic programming uses what is called negation as failure or weak negation: This means that if it is not possible to derive some clause [math]\displaystyle{ p }[/math] from the facts and rules, the system will assume that its negation is true.

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