Dedekind cut

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MetadadosDescriçãoIdioma
Autor(es): dc.contributorUniversidade Estadual Paulista (UNESP)-
Autor(es): dc.creatorSchreiber, Michael-
Data de aceite: dc.date.accessioned2019-08-21T17:40:25Z-
Data de disponibilização: dc.date.available2019-08-21T17:40:25Z-
Data de envio: dc.date.issued2011-05-30-
Data de envio: dc.date.issued2011-05-30-
Data de envio: dc.date.issued2011-05-30-
Fonte completa do material: dc.identifierhttp://acervodigital.unesp.br/handle/123456789/22048-
Fonte completa do material: dc.identifierhttp://objetoseducacionais2.mec.gov.br/handle/mec/13742-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/capes/452943-
Descrição: dc.descriptionEducação Superior::Ciências Exatas e da Terra::Matemática-
Descrição: dc.descriptionDedekind invented cuts to construct the real numbers from the rationals. Another method is to use Cauchy sequences. Split the rationals in two disjoint sets A and B, such that all the elements of A are smaller than all the element of B. This is called a cut. There are four cases: A has a largest element or not, and B has a smallest element or not. The case where A has a largest element x and B has a smallest element y is impossible. On the one hand, the average of x and y, being a rational, must belong to one of A or B. On the other hand, their average cannot belong to A (because x < (x+y)/2) nor to B (because (x+y)/2 < y). If there is a largest element of A or a smallest element of B, then the cut is rational. In the fourth case, the most interesting one, A does not have a largest element and B does not have a smallest element. In that case the cut is irrational. This visualization draws circles with rational radii smaller than 1. Examples of rational cuts are selected from these, with a red circle used to indicate that the rational is included in one of the two sets. Examples for irrational cuts are generated as multiples of √2/2-
Publicador: dc.publisherWolfram demonstrations project-
Relação: dc.relationDedekindCut.nbp-
Direitos: dc.rightsDemonstration freeware using MathematicaPlayer-
Palavras-chave: dc.subjectEducação Superior::Ciências Exatas e da Terra::Matemática::Teoria dos Números-
Palavras-chave: dc.subjectRepresentações de números-
Título: dc.titleDedekind cut-
Aparece nas coleções:Repositório Institucional - Acervo Digital Unesp

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