Open AccessSOBRE O CARÁTER INTUITIVO DA TEORIA DOS CONJUNTOS DE DEDEKIND: CONSIDERAÇÕES SOBRE O AXIOMA DA REGULARIDADE
Author(s) -
Walter Gomide
Publication year - 1969
Publication title -
revista eletrônica informação e cognição
Language(s) - English
Resource type - Journals
ISSN - 1807-8281
DOI - 10.36311/1807-8281.2007.v6n2.754
Subject(s) - dedekind cut , axiom of choice , axiom , zermelo–fraenkel set theory , set theory , mathematics , character (mathematics) , urelement , set (abstract data type) , pure mathematics , computer science , geometry , programming language
In this article, I intend to show that Dedekind’s set theory has not an intuitive character, once in Dedekind’s set theory the axiom of regularity is not valid. Since such axiom guarantees that the notion of pertinence has a behavior related to our intuitions about sets, Dedekind’s set theory is not an intuitive one, but rather an abstract set theory, in which our normal conceptions about sets and their properties are not valid.