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Chargement... Contributions to the Founding of the Theory of Transfinite Numbers (1911)par Georg Cantor
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Inscrivez-vous à LibraryThing pour découvrir si vous aimerez ce livre Actuellement, il n'y a pas de discussions au sujet de ce livre. As a teenager studying mathematics, I was fascinated by Cantor's notion of an infinity of infinities. Then I bought this book and read the arguments behind his theories, and realized that, although he had invented an interesting new mathematical game, it was not a part of the standard arithmetical game, for he made several errors. There are many I could list, but two are crucial. Firstly he makes a subtle change in the meaning of equinumerous sets, which should mean that all bijections between the members of two sets hold - Cantor reduces this to the sets being equinumerous as long as there is at least one bijection which holds, ie his sense of the notion is weaker than the standard interpretation. Secondly his diagonal proceedure requires the ability to complete an infinite process, which is impossible. He claims that at any stage he produces a number that differs from all those so far processed, which is true, but there always remain an infinite number of numbers which may contain the "different" number he has constructed, and since he must work his process an infinite number of times to produce a number different from all in an infinite set he has to shew that an infinite process can be completed, which is not possible. Nice try Georg, but yours is a game I can admire, but not one I can play! ( ) aucune critique | ajouter une critique
The famous articles, 1895-7, that founded a new branch of mathematics.Covers addition, multiplication and exponentiation of cardinal numbers, smallest transfinite cardinal numbers, ordinal types of simple ordered aggregates and operations on ordinal types. Develops theory of well-ordered aggregates; investigates ordinal numbers of well-ordered aggregates and more. Translated with introduction by P. Jourdain. Aucune description trouvée dans une bibliothèque |
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Google Books — Chargement... GenresClassification décimale de Melvil (CDD)511Natural sciences and mathematics Mathematics General PrinciplesClassification de la Bibliothèque du CongrèsÉvaluationMoyenne:
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