Burali-Forti's paradox

Burali-Forti's paradox
The first paradox discovered in the modern theory of sets. Every well-ordered set has an ordinal number assigned to it. These ordinals can be compared: of any two, either they are equal, or one is smaller and one is larger. They therefore form a well-ordered set. The ordinal of this set must be greater than any ordinal within the set. Let S be the set of all ordinals. Since it is well-ordered it has an ordinal number, ω, that must be greater than any element in the set. But S was the set of all ordinals, and must include ω.

Philosophy dictionary. . 2011.

Игры ⚽ Поможем написать курсовую

Look at other dictionaries:

  • Burali-Forti — s paradox …   Philosophy dictionary

  • Burali-Forti paradox — In set theory, a field of mathematics, the Burali Forti paradox demonstrates that naively constructing the set of all ordinal numbers leads to a contradiction and therefore shows an antinomy in a system that allows its construction. It is named… …   Wikipedia

  • Burali-Forti paradox — noun The following paradox: Let L be the set of all ordinal numbers. This set is well ordered, so it has an ordinal number gamma;. Since L is the set of all ordinal numbers, L contains gamma;. But gamma; is equal to the well ordered set of all… …   Wiktionary

  • Cesare Burali-Forti — Born 13 August 1861 Arezzo Died 21 January 1931 Turin Fields …   Wikipedia

  • Paradox — Ein Paradoxon oder Paradox (altgriechisch παράδοξον, von παρα , para – gegen und δόξα, dóxa – Meinung, Ansicht), auch Paradoxie (παραδοξία) und in der Mehrzahl Paradoxa g …   Deutsch Wikipedia

  • Cantor's paradox — In set theory, Cantor s paradox is the theorem that there is no greatest cardinal number, so that the collection of infinite sizes is itself infinite. Furthermore, it follows from this fact that this collection is not a set but a proper class; in …   Wikipedia

  • Epimenides paradox — Epimenides from Promptuarii Iconum Insigniorum The Epimenides paradox is a problem in logic. It is named after the Cretan philosopher Epimenides of Knossos (alive circa 600 BC), There is no single statement of the problem; a typical variation is… …   Wikipedia

  • Russell Paradox — Die Russellsche Antinomie ist ein von Bertrand Russell und Ernst Zermelo entdecktes Paradoxon der Naiven Mengenlehre, das Russell 1903 publizierte und daher seinen Namen trägt. Inhaltsverzeichnis 1 Begriff und Problematik 2 Geschichte und… …   Deutsch Wikipedia

  • Russells Paradox — Die Russellsche Antinomie ist ein von Bertrand Russell und Ernst Zermelo entdecktes Paradoxon der Naiven Mengenlehre, das Russell 1903 publizierte und daher seinen Namen trägt. Inhaltsverzeichnis 1 Begriff und Problematik 2 Geschichte und… …   Deutsch Wikipedia

  • Russellsches Paradox — Die Russellsche Antinomie ist ein von Bertrand Russell und Ernst Zermelo entdecktes Paradoxon der Naiven Mengenlehre, das Russell 1903 publizierte und daher seinen Namen trägt. Inhaltsverzeichnis 1 Begriff und Problematik 2 Geschichte und… …   Deutsch Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”