transfinite ordinal

См. также в других словарях:

• Transfinite number — Transfinite numbers are cardinal numbers or ordinal numbers that are larger than all finite numbers, yet not necessarily absolutely infinite. The term transfinite was coined by Georg Cantor, who wished to avoid some of the implications of the… …   Wikipedia

• Ordinal arithmetic — In the mathematical field of set theory, ordinal arithmetic describes the three usual operations on ordinal numbers: addition, multiplication, and exponentiation. Each can be defined in essentially two different ways: either by constructing an… …   Wikipedia

• Transfinite induction — is an extension of mathematical induction to well ordered sets, for instance to sets of ordinals or cardinals. Transfinite induction Let P(α) be a property defined for all ordinals α. Suppose that whenever P(β) is true for all β < α, then P(α) is …   Wikipedia

• transfinite — [transfī′nīt] adj. 1. extending beyond or surpassing the finite 2. Math. designating or of a cardinal or ordinal number that is larger than any positive integer …   English World dictionary

• Ordinal number — This article is about the mathematical concept. For number words denoting a position in a sequence ( first , second , third , etc.), see Ordinal number (linguistics). Representation of the ordinal numbers up to ωω. Each turn of the spiral… …   Wikipedia

• Ordinal notation — In mathematical logic and set theory, an ordinal notation is a finite sequence of symbols from a finite alphabet which names an ordinal number according to some scheme which gives meaning to the language. There are many such schemes of ordinal… …   Wikipedia

• Ordinal analysis — In proof theory, ordinal analysis assigns ordinals (often large countable ordinals) to mathematical theories as a measure of their strength. The field was formed when Gerhard Gentzen in 1934 used cut elimination to prove, in modern terms, that… …   Wikipedia

• Transfinite Zahl — Die transfinite Arithmetik ist die Arithmetik der Ordinalzahlen. Die arithmetischen Operationen zwischen Ordinalzahlen kann man mittels transfiniter Rekursion als stetige Fortsetzung der finiten Rechenoperationen einführen oder durch geeignete… …   Deutsch Wikipedia

• Transfinite Arithmetik — Die transfinite Arithmetik ist die Arithmetik der Ordinalzahlen. Die arithmetischen Operationen zwischen Ordinalzahlen kann man mittels transfiniter Rekursion als stetige Fortsetzung der finiten Rechenoperationen einführen oder durch geeignete… …   Deutsch Wikipedia

• Transfinite arithmetic — In mathematics, transfinite arithmetic is the generalization of elementary arithmetic to infinite quantities like infinite sets. It was originally invented by the German mathematician Georg Cantor. See also * transfinite number * cardinal… …   Wikipedia

• transfinite — adjective Etymology: German transfinit, from trans (from Latin) + finit finite, from Latin finitus Date: 1902 1. going beyond or surpassing any finite number, group, or magnitude 2. being or relating to the cardinal and ordinal numbers of… …   New Collegiate Dictionary