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transfinite sequence

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  • 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

  • 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

  • Cardinal number — This article describes cardinal numbers in mathematics. For cardinals in linguistics, see Names of numbers in English. In mathematics, cardinal numbers, or cardinals for short, are generalized numbers used to measure the cardinality (size) of… …   Wikipedia

  • Veblen function — In mathematics, the Veblen functions are a hierarchy of functions from ordinals to ordinals, introduced by harvtxt|Veblen|1908. If phi;0 is any continuous strictly increasing function from ordinals to ordinals, then for any non zero ordinal α,… …   Wikipedia

  • Order topology — In mathematics, an order topology is a certain topology that can be defined on any totally ordered set. It is a natural generalization of the topology of the real numbers to arbitrary totally ordered sets. If X is a totally ordered set, the order …   Wikipedia

  • Derived set (mathematics) — In mathematics, more specifically in point set topology, the derived set of a subset S of a topological space is the set of all limit points of S. It is usually denoted by S′. The concept was first introduced by Georg Cantor in 1872 and he… …   Wikipedia

  • NWTST — Nash Williams Transfinite Sequence Theorem (Academic & Science » Mathematics) …   Abbreviations dictionary

  • Ε₀ — In mathematics, the epsilon numbers are a collection of transfinite numbers whose defining property is that they are fixed points of an exponential map. Consequently, they are not reachable from 0 via a series of applications of the chosen… …   Wikipedia

  • Surreal number — In mathematics, the surreal number system is an arithmetic continuum containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number. The surreals share… …   Wikipedia

  • Reverse mathematics — is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. The method can briefly be described as going backwards from the theorems to the axioms. This contrasts with the ordinary… …   Wikipedia

  • Large countable ordinal — In the mathematical discipline of set theory, there are many ways of describing specific countable ordinals. The smallest ones can be usefully and non circularly expressed in terms of their Cantor normal forms. Beyond that, many ordinals of… …   Wikipedia

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