Inductive set (axiom of infinity)

Inductive set (axiom of infinity)

In the context of the axiom of infinity, an inductive set (also known as a successor set) is a set X with the property that, for every x in X, the successor x' of x is also an element of X.

An example of an inductive set is the set of natural numbers.

ee also

* Natural number
* Peano axioms

External links

* [http://mathworld.wolfram.com/InductiveSet.html Mathworld: "Inductive set"]

----


Wikimedia Foundation. 2010.

Игры ⚽ Нужно сделать НИР?

Look at other dictionaries:

  • Inductive set — This article relates to the notion of inductive sets from descriptive set theory. For the notion in the context of the axiom of infinity, see Inductive set (axiom of infinity). In descriptive set theory, an inductive set of real numbers (or more… …   Wikipedia

  • Axiom of infinity — In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of infinity is one of the axioms of Zermelo Fraenkel set theory. Formal statement In the formal language of the Zermelo Fraenkel axioms,… …   Wikipedia

  • Morse–Kelley set theory — In the foundation of mathematics, Morse–Kelley set theory (MK) or Kelley–Morse set theory (KM) is a first order axiomatic set theory that is closely related to von Neumann–Bernays–Gödel set theory (NBG). While von Neumann–Bernays–Gödel set theory …   Wikipedia

  • Scott–Potter set theory — An approach to the foundations of mathematics that is of relatively recent origin, Scott–Potter set theory is a collection of nested axiomatic set theories set out by the philosopher Michael Potter, building on earlier work by the mathematician… …   Wikipedia

  • Von Neumann–Bernays–Gödel set theory — In the foundations of mathematics, von Neumann–Bernays–Gödel set theory (NBG) is an axiomatic set theory that is a conservative extension of the canonical axiomatic set theory ZFC. A statement in the language of ZFC is provable in NBG if and only …   Wikipedia

  • Hereditarily countable set — In set theory, a set is called hereditarily countable if and only if it is a countable set of hereditarily countable sets. This inductive definition is in fact well founded and can be expressed in the language of first order set theory. A set is… …   Wikipedia

  • List of mathematics articles (I) — NOTOC Ia IA automorphism ICER Icosagon Icosahedral 120 cell Icosahedral prism Icosahedral symmetry Icosahedron Icosian Calculus Icosian game Icosidodecadodecahedron Icosidodecahedron Icositetrachoric honeycomb Icositruncated dodecadodecahedron… …   Wikipedia

  • New Foundations — In mathematical logic, New Foundations (NF) is an axiomatic set theory, conceived by Willard Van Orman Quine as a simplification of the theory of types of Principia Mathematica. Quine first proposed NF in a 1937 article titled New Foundations for …   Wikipedia

  • logic, history of — Introduction       the history of the discipline from its origins among the ancient Greeks to the present time. Origins of logic in the West Precursors of ancient logic       There was a medieval tradition according to which the Greek philosopher …   Universalium

  • Type theory — In mathematics, logic and computer science, type theory is any of several formal systems that can serve as alternatives to naive set theory, or the study of such formalisms in general. In programming language theory, a branch of computer science …   Wikipedia

Share the article and excerpts

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