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densely ordered set

См. также в других словарях:

  • Second-order logic — In logic and mathematics second order logic is an extension of first order logic, which itself is an extension of propositional logic.[1] Second order logic is in turn extended by higher order logic and type theory. First order logic uses only… …   Wikipedia

  • Rational number — In mathematics, a rational number is any number that can be expressed as the quotient or fraction a/b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer is a rational number. The set of all… …   Wikipedia

  • Dense order — In mathematics, a partial order ≤ on a set X is said to be dense if, for all x and y in X for which x < y, there is a z in X such that x < z < y. The rational numbers with the ordinary ordering are a densely ordered set in this sense, as …   Wikipedia

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  • Glossary of order theory — This is a glossary of some terms used in various branches of mathematics that are related to the fields of order, lattice, and domain theory. Note that there is a structured list of order topics available as well. Other helpful resources might be …   Wikipedia

  • Linear continuum — In the mathematical field of order theory, a continuum or linear continuum is a generalization of the real line. Formally, a linear continuum is a linearly ordered set S of more than one element that is densely ordered , i.e., between any two… …   Wikipedia

  • Quantum logic — In mathematical physics and quantum mechanics, quantum logic is a set of rules for reasoning about propositions which takes the principles of quantum theory into account. This research area and its name originated in the 1936 paper by Garrett… …   Wikipedia

  • Cantor's first uncountability proof — Georg Cantor s first uncountability proof demonstrates that the set of all real numbers is uncountable. Cantor formulated the proof in December 1873 and published it in 1874 in Crelle s Journal [cite… …   Wikipedia

  • Continuum (mathematics) — In mathematics, the word continuum has at least two distinct meanings, outlined in the sections below. For other uses see Continuum.Ordered setThe term the continuum sometimes denotes the real line. Somewhat more generally a continuum is a… …   Wikipedia

  • Non-standard model of arithmetic — In mathematical logic, a nonstandard model of arithmetic is a model of (first order) Peano arithmetic that contains nonstandard numbers. The standard model of arithmetic consists of the set of standard natural numbers {0, 1, 2, …}. The elements… …   Wikipedia

  • Non-standard arithmetic — In mathematical logic, a nonstandard model of arithmetic is a model of (first order) Peano arithmetic that contains nonstandard numbers. The standard model of arithmetic consists of the set of standard natural numbers {0, 1, 2, hellip;}. The… …   Wikipedia

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