continuum of real numbers

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• Continuum — may refer to: Continuum (theory), anything that goes through a gradual transition from one condition, to a different condition, without any abrupt changes Contents 1 Linguistics 2 Mathematics …   Wikipedia

• continuum — [kən tin′yo͞o əm] n. pl. continua [kən tin′yo͞o ə] or continuums [L, neut. of continuus] 1. a continuous whole, quantity, or series; thing whose parts cannot be separated or separately discerned 2. Math. the set of all real numbers: See also… …   English World dictionary

• Continuum hypothesis — This article is about the hypothesis in set theory. For the assumption in fluid mechanics, see Fluid mechanics. In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis, advanced by Georg Cantor in 1877[citation needed], about… …   Wikipedia

• Real number — For the real numbers used in descriptive set theory, see Baire space (set theory). For the computing datatype, see Floating point number. A symbol of the set of real numbers …   Wikipedia

• Real closed field — In mathematics, a real closed field is a field F in which any of the following equivalent conditions are true:#There is a total order on F making it an ordered field such that, in this ordering, every positive element of F is a square in F and… …   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

• continuum hypothesis — Math. a conjecture of set theory that the first infinite cardinal number greater than the cardinal number of the set of all positive integers is the cardinal number of the set of all real numbers. [1935 40] * * * ▪ mathematics       statement of… …   Universalium

• Continuum (set theory) — In the mathematical field of set theory, the continuum means the real numbers, or the corresponding cardinal number, . The cardinality of the continuum is the size of the real numbers. The continuum hypothesis is sometimes stated by saying that… …   Wikipedia

• Real line — In mathematics, the real line is simply the set R of singleton real numbers.However, this term is usually used when R is to be treated as a space of some sort, such as a topological space or a vector space.The real line has been studied at least… …   Wikipedia

• continuum — noun /kənˈtɪnjuəm/ a) A continuous series or whole, no part of which is noticeably different from its adjacent parts, although the ends or extremes of it are very different from each other. b) The set of all real numbers and, more generally, a… …   Wiktionary

• continuum — /kənˈtɪnjuəm / (say kuhn tinyoohuhm) noun (plural continuums or continua /kənˈtɪnjuə/ (say kuhn tinyoohuh)) 1. a continuous extent, series, or whole. 2. Mathematics the continuum, the set of all real numbers. 3. four dimensional continuum,… …