continuum

con·tin·u·um

C0603800 (kən-tĭn′yo͞o-əm)n. pl. con·tin·u·a (-tĭn′yo͞o-ə) or con·tin·u·ums 1. A continuous extent, succession, or whole, no part of which can be distinguished from neighboring parts except by arbitrary division.2. Mathematics a. A set having the same number of points as all the real numbers in an interval.b. The set of all real numbers.

[Latin, neuter of continuus, continuous; see continue.]

continuum

(kənˈtɪnjʊəm) n, pl -tinua (-ˈtɪnjʊə) or -tinuumsa continuous series or whole, no part of which is perceptibly different from the adjacent parts[C17: from Latin, neuter of continuus continuous]

con•tin•u•um

(kənˈtɪn yu əm)

n., pl. -tin•u•a (-ˈtɪn yu ə) 1. a continuous extent, series, or whole, with no discernible division into parts. 2. Math. a. a set of elements such that between any two of them there is a third element. b. the set of all real numbers. [1640–50; < Latin, n. use of neuter of continuus continuous]

Thesaurus

Noun

continuum - a continuous nonspatial whole or extent or succession in which no part or portion is distinct or distinguishable from adjacent partstime - the continuum of experience in which events pass from the future through the present to the pasthistory - the continuum of events occurring in succession leading from the past to the present and even into the future; "all of human history"

continuum

nounUninterrupted existence or succession:continuance, continuation, continuity, duration, endurance, persistence, persistency.

Translations

Continuum

continuum

(kŏn-tin -yoo-ŭm) The continuous spectrum that would be measured for a body if no absorption or emission lines were present.

Continuum

in mathematics a term used to denote structures that have certain properties of continuity [see (1) and (2) below for complete formulations] and to denote [not quite consistently in view of (2) below] the real numbers in discussing their cardinality.

(1) The most throughly studied continuous structure in mathematics is the system of real numbers, the number continuum. The properties of continuity of the system of real numbers can be characterized by different methods (using different “axioms of continuity”). If the concept of inequality (a < b) is used as the fundamental concept, then the continuity of the number continuum can be characterized, for example, by the following two statements: (a) between any two numbers a and b, where a < b, there lies at least one other number c (such that a < c < b ) and (b) if all the numbers are divided into two (nonempty) classes A and B such that every number a of A is less than any number b of B, then there exists either a greatest number in A or a least number in B (Dedekind’s axiom of continuity).

(2) In topology, which is the study of the geometry of continuity, the properties of the continuity of space or of any set are formulated using the concept of limit point. The fundamental concept of the connectivity of a set lying in a topological space (or of all space) is defined as follows: A set M is called connected if for any partition of M into two disjoint and nonempty subsets A and B there is at least one point that belongs to one of them and is a limit point of the other. In topology any connected compact Hausdorff space is called a continuum. Among sets on a line or in n -dimensional Euclidean space, the compact sets are the closed bounded sets. Thus, in Euclidean space a continuum can be defined as a connected closed bounded set. In particular, the only compact sets on the number line are closed intervals (that is, sets of numbers satisfying inequalities of the type a ≤ x ≤ b. In the strict sense of the topological definition of a continuum, the set of all real numbers is not a continuum.

(3) The cardinal number of the set of real numbers is called the cardinal number of the continuum and is denoted by either the Gothic letter C or by the Hebrew letter aleph א (without a subscript, in contrast to the other cardinal numbers). Every topological continuum has the same cardinal number C. The cardinal number C is greater than the cardinal number א₀ of countable sets. The continuum problem consists in deciding whether the cardinal number of the continuum is the next cardinal number after א₀

continuum

[kən′tin·yə·wəm] (mathematics) A compact, connected set.

Continuum

Starting in Windows 10, Continuum is a feature for hybrid and convertible laptops that automatically adjusts the user interface to Tablet Mode. When the keyboard is detached or flipped over, apps are run full screen and the Start screen is displayed rather than the traditional Start menu. Continuum can also be configured to prompt the user before switching modes. See Windows 10.

continuum

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Synonyms for continuum

noun uninterrupted existence or succession

Synonyms

Words related to continuum

noun a continuous nonspatial whole or extent or succession in which no part or portion is distinct or distinguishable from adjacent parts

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