continuous

      English

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      Etymology

      Either via French or directly, from Latin continuus.

      Pronunciation

      • enPR: kən-tĭnʹyo͞o-əs, IPA: /kənˈtɪnjuəs/, X-SAMPA: /k@n"tInju@s/
      • Audio (US)
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      Adjective

      continuous (not comparable)

      1. Without break, cessation, or interruption; without intervening time.
        a continuous current of electricity
      2. Without intervening space; continued; protracted; extended.
        a continuous line of railroad
      3. (botany) Not deviating or varying from uniformity; not interrupted; not joined or articulated.
      4. (analysis, of a function) Such that, for every x in the domain, for each small open interval D about f(x), there's an interval containing x whose image is in D.
      5. (mathematics, more generally, of a function) Such that each open set in the range has an open preimage.
        Each continuous function from the real line to the rationals is constant, since the rationals are totally disconnected.
      6. (grammar) Expressing an ongoing action or state.

      Usage notes

      • Continuous is stronger than continual. It denotes that the continuity or union of parts is absolute and uninterrupted, as in a continuous sheet of ice, or a continuous flow of water or of argument. So Daniel Webster speaks of "a continuous and unbroken strain of the martial airs of England." By contrast, continual usually marks a close and unbroken succession of things, rather than absolute continuity. Thus we speak of continual showers, implying a repetition with occasional interruptions; we speak of a person as liable to continual calls, or as subject to continual applications for aid.[1]

      Synonyms

      Antonyms

      Derived terms

      in mathematics
      • continuous distribution
      • continuous function
      • continuous group
      • continuous line illusion
      • continuous map
      • continuous mapping theorem
      • continuous space
      • continuous vector bundle
      • continuously differentiable function
      • uniformly continuous

      Related terms

      Translations

      without break, cessation, or interruption in time
      without break, cessation, or interruption in space
      in botany
      in mathematical analysis
      in grammar

      See also

      References

      1. ^ “continual/continuous”, Brians, Paul Common Errors in English Usage, (2nd Edition, November 17, 2008), William, James & Company, 304 pp., ISBN 978-1-59028207-6
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      Last modified on 18 June 2013, at 22:10