continuous

English

Etymology

Either via Old French continueus, or directly from Latin continuus, from contineō (“hold together”).

Pronunciation
  • enPR: kən-tĭnʹyo͞o-əs, IPA(key): /kənˈtɪnjuːəs/
  • Audio (US)(file)

Adjective

continuous (not comparable)

  1. Without stopping; without a break, cessation, or interruption
    Synonym: nonstop
    a continuous current of electricity
  2. Without intervening space; continued
    Synonyms: protracted, extended
    a continuous line of railroad
  3. (botany) Not deviating or varying from uniformity; not interrupted; not joined or articulated.
  4. (mathematical 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 between two topological spaces) Such that each open set in the target space has an open preimage (in the domain space, with respect to the given function).
    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

Translations

See also

References
  1. “continual” in Paul Brians, Common Errors in English Usage, 2nd rev. and exp. edition, Wilsonville, Or.: William, James & Company, 2009, ISBN 978-1-59028-207-6.
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