continuous

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Continuity

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From Latin continuus, from contineō (“hold together”). Displaced native Old English singal.

• enPR: kən-tĭnʹyo͞o-əs, IPA^(key): /kənˈtɪn.juː.əs/, /-(j)ɪu̯.əs/

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continuous (not comparable)

1. Without stopping; without a break, cessation, or interruption.

   Synonyms: perpetual, nonstop, incessant, ongoing; see also Thesaurus:continuous

   Antonyms: broken, discontinuous, discrete, intermittent, interrupted

   a continuous current of electricity

   • 1847 November 1, Henry Wadsworth Longfellow, Evangeline, a Tale of Acadie, Boston, Mass.: William D. Ticknor & Company, →OCLC, (please specify either |part=I or II):

     he can hear its continuous murmur

2. Without intervening space; continued.

   Synonyms: protracted, extended, connected, continued, unbroken

   Antonyms: broken, disconnected, disjoint

   a continuous line of railroad

   • 2023 November 29, Philip Haigh, “New Piccadilly Line trains put to the test”, in RAIL, number 997, page 26:

     The dynamic tests at Wildenrath use continuous test tracks built on the site of a former Royal Air Force station that was vacated after the end of the Cold War.

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.

• 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.

• discontinuous
• non-continuous, noncontinuous

• contain
• continuity
• continued
• continuum

• constant
• contiguous