Continuous definition

kən-tĭnyo͝o-əs
Uninterrupted in time, sequence, substance, or extent.
adjective
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Attached together in repeated units.

A continuous form fed into a printer.

adjective
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A function in which changes, however small, to any x- value result in small changes to the corresponding y- value, without sudden jumps. Technically, a function is continuous at the point c if it meets the following condition: for any positive number Ɛ, however small, there exists a positive number ẟ such that for all x within the distance ẟ from c , the value of f ( x ) will be within the distance Ɛ from f ( c ). Polynomials, exponential functions, and trigonometric functions are examples of continuous functions.
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Going on or extending without interruption or break; unbroken; connected.
adjective
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(math.) Designating a function whose value at each point is closely approached by its values at neighboring points.
adjective
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The definition of continuous is going on without being interrupted.

An example of continuous is a show that runs for 20 years.

adjective
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Of or relating to a line or curve that extends without a break or irregularity.
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Of or relating to a function between two topological spaces such that the preimage of any open set in the range is an open set in the domain.
adjective
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Without break, cessation, or interruption; without intervening time.

A continuous current of electricity.

adjective
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Without intervening space; continued; protracted; extended.

A continuous line of railroad.

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(botany) Not deviating or varying from uniformity; not interrupted; not joined or articulated.
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(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.
adjective
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(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.

adjective
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(grammar) Expressing an ongoing action or state.
adjective
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Relating to a line or curve that extends without a break or irregularity.
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Origin of continuous

  • From Latin continuus continue

    From American Heritage Dictionary of the English Language, 5th Edition

  • Either via French or directly, from Latin continuus.

    From Wiktionary