# continuous

## EnglishEdit

English Wikipedia has an article on:

Wikipedia en

### EtymologyEdit

Either via French or directly, from Latin continuus.

### PronunciationEdit

• enPR: kən-tĭnʹyo͞o-əs, IPA(key): /kənˈtɪnjuəs/
•  Audio (US) Sorry, your browser either has JavaScript disabled or does not have any supported player. You can download the clip or download a player to play the clip in your browser. (file)

continuous (not comparable)

1. Without break, cessation, or interruption; without intervening time.
a continuous current of electricity
2. Without intervening space; continued; protracted; extended.
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 notesEdit

• 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]