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# continuous

It is vanity to desire a long life and to take no heed of a good life.
Thomas γ Kempis
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## English

### Etymology

From [[w:Template:lang:la language|Template:lang:la]][[Category:Template:lang:la derivations]] continuus, from continere, ‘to hold together’.

### Pronunciation

continuous (not comparable)
 Positive continuous Superlativenone (absolute)
1. Without break, cessation, or interruption; without intervening time.
• a continuous current of electricity
• (A date for this quote is being sought): He can hear its continuous murmur. - Longfellow.
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 map, having the mathematical property that has the following formal $\epsilon$-$\delta$-definition: Given $I,D\subset\mathbb{R}$ (I and D are subsets of the real numbers), continuity of $f(x):I \to D$ ($f(x)$ maps the interval I to the interval D) at $c\in\mathbb{R}$ means, for all $\varepsilon>0$, there exists a $\delta>0$ such that $|x-c|<\delta$ and $x\in I$ implies $|f(x)-f(c)|<\varepsilon$.
5. (grammar) Expressing an ongoing action or state.

#### Usage notes

• Continuous is the stronger word, and denotes that the continuity or union of parts is absolute and uninterrupted; as, a continuous sheet of ice; a continuous flow of water or of argument. So Daniel Webster speaks of "a continuous and unbroken strain of the martial airs of England."
• Continual, in most cases, 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, etc.

In mathematics

## Elsewhere on the web

### En-De

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