Definition from Wiktionary, the free dictionary
Either via French or directly, from Latin continuus.
continuous (not comparable)
- Without break, cessation, or interruption; without intervening time.
- a continuous current of electricity
- Without intervening space; continued; protracted; extended.
- a continuous line of railroad
- (botany) Not deviating or varying from uniformity; not interrupted; not joined or articulated.
- (analysis, of a function) Such that, for every in the domain, for each small open interval about , there's an interval containing whose image is in .
- (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.
- (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.
- (without break, cessation, or interruption in time): constant, continual (but see usage notes above), incessant, never-ending, ongoing, unbroken, unceasing, unending, uninterrupted
- (without break, cessation, or interruption in space): connected, unbroken
- See also Wikisaurus:continuous
- (without break, cessation, or interruption in time): broken, discontinuous, discrete, intermittent, interrupted
- (without break, cessation, or interruption in space): broken, disconnected, disjoint, unbroken
- (in mathematical analysis): discontinuous, stepwise
Derived terms 
Related terms 
without break, cessation, or interruption in time
without break, cessation, or interruption in space
in mathematical analysis