(analysis, of a function) Such that, for every x in the domain, for each small openinterval D about f(x), there's an interval containing x whose image is in D.
(mathematics, more generally, of a function) Such that each open set in the range has an open preimage.
(grammar) Expressing an ongoing action or state.
Esimerkit
a continuous current of electricity
he can hear its continuous murmur
a continuous line of railroad
Each continuous function from the real line to the rationals is constant, since the rationals are totally disconnected.