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Bharat268
defination of continuity
The values of a function f(x) at points near a are good predictors of the value of f at a. The graph of f is a connected curve with no jumps, gaps, or holes.
Definition: (continuity at a point) If f(x) is defined on an open interval containing c, then f(x) is said to be continuous at c if and only if . source: http://en.wikibooks.org/wiki/Calculus/Continuity
google it and find an explanation you like it may be much clearer than all the opinions you are about to get
a real-valued function f of a real variable is continuous at a point a precisely if the difference f(a + δ) − f(a) is infinitesimal whenever δ is infinitesimal.
the preimage of any open set is open