defination of continuity

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defination of continuity

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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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
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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

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