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Nowhere Continuous Function: Nowhere Continuous Function, Mathematics, Real Number, Function (mathematics) -

English
2026-03-17
€179.62 €224.53

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High Quality Content by WIKIPEDIA articles! In mathematics, a nowhere continuous function, also called an everywhere discontinuous function, is a function that is not continuous at any point of its domain. If f is a function from real numbers to real numbers, then f(x) is nowhere continuous if for each point x there is an ¿ > 0 such that for each ¿ > 0 we can find a point y such that |x ¿ y| < ¿ and |f(x) ¿ ... Full description

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High Quality Content by WIKIPEDIA articles! In mathematics, a nowhere continuous function, also called an everywhere discontinuous function, is a function that is not continuous at any point of its domain. If f is a function from real numbers to real numbers, then f(x) is nowhere continuous if for each point x there is an ¿ > 0 such that for each ¿ > 0 we can find a point y such that |x ¿ y| < ¿ and |f(x) ¿ f(y)| ¿ ¿. The import of this statement is that no matter how close we get to any fixed point, there are even closer points at which the function takes not-nearby values. More general definitions of this kind of function can be obtained, by replacing the absolute value by the distance function in a metric space, or by using the definition of continuity in a topological space.

More Information

Publisher OmniScriptum
Release year 2026
Cover type Softcover
EAN 9786131117886
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€179.62 €224.53