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) ¿ ...Täydellinen kuvaus
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.