Nowhere continuous function

Function which is not continuous at any point of its domain

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 is a function from real numbers to real numbers, then is nowhere continuous if for each point there is some such that for every we can find a point such that and . Therefore, no matter how close it gets to any fixed point, there are even closer points at which the function takes not-nearby values.

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