Nowhere continuous function

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 {\displaystyle f} is a function from real numbers to real numbers, then f {\displaystyle f} is nowhere continuous if for each point x {\displaystyle x} there is some ε > 0 {\displaystyle \varepsilon >0} such that for every δ > 0 , {\displaystyle \delta >0,} we can find a point y {\displaystyle y} such that | x − y | < δ {\displaystyle |x-y|<\delta } and | f ( x ) − f ( y ) | ≥ ε {\displaystyle |f(x)-f(y)|\geq \varepsilon } .

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