Editing Nowhere continuous function (section)

{{Short description|Function which is not continuous at any point of its domain}}
{{more citations needed|date=September 2012}}
In [[mathematics]], a '''nowhere continuous function''', also called an '''everywhere discontinuous function''', is a [[function (mathematics)|function]] that is not [[continuous function|continuous]] at any point of its [[domain of a function|domain]]. If <math>f</math> is a function from [[real number]]s to real numbers, then <math>f</math> is nowhere continuous if for each point <math>x</math> there is some <math>\varepsilon > 0</math> such that for every <math>\delta > 0,</math> we can find a point <math>y</math> such that <math>|x - y| < \delta</math> and <math>|f(x) - f(y)| \geq \varepsilon</math>. Therefore, no matter how close it gets 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]].