A nowhere continuous function is a function that is discontinuous at every point
of its domain. A standard example on 
is the Dirichlet function,
which takes the value 1 at each rational number
and 0 at each irrational number. Every open
interval contains both rational and irrational numbers, so these values cannot
approach a common limit at any point.
In particular, a nowhere continuous function can be a bounded function. Nowhere continuity should not be confused with nowhere differentiability. A nowhere differentiable function, such as the Weierstrass function, can be continuous everywhere.
