Name a function with a domain of all real numbers that is continuous only at a single point.

Definition: A function is continuous at point B if and only if the limit of f(x) as x approaches B is equal to f(B).

The function

f(x) = Abs(x) if x is rational; f(x) = - Abs(x) otherwise

is continuous at x = 0 but not otherwise since sequences in rational and irrationals will tend to different limits.

Posted by goFish on 2005-12-15 08:19:35