Quote:
Originally Posted by ewmayer
Also, it makes no sense to speak of a function being continuous at a single point  continuity only makes sense in regions, i.e. neighborhoods of a point.

Although we usually think of it this way, continuity is classically defined at a point. The classic counterintuitive case is
f(x) = 1/q if x is rational p/q in lowest form,
f(x)= 0 if x is irrational
This function is continuous at irrational points.
(f(x) is continuous at x' if, for every epsilon > 0 there exists a delta such that
for every x such that xx'<delta, f(x)f(x')<epsilon)
William