>>11190943 Not at all, no. For instance, take f(x) = 2x. If f(x) is continuous, then at all points a, . We can verify this limit at any real a by taking delta = epsilon/2, so that abs(f(x)-f(a)) < epsilon when x is within delta of a, for all epsilon > 0. Continuity is something that can be verified at individual points, but since it's verified at all points, the function itself is said to be continuous.
