1, the oscillation is discontinuous, and the limit oscillation does not exist, which belongs to the second discontinuity. Note that there is no oscillation here, not infinite limit, so don't confuse it.

2. Among the four kinds of discontinuity points in higher mathematics, oscillation discontinuity point is the most special and important discontinuity point, because oscillation is the only discontinuity point that may have indefinite integral (the existence theorem of original function) and the only discontinuity point of the second kind that may be integrated.