Discontinuous points in higher mathematics are discontinuous points. The function f(x) is defined as lim {x- > when x=a is continuous. A}f(x)=f(a) This equation has three meanings: the limit on the left exists, and the function value on the right exists (the function is defined as x=a), and they are equal. One of the points of dissatisfaction is discontinuity. The point where the left and right limits exist at the same time is called the first kind of discontinuous point. Where the left and right limits are equal (the limit exists), but f(a) does not exist, or the limit does not mean that f(a) is a removable discontinuous point; Unequal left and right limits (limit does not exist) means jump discontinuity. If one of the left and right limits does not exist, it is called the second kind of discontinuity, including (unilateral or bilateral) infinite discontinuity and oscillation discontinuity (such as sin( 1/ small)).