In the textbook of Advanced Mathematics (Tongji Edition), the definition of X tends to the limit of x0 function. Why to remove the point of x0? The limit of composite function also emphasizes this problem. What will happen if it goes

In the textbook of Advanced Mathematics (Tongji Edition), the definition of X tends to the limit of x0 function. Why to remove the point of x0? The limit of composite function also emphasizes this problem. What will happen if it goes

Because in some cases, the function is meaningless at x = x0, for example, f (x) = (x-1) / (x + 1). When x = - 1, the function is meaningless, that is, there is no f (- 1), but only f (x) limx tends to (- 1) in the way of finding limit
For f (x) = (x-1) / (x + 1), x = - 1 must be removed because it does not exist
For continuous function, temporary sampling is only a method of speculation, but it can not be removed objectively through demonstration, that is, when x tends to x0 from "x0 -" and "x0 +", its limit value is equal to f (x0), which is the difference between continuous function and discontinuous function