The right limit at x=0 represents the value from x >; 0 direction tends to 0, such as x=0.000 1, at this time [x]->; 0。

The left limit at x=0 represents the value from X.

An image with integer function f(x)=[x] is a step polyline. Obviously, the left limit lim [x] of the function f(x) is 0 (x→0+), while the right limit lim [x] is-1 (x → 0-). Although the function f(x) has left and right limits,

Modern definition of function

Given a number set A, assuming that the element in it is X, the corresponding rule F is applied to the element X in A, denoted as f(x), and another number set B is obtained. Assume that the element in B is Y, and the equivalence relation between Y and X can be expressed as y=f(x). The concept of function includes three elements: domain A, range B and corresponding rule F, among which the core is corresponding rule F, which is the essential feature of function relationship. ?