The definition of limit in advanced mathematics is that a variable in a function gradually approaches a certain value A in the process of permanent change and can never be reached. The change of this variable is artificially defined as always approaching, and there is a tendency to be extremely close to point A.

Limit is a description of the changing state, and the value A that this variable approaches forever is called the limit value (of course, it can also be expressed by other symbols). Limit is the basic concept of calculus and a branch of mathematics.

Limit is a basic concept in mathematics and an important tool to study the properties of functions and develop limit theory. It describes the changing trend and result of a variable in the process of infinite change of a function. In mathematics, the concept of limit is widely used, such as calculus, real number theory, series theory and other fields.

The definition of limit can be summarized as the case that the value of function f(x) infinitely approaches a constant a when the independent variable x infinitely approaches a certain point x0. In this case, we say that the function f(x) converges to a at point x0, or the limit lim (x→ x0) f (x) = a.

There are two important factors in the definition of limit:

One is a positive number ε, which means that we are looking for an interval range close to the constant A; The other is a positive number δ, which means that the difference between the value of the function f(x) and the constant a can be arbitrarily small in the interval (x0-δ, x0+δ).

According to the definition of limit, we can get some important limit properties. For example, if lim(x→x0)f(x)=A and lim(x→x0)g(x)=B, we can get lim(x→x0)[f(x)+g(x)]=A+B, lim(x→x0)[f(x).