In mathematics, "limit" means that a variable in a function gradually approaches a certain value A in the process of getting bigger (or smaller), and "it can never coincide with A" ("it can never be equal to A, but taking a value equal to A' is enough to obtain a high-precision calculation result), and the change of this variable is artificially defined as" forever approaching ".

Extended data:

Extreme thinking method runs through the whole process of mathematical analysis. It can be said that almost all concepts in mathematical analysis are inseparable from the limit. In almost all mathematical analysis works, the theory of function and the thinking method of limit are introduced first, and then the concepts of continuous function, derivative, definite integral, convergence and divergence of series, partial derivative of multivariate function, convergence and divergence of generalized integral, multiple integral, curve integral and surface integral are given by the thinking method of limit. For example:

The point continuity of (1) function is defined as the limit that the increment of independent variable tends to zero and the increment of function value tends to zero.

(2) The definition of the derivative of a function at a point is the ratio of the increment of the function value to the increment of the independent variable, and it has a time limit.

(3) The definition of the definite integral of a function at one point is the limit of the integral sum formula when the fineness of division tends to zero.

(4) The convergence and divergence of term series is defined by the limit of partial sum series.

(5) Generalized integral is definite integral, where the limit of any real number is greater than, and so on.