Let {Xn} be an infinite sequence. If there is a constant a for any given positive number ε (no matter how small it is), there is always a positive integer n, so that when n >: all Xn, when n has the inequality | xn-a |.

The' extreme thinking' method in data expansion is an indispensable and important method in mathematical analysis and even in all higher mathematics, and it is also the development of' mathematical analysis' and a further thinking based on' elementary mathematics'.

Mathematical analysis can solve many problems that elementary mathematics can't solve (such as finding instantaneous velocity, curve arc length, curved edge area, surface volume, etc.). ), it is precisely because it adopts the thinking method of "limit" and "infinite approximation" that it can get extremely accurate calculation answers.

People can scientifically determine the extremely accurate value of a certain quantity by investigating a series of countless more and more accurate approximation trends of some functions, which requires the use of the concept of limit and the thinking method of the above limit.

Reference limit (mathematical term) Baidu Encyclopedia