In mathematical analysis, convergence is a concept used to describe the limit of sequence, function or sequence.

If a series starts from a certain term and the subsequent terms get closer to a specific number (called limit), that is, the absolute value of the difference between each term after the term and the limit can be less than any given positive number, then we say that the series converges.

More specifically, for a sequence {xn}, if there is a number a, then there is a positive integer n for any positive integer ε (no matter how small), so that for all n greater than n, there is | xn-a | < ε, then we say that the sequence {xn} converges to a.

In addition, for the function f(x), if there is a real number A, there is a constant δ(delta) for any X, so 0.

In functional analysis, the concept of convergence is more complicated. In this context, convergence usually refers to the convergence of a sequence or network in a topological space to another element. This type of convergence includes weak convergence, strong convergence, almost everywhere convergence and so on.

Application of high order convergence;

1. In the field of mathematics, convergence is used to describe the limit of a sequence, function or sequence. The limit of sequence and function can be studied through convergence, which is the basis of mathematical analysis. In addition, convergence is also used to study the solutions of differential equations and some problems in real and complex number analysis.

2. In the field of physics, convergence is also widely used. For example, in quantum mechanics and statistical physics, we often use wave function to describe the state of particles, and the convergence of wave function determines the stability and properties of the system. In addition, the concept of convergence often appears in physical fields such as fluid mechanics and electromagnetism.

3. In engineering and other application fields, convergence has practical applications. For example, in computer science, convergence is used to study the convergence speed and optimization of algorithms. In economics, convergence is used to study economic growth and convergence. In addition, the concept of convergence is also widely used in social sciences and other fields.