Infinity has an important application in higher mathematics. First of all, infinity plays a key role in limit and calculus. Limit is a concept that describes the behavior of a function near a certain point, and infinity can represent a value that is infinitely close but can never be reached. By introducing the concept of infinity, we can study the limit properties of functions, and thus derive some important concepts such as derivatives and integrals.

Secondly, infinity also plays an important role in series and series convergence theory. Series is the process of adding or multiplying infinite numbers, and infinity means that this process can continue indefinitely. By studying the convergence of series, we can judge whether the series tends to a certain value and how to calculate this value. This is of great significance for solving many practical problems, such as solving equations and estimating values.

In addition, infinity is widely used in complex analysis and analytical science. Complex number is a number with real part and imaginary part, and infinity can be expressed as a point on the complex plane. By introducing the concept of infinity, we can study the properties of complex variable functions, such as continuity and differentiability. This is of great significance for solving many complicated mathematical problems, such as analytic continuation and residue theorem.

In a word, infinity is widely used in higher mathematics. It not only helps us to understand and learn basic concepts such as limit, calculus and series, but also promotes the development of many important mathematical theories. Therefore, it is very important for people who study and apply advanced mathematics to understand and master the concept of infinity.