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Limit theory:

Since17th century, the concepts and skills of calculus have been continuously expanded and widely used to solve various practical problems in astronomy and physics, and great achievements have been made. But until19th century, in the development of calculus, the rigor of its mathematical analysis has not been solved.

In the eighteenth century, many great mathematicians, including Newton and Leibniz, realized this problem and tried to solve it, but they failed to solve it successfully.

Throughout the18th century, the foundation of calculus was confusing. Many British mathematicians may still be bound by the geometry of ancient Greece, so they doubt all the work of calculus.

This problem was not completely solved by French mathematician Cauchy until the second half of the19th century. Cauchy's limit existence criterion injects rigor into calculus and is the basis of limit theory. The establishment of limit theory makes calculus based on strict analysis, which also laid the foundation for the development of mathematics in the 20th century.