Limit thought is an important thought in modern mathematics, and mathematical analysis is a subject that studies functions with the concept of limit and limit theory (including series) as the main tools. The thought of limit refers to "a mathematical thought to analyze and solve problems with the concept of limit".
The general steps to solve problems with extreme ideas can be summarized as follows:
For the unknown quantity to be investigated, first try to correctly conceive another variable related to its change, and confirm the influence trend of this variable through the infinite change process. The result is very accurate and approximately equal to the unknown quantity. The result of the unknown quantity under investigation can be calculated by the limit principle.
Extended data:
The emergence and development of limit;
1, origin
Like all scientific thinking methods, extreme thinking is also the product of abstract thinking in social practice. The idea of limit can be traced back to ancient times. For example, secant technology in Liu Hui is an original and reliable application of the limit idea of "approaching constantly" on the basis of studying intuitive graphics.
The ancient Greeks' exhaustive method also contained the idea of limit, but because of their "fear of infinity", they obviously avoided artificially "taking the limit" and completed the relevant proof by indirect proof-reduction to absurdity.
/kloc-in the 6th century, Steven, a Dutch mathematician, improved the ancient Greek exhaustive method in the process of investigating the center of gravity of a triangle. With the help of geometric intuition, he boldly used limit thought to think about problems and gave up the proof of reduction law. In this way, he inadvertently "pointed out the direction of the development of the limit method into a practical concept."
2. Development
The further development of limit thought is closely related to the establishment of calculus. /kloc-in the 0/6th century, Europe was in the embryonic stage of capitalism, with great development of productivity and many technical problems in production.
At first, people can't solve it with elementary mathematics, which requires mathematics to break through the traditional scope of' only studying constants' and find new tools that can describe and study the process of motion change, which is the social background to promote the development of' extreme' thinking and establish calculus.
Baidu Encyclopedia-Limit (Mathematical Term)