Five cases of application of extreme thoughts Tang Yong used extreme thoughts to deal with some mathematical problems, which often turned difficult into easy. Two people sit at a square table, one by one, and put a coin of the same size flat on the table. When there is only one seat left on the table, whoever puts down the last one wins. Let's assume that they are both masters. Who wins first, who wins later? (Gbaolia calls it a "long-standing problem") Gbaolia's ingenious solution is "one guess and two certificates": guess (extreme the problem) if the desktop is so small that only one coin can be put down, then the first one wins. It is proved (by using symmetry) that because the square table has a symmetrical center, the first player can occupy the center of the table, and then every time the coin is placed in the symmetrical position of the opponent's coin about the center of the table, the first player wins. From Paulia's ingenious solution, we can see that he used the idea of limit to examine the extreme state of the problem and explore the direction of solving the problem or the way of transformation. Limit thought is an important mathematical thought. Flexible use of limit thought can avoid complex operations and explore new ideas to solve problems. Here are five examples to illustrate the application of extreme thinking. Example 1 known 0; 0 is not a constant, exclude ② and choose ① ③. Example 3 known sequence {a