“逆”是数学中的一个重要概念。设由A则B为“正向”,那末由B则A就为“逆向”,由此给出了一连串可逆的知识。例如:逆运算,逆命题、逆定理、逆对应、逆证法、逆推理等。当然,“正向”的成立并不表示“逆向”亦成立,但事实上,数学中不少知识确是可逆的,这就需要我们去认真研究。一般地说,学生对于“正向”知识应用起来较为熟练还不足以说明是真正的掌握了知识。许多综合题,难就难在知识的“逆向”应用上,而在解法上,巧也就巧在“逆向”应用了某些知识。一、可逆的运算。加法和减法、乘法和除法、乘方和开方等等都是互为逆运算,这是大家所熟知的,但还有一些可逆的运算,虽不那么明显,但却是很重要的。 “Reverse” is an important concept in mathematics. Let A be B “forward”, then B then A is “reverse”, which gives a series of reversible knowledge. For example: inverse operation, inverse proposition, inverse theorem, inverse correspondence, inverse proof, inverse reasoning and so on. Of course, the establishment of “positive” does not mean that “reverse” is also true. However, in fact, many knowledge in mathematics is indeed reversible. This requires us to study it carefully. In general, students are more proficient in applying “forward” knowledge to their knowledge. Many comprehensive questions are difficult to apply in the “reverse” application of knowledge. In the solution, Qiao also uses some knowledge in “reverse”. First, reversible operations. Addition and subtraction, multiplication and division, powers and squares are all inverse operations. This is well known to everyone, but there are some reversible operations. Although not so obvious, it is very important.