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高中数学课本《代数》(甲种本)第二册 P.195,有这样一段话:“两个复数,如果不全是实数,就不能比较它们的大小。”虽然,课本中指出:“关于这个命题的证明,本书从略。”但是,对于求知欲很强的学生,这个问题是必须要求教师解答的。如果仅像教学参考书上那样,只举两个例子也是不能圆满解释清楚的。笔者认为,对于这个问题要从以下三个方面进行解释。一.两个复数问存在顺序关系首先我们给出数集扩大原则。即“在扩大数集中,对于某些运算与关系应重新定义,并且当其将原来数集中的数看成扩大数集中的数时,要与新定义一致。”根据这条原则。我们就可以研究复数的顺序问题了。对于复数 x+yi(x、y∈R,本文中 R 表
In the second volume P.195 of the high school mathematics textbook “Algebra” (A type), there is a saying: “Two plural numbers, if not all real numbers, cannot compare their sizes.” Although the textbook states: “About this Proof of the proposition, the book is abbreviated.” However, for students with strong curiosity, this question must be asked by the teacher. If you only use two examples as in the reference book, you can’t explain it clearly. The author believes that this issue should be explained in the following three aspects. I. The Order of Existence of Two Complex Numbers First we give the principle of expanding the number sets. That is, “in the expansion of the number of sets, some operations and relations should be redefined, and when the number of the original set of numbers is considered to be a number in the enlarged set of numbers, it is consistent with the new definition.” According to this principle. We can study the sequence of plurals. For complex numbers x+yi (x, y∈R, R in this article