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中学数学教学中,每因一时要避免解释上的麻烦,或定义上的复杂,而引进了些容易发生矛盾的观念,使学生永远摆脱不了错误的习惯,这是应该克服的。在中学的代数中,我们不能给实数系统一个很精确的定义。不过我们可以说,凡是能表示长短的全是实数。中学学生看实数是个别来看的。但是,实数系统中有些基本精神,是不可忽略的,最要紧的精神是每一个符号或运算是只有一个意义的,譬如二数相乘只得一个数,不会得到二个或二个以上
In mathematics teaching in middle school, every time it is necessary to avoid the troubles in interpretation, or the complexity of the definitions, we introduce some ideas that are prone to contradictions so that students can never get rid of wrong habits. This should be overcome. In algebra of secondary school, we cannot give a very precise definition of the real number system. However, we can say that all the lengths that can be expressed are real numbers. Secondary school students look at real numbers on an individual basis. However, some basic spirits in the real number system cannot be ignored. The most important spirit is that each symbol or operation has only one meaning. For example, if two numbers are multiplied by only one number, they will not get two or more.