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加减、乘除是否分别互为逆运算关系?传统算术教材肯定了它们的逆运算关系,但现行中师小学数学基础理论教材则仅指明减法是加法的逆运算,除法是乘法的逆运算,而不再提及“互逆关系”了。八四年《江苏教育》更载文指出“‘加减、乘除互为逆运算关系’不能成立”。一些杂志摘编或转载,影响很广。事实上,这一观点是很值得商榷的。我们知道,所谓概念明确,就是正确地掌握了概念的内涵和外延,揭示概念内涵的逻辑方法是定义,不同的“逆运算”定义下有不同的外延。传统的逆运算定义是:“两种运算中,第一种运算的条件是第二种运算的结果,而第二种运算的结果是第一种运算的条件,这两种运算叫做互为逆运算。”(注1)
Addition and subtraction, multiplication and division are the inverse of each other? Conventional arithmetic textbooks affirmed their inverse relationship, but the current basic mathematics textbooks for primary schools only indicate that subtraction is the addition of the inverse operation, division is the inverse of multiplication, and No longer mention “reciprocal relationship”. In 1984, “Jiangsu Education” contained more articles that pointed out: “'Addition and subtraction, multiplication and division, except for reciprocal operations, can not be established.' Some magazine excerpts or reprinted, a wide range of influence. In fact, this view is quite debatable. We know that the so-called concept is clear, that is, correctly grasp the concept of connotation and denotation, to reveal the connotation of the logic of the concept is defined, different ”inverse operation“ under the definition of different extensions. The traditional definition of inverse operation is: ”In the two operations, the condition of the first operation is the result of the second operation, and the result of the second operation is the condition of the first operation, which is called inverse of each other Operation. "(Note 1)