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《教师之友》今年第5期刊登的文章《不能说它们“互为逆运算”》一文认为:虽然加法只有一种逆运算减法,但减法却有加法和减法两种逆运算,所以不能说加法与减法“互为逆运算”;同样,虽然乘法只有一种逆运算除法,但除法却有乘法和除法两种逆运算,所以不能说乘法与除法“互为逆运算”。我认为说“减法有加法和减法两种逆运算,除法有乘法和除法两种逆运算”是不对的。事实上,减法没有逆运算,除法没有逆运算。数的运算和逆运算,通常总是在给定的数集上定义的。我们知道,普通加法“+”和减法“-”都是非负有理数集Q(下同)的一种运算,并且加法“+”的逆运算是减法“-”;普通乘法“×”和除法“÷”都是正有理数集Q”(下同)的一种运算,并且乘法“×”的逆运算是除法“÷”。
The article “Friends of Teachers” published in the fifth issue of this year, “Can not say that they are mutually inverse operations.” The article states that although addition has only one kind of inverse operation subtraction, subtraction has two inverse operations of addition and subtraction, so we can not say Similarly, although multiplication has only one type of inverse operation, multiplication and division have two kinds of inverse operations, so multiplication and division can not be said to be mutually inverse operations. I think it is wrong to say that subtraction has two kinds of inverse operations, addition and subtraction, division and multiplication. In fact, subtraction has no inverse operation, division does not have an inverse operation. Number and inverse operations are usually always defined on a given number set. We know that both the normal addition “+” and the subtraction “-” are operations of the nonnegative rational number set Q (the same below) and the inverse of the addition “+” is the subtraction “-”; the ordinary multiplication “×” and the division “ ÷ ”is a positive rational set Q“ (the same below), and the inverse of the multiplication ”ד is the division ”÷".