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在数学的概念和公式中,到处都能遇到辩证法规律的表现。这里收集整理了中学程度的数学辩证法几例,它既有利于人们学好数学的基础知识,也有助于形成辩证法思想。例一,在中学数学中的每一种数,都有和它对立的数,矛盾的双方,各以和它对立的方面为自己存在的前提,并在一定条件下互相转化。例如整数和分数是对立的,但当把“1’作分母时,则整数就转化为分数,如5=5/1;而分数5/7乘上它的倒数7/5就等于整数1;正数和负数是对立的数,但当有了相反数概念时,则正数可用负数形式来表示,如5=-(-5),而
In mathematical concepts and formulas, the manifestations of dialectical laws can be encountered everywhere. Here is a collection of examples of mathematical dialectic at the secondary level. It is not only helpful for people to learn the basic knowledge of mathematics, but also helps to form dialectical ideas. For example, each number in middle school mathematics has its opposite number, its contradictory sides, and its opposites are its preconditions for existence, and they convert each other under certain conditions. For example, the integer and score are opposite, but when “1” is the denominator, the integer is converted into a fraction, such as 5 = 5/1; and the fraction 5/7 times its inverse 7/5 is equal to the integer 1; Positive numbers and negative numbers are opposite numbers, but when there is a concept of opposite numbers, positive numbers can be expressed in the form of negative numbers, such as 5=-(-5), and