论文部分内容阅读
数学——那怕是初等数学,如果离开了变数则是不可想象的事。恩格斯在自然辩证法中说:“笛卡儿的变数是数学中的转折点。因为有了变数,所以运动和辩证法就通行到数学中去了;……”初接触变量、数列及极限……等概念的人,常常发生很多疑问。他们不理解数列的通项的确切意义,认为0.9<1,把无穷小看成为一个非常小的定量,形式地理解瞬时速率这一概念,……。产生这些疑问的原因虽多,而其中最根本的原因应该归结于思想方法之运用。
Mathematics - even elementary mathematics, if you leave the variables is unthinkable. Engels said in the dialectics of nature: “Descartes’s variable is a turning point in mathematics. Because of the variables, movement and dialectics pass to mathematics....” Concepts such as initial exposure to variables, series, and limits... People often have many questions. They do not understand the exact meaning of the general term of the series, thinking that 0.9<1, seeing infinitesimal as a very small quantitative, formal understanding of the concept of instantaneous rate,... Although there are many reasons for these doubts, the most fundamental reason should be attributed to the use of ideas and methods.