摘要
本文通过对话形式 ,以微分三角形的弦弧同一或曲直等同 ,曲边梯形与“诸矩形元素之总和”及回转体体积与“诸元圆柱之总和”如何达到极限同一 ,δ -ε语言如何把握潜无穷的逻辑确定性 ,数学中包括微分与积分在内的各种对立运算如何辩证地相互转化 ,以及关于微分方程的否定之否定等丰富案例 ,并且借助于数学与逻辑之间的巧妙类比 。
This article be written in dialogue.It expounds the dialectical intension of infinitesimal calculus in many ways which includes the identity of bowstring and arc or the equivalent of bent and straight in differential triangle, how to attain the identical limit from trapezium with crooked side and 'the sum of cylinder elements '?or from solid of revolution and 'the sum of cylinder elements', the 'δ-ε'language how to grasp the logical determinacy of potential limit,the all opposite operations include differential and calculus how to transform each other dialectically. In this easy,we provide abundant cases of negation of negation about differential equation and draw support from the ingenious analogy between matematics and logic.
出处
《自然辩证法研究》
CSSCI
北大核心
2002年第5期27-31,共5页
Studies in Dialectics of Nature
关键词
微积分
辩证法
曲直等同
δ-ε语言
否定之否定
the infinitesimal dialectics
the equivalent of bent and straight
the 'δ-ε'language
negation of negation.
