关于贝克莱悖论不存在的论证暨微分精确性的讨论

On the Existence of Berkeley Paradox and the Discussion of Differential Precision

摘要: 贝克莱悖论只能在古典微积分中存在，在极限微积中已经不复存在了。但是，国内总是有人因没有领会极限微积分的真谛而重提贝克莱悖论或者类似的问题。揭示微积分的真谛，纠正一些人的偏见也就有必要了。几乎所有的人都认为极限微积分的微分结果只是一个近似结果而不是精确结果(原因是忽略了包含Δx的项)。这是一种错误的直觉。实际情况正好相反。通过严密的逻辑分析得到的结论是“根据极限微积分方法求得的微分是精确结果，保留包含Δx的项一定会导致微分结果不准确”。

Abstract: The Berkeley paradox can only exist in classical calculus, but no longer exists in limit calculus. However, there are always people in the country who have repeatedly mentioned the Berkeley paradox or similar problems because they have not grasped the true meaning of the extreme cal-culus. It is necessary to reveal the true meaning of calculus and correct some people’s prejudice. Almost everyone believes that the differential result of the limit calculus is only an approximate result rather than an exact result (the reason is that the item containing Δx is ignored). This is a wrong intuition. The opposite is true. The conclusion from the rigorous logic analysis is that The differential obtained by the limit calculus method is an accurate result, and retaining the term containing Δx must result in inaccurate differential results.