关于不同无穷小比较的新解释

New Concept of Infinitesimal Comparison

无穷小量在《高等数学》课程中是一个最基本、最重要的概念.对两个无穷小进行比较时,多种版本的《高等数学》教材中都认为两个无穷小比值极限的大小是反映它们趋向零的‘快慢’程度不同的量.就"两个无穷小之比的极限的不同取值情况(limβ/α=k),反映两个无穷小趋向与零的‘快慢’程度不同"这种解释方式提出了不同的意见,认为limβ/α=k,应该反映两个无穷小贴近零的程度不同.这对加深理解无穷小的概念很有帮助.

The concept of infinitesimal is the most fundamental and important in Calculus courses. When comparing the two infinitesimals, the value of the ratio of two infinitesimals will be different （limβ/α=k）. In various versions of ＂Calculus＂ materials, the limit of value is described as reflection on the different ＂speed＂ is close to zero. This paper focuses on the interpretation of different views. When lim β/α=k is established, it reflects two infinitesimals close to zero to varying degrees.