理解无穷小阶的比较的两种视角

Two Perspectives to Understand the Comparison of Infinitesimal Order

本文介绍了从无穷小的可比较定义角度和从无穷小收敛快慢比较的角度对无穷小收敛阶的比较的理解,结果表明,高阶无穷小、低阶无穷小和同阶无穷小等概念,无论是在无穷小的可比较特征上还是在无穷小收敛快慢比较特征上都有着相应而明确的含义,本文给出的定义、定理和结论有利于我们和初学者对无穷小阶的比较形成正确的理解。

This article describes the infinitesimal comparable definition of angles and from infinitesimal convergence speed comparative perspective on the infinitesimal convergence order to understand the comparison, results show that higher-order infinitesimal, low-order infinitesimal and with infinitesimal concepts, both in the infinitely small can com-pare features on or in the infinitesimal convergence speed comparison features and have a corresponding clear meaning, the definition given herein, theorems and conclusions will help us and beginners properly understand the comparison of infinitesimal order.