关于高等数学中几个易错命题的举例说明

摘要

We analyze several easily-confused propositions in calculus by specific examples. Particularly, we deal with the question of infinite sum and infinite product of infinitesimal. We also get it is not necessarily the case that infinite product of infinitude is infinitude. Additionally, we give two sufficient conditions with which infinite product of infinitesimal and infinitude will be still infinitesimal and infinitude. All examples of this paper are helpful for us to comprehend the definition of infinitesimal and infinitude. When we want to understand the difference of finite operation and infinite operation, these examples are useful.%本文通过构造具体的典型例子对高等数学中的几个易错命题进行了阐述和说明.对无限多个无穷小量的和与积的性质进行了探讨,举例说明了无限多个无穷大量的乘积不一定是无穷大量.给出了无限乘积运算时仍然是无穷大量或无穷小量的充分条件.这有助于更好地理解无穷大量和无穷小量两个概念的本质内涵,也有助于认识无限运算和有限运算的根本差异.