无穷小阶的比较与函数的连续、可导间的关系

Relationship between Comparison of Order Infinitesimals and Continuousness and Differentiability of Functions

并不是每对无穷小阶都可以作阶的比较,用无穷小阶的比较来解释函数的连续、可导之间的关系更直观,更易理解,同时给出构造连续与可导函数的一种方法。

Not each pair of order infinitesimal has order comparisons. Comparison of order.infinitesimal makes it more intuitive and understandable to explain the connection between the continuousness and differentiability of functions. Meanwhile, it provides another method of constructing continuous and differentiable functions.