This paper mainly discusses the order of infinitesimal,gets some conclusions of the comparison of infinitesimal order,and applies these conclusions to the calculation of limit and the sorting of infinitesimal.
文章对无穷小的阶进行了一些探讨,得到了几个关于无穷小阶的比较的结论,并应用于极限的计算与无穷小排序中去。
Theorem 2 The product of a bounded function and an infinitesimal is an infinitesimal.
推论1常数与无穷小的乘积是无穷小。
Corollary 1 The product of a constant and an infinitesimal is an infinitesimal.
推论2有限个无穷小的乘积是无穷小。
Theorem 1 The sum of finite number of infinitesimal is an infinitesimal.
定理1有限个无穷小的和也是无穷小。
Some Sufficient Conditions about the Product of Countable Infinitesimal for Infinitesimal;
可列个无穷小乘积仍为无穷小的若干充分条件
The Thinking about the Product of Infinite Infinitesimals;
关于无穷多个无穷小的乘积的一些思考
An immeasurably or incalculably minute amount or quantity.
无穷小的数量非常小，几乎无法测量的数量
Seeking Functional Limit by Equivalent Infinitesimal Replacement;
利用“等价无穷小的替换”求函数的极限
Determination about the integrand of infinite integto be infinitesimal;
关于广义积分的被积函数为无穷小的判定准则
Order of Infinitesimal and Its Application to Criterion of Convergence and Divergence;
无穷小的阶数及其在敛散性判定中的应用
Notes On Infinity And Infintesimal;
关于无穷小与无穷大关系的一点注记
infinitesimal area
无穷小邻域[面积]
Capable of having values approaching zero as a limit.
近零的，极小的无穷小地接近于零的
Being neither infinite nor infinitesimal.
非极限的，非无限小的既非无穷大也非无限小
Infinitesimal Quantum gl_n and Associated Little q-Schur Algebras;
无穷小量子gl_n和相关的小q-Schur代数
My baby finds nature fascinating.
我的小孩发现了大自然的无穷魅力。
And roam it does, from the infinitesimal to the infinite, from the subatomic realm to the far reaches of the universe.
并且智慧遨游，从无穷小到无穷大，从亚原子王国到遥远的宇宙。
But for humankind, it is infinite.
对于人类，这曲折的小路将永无穷
The Simple Way of Calculating Limit by Using Equivalence Infinit Small;
利用等价无穷小求解极限的简便方法