关于Gossamer数的微积分基本定理
The Fundamental Theorem of Calculus with Gossamer numbers
摘要：
在扩展了实数的游丝数中，我们证明了微积分基本定理（FTC）。黎曼和也被认为是在gossamer数系统，和他们的非唯一性在无穷远。我们可以通过在间断处插入无穷小的间隔，并在间断和之间形成螺纹曲线，将和表示为游丝数制中的连续函数。由于FTC是端点处积分的差，因此求和也是如此。
英文摘要：
Within the gossamer numbers which extend the real numbers to include infinitesimals and infinities we prove the Fundamental Theorem of Calculus (FTC). Riemann sums are also considered in the gossamer number system, and their non-uniqueness at infinity. We can represent the sum as a continuous function in the gossamer number system by inserting infinitesimal intervals at the discontinuities, and threading curves between the sums discontinuities. As the FTC is a difference of integrals at the end points, the same is true of sums.
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