Authors: Chelton D. Evans, William K. Pattinson
Within the gossamer numbers ∗G which extend R to include infinitesimals and infinities we prove the Fundamental Theorem of Calculus (FTC). Riemann sums are also considered in ∗G, and their non-uniqueness at infinity. We can represent the sum as a continuous function in ∗G 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 for sums.
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