柯西连续统
Cauchy's continuum
摘要：
柯西的总和定理的1821年一直是主题的竞争对手的解释，因为罗宾逊提出了一个新的阅读在20世纪60年代。有些人声称柯西在1853年通过引入一致收敛性修正了他的定理的假设，而一致收敛的传统公式需要一对自变量。同时，柯西假设是用一个变量x而不是一对变量来表述的，并且要求误差项r_n = r_n（x）在所有x值处都为零，包括柯西明确指定的由1/n产生的无穷小值。如果一个人希望理解柯西在1853年对和定理假设的修改/澄清，他必须抛弃自动逼近极限。
英文摘要：
Cauchy's sum theorem of 1821 has been the subject of rival interpretations ever since Robinson proposed a novel reading in the 1960s. Some claim that Cauchy modified the hypothesis of his theorem in 1853 by introducing uniform convergence, whose traditional formulation requires a pair of independent variables. Meanwhile, Cauchy's hypothesis is formulated in terms of a single variable x, rather than a pair of variables, and requires the error term r_n = r_n(x) to go to zero at all values of x, including the infinitesimal value generated by 1/n, explicitly specified by Cauchy. If one wishes to understand Cauchy's modification/clarification of the hypothesis of the sum theorem in 1853, one has to jettison the automatic translation-to-limits.
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