  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.
