  A refinement of the classic equivalence relation among Cauchy sequences
yields a useful infinitesimal-enriched number system. Such an approach can be
seen as formalizing Cauchy's sentiment that a null sequence "becomes" an
infinitesimal. We signal a little-noticed construction of a system with
infinitesimals in a 1910 publication by Giuseppe Peano, reversing his earlier
endorsement of Cantor's belittling of infinitesimals.
