Abstract
In [MR3], Reyes and the author described a model for “synthetic differential geometry” (see [K]) in which both nilpotent infinitesimals and invertible infinite-simals are present. The first type of infinitesimals occur in the work of geometers like G. Darboux, S. Lie, and E. Cartan, who often used “synthetic” reasoning. The second type of infinitesimals occur in the work of many physicists, for example in the discussion of the δ-function of Dirac. These invertible infinitesimals have been extensively studied in nonstandard analysis (NSA, see [R]), but NSA is inconsistent with the existence of niipofent infinitesimals as used in synthetic differential geometry, as pointed out in [K].
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