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We examine an argument of Reeder suggesting that the nilpotent infinitesimals in Paolo Giordano’s ring extension of the real numbers ...R are smaller than any infinitesimal hyperreal number of Abraham Robinson’s nonstandard extension of the real numbers ...R. Our approach consists in the study of two canonical order-preserving homomorphisms taking values in ...R and ...R, respectively, and whose domain is Henle’s extension of the real numbers in the framework of “non-nonstandard” analysis. The existence of a nonzero element in Henle’s ring that is mapped to 0 in ...R while it is seen as a nonzero infinitesimal in ...R suggests that some infinitesimals in ...R are smaller than the infinitesimals in ...R. We argue that the apparent contradiction with the conclusions by Reeder is only due to the presence of nilpotent elements in ...R. [ABSTRACT FROM AUTHOR]