Non-nonstandard analysis: Real infinitesimals
The author reconsiders, as he says, the pre-nonstandard approach initiated by C. Schmieden and the reviewer in 1958. Real sequences defined for almost all subscripts represent the elements of the number system, and infinitesimals are represented by sequences tending to zero. The basic theorems on derivatives, integrals, and continuity are obtained. (Since zero divisors exist, denominators must be avoided, and some of the proofs here are not correct).
scientific article; zbMATH DE number 1283654