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This paper develops an infinitesimal order of magnitude coupled with overflowtechnique that allows nonnumerical proofs of nondegenerate and degenerateinverse mapping theorems for mappings minimally regular at a point. Thisapproach is used first to give a transparent proof of the inverse mappingtheorem of Behrens and Nijenhuis and then is deployed to prove an inversemapping result for mappings whose linear part vanishes at the differentiablepoint. We finish by indicating further possible capacities of this approach.

Magnification Spaces: A nonstandard approach to inverse mapping theorems