Approaches to analysis with infinitesimals following Robinson, Nelson, and others

@article{Fletcher2017ApproachesTA,
  title={Approaches to analysis with infinitesimals following Robinson, Nelson, and others},
  author={Peter Fletcher and Karel Hrbacek and Vladimir Kanovei and Mikhail G. Katz and Claude Lobry and Sam Sanders},
  journal={arXiv: Classical Analysis and ODEs},
  year={2017}
}
This is a survey of several approaches to the framework for working with infinitesimals and infinite numbers, originally developed by Abraham Robinson in the 1960s, and their constructive engagement with the Cantor-Dedekind postulate and the Intended Interpretation hypothesis. We highlight some applications including (1) Loeb's approach to the Lebesgue measure, (2) a radically elementary approach to the vibrating string, (3) true infinitesimal differential geometry. We explore the relation of… 
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