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Nonstandard analysis is a way of doing calculus and analysis with infinitesimals. The historical approach of Leibniz, Euler, and others to infinitesimal calculus was gradually replaced by epsilon, delta techniques in the context of a real continuum, in the 19th century. It was not until the 1960s that Abraham Robinson developed a theory of a hyperreal continuum that allows for a development of analysis procedurally akin to that of its founders.

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Standard models of N and R: An Alice/Bob approach

This is way too long for a remark, therefore I post it as an answer. Although I agree with the previous answers that there is probably no clear “intended” model of set theory, there are perhaps two pr …
Martin Väth's user avatar
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