Foundations and applications of non-standard analysis
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Bachelor Thesis
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Abstract
We shall introduce a superstructure, which allows us to reformulate analysis in the language of set theory. We can then use filter theory to make an extension of this superstructure. In this extension, there will be infinitesimal numbers. Finally, we shall study how we can do analysis with these infinitesimal numbers.
Keywords
non-standard analysis, analysis, mathematical logic, set theory, filter theory, superstructure, ultrapower, analysis, infinitesimals