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Real analysis in reverse. (English) Zbl 1305.12002

Summary: Many of the theorems of real analysis, against the background of the ordered field axioms, are equivalent to Dedekind completeness, and hence can serve as completeness axioms for the reals. In the course of demonstrating this, the article offers a tour of some less-familiar ordered fields, provides some of the relevant history, and considers pedagogical implications.

MSC:

12J15 Ordered fields
97H40 Groups, rings, fields (educational aspects)
97H50 Ordered algebraic structures (educational aspects)
97I99 Analysis education
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