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The Foundations of Analysis

The Foundations of Analysis
by Larry Clifton

Publisher: arXiv 2013
Number of pages: 48

This is a detailed and self-contained introduction to the real number system from a categorical perspective. We begin with the categorical definition of the natural numbers, review the Eudoxus theory of ratios as presented in Book V of Euclid, and then use these classical results to define the positive real numbers categorically.

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