English

The Foundations of Analysis

History and Overview 2013-03-27 v1

Abstract

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.

Cite

@article{arxiv.1303.6576,
  title  = {The Foundations of Analysis},
  author = {Larry Clifton},
  journal= {arXiv preprint arXiv:1303.6576},
  year   = {2013}
}

Comments

48 pages

R2 v1 2026-06-21T23:48:37.041Z