Logo

The Foundations of Analysis

Small book cover: The Foundations of Analysis

The Foundations of Analysis
by

Publisher: arXiv
Number of pages: 48

Description:
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.

Home page url

Download or read it online for free here:
Download link
(370KB, PDF)

Similar books

Book cover: An Introduction to Real AnalysisAn Introduction to Real Analysis
by - University of California Davis
These are some notes on introductory real analysis. They cover the properties of the real numbers, sequences and series of real numbers, limits of functions, continuity, differentiability, sequences and series of functions, and Riemann integration.
(2939 views)
Book cover: Theory of the IntegralTheory of the Integral
by - ClassicalRealAnalysis.info
This text is intended as a treatise for a rigorous course introducing the elements of integration theory on the real line. All of the important features of the Riemann integral, the Lebesgue integral, and the Henstock-Kurzweil integral are covered.
(14673 views)
Book cover: Homeomorphisms in AnalysisHomeomorphisms in Analysis
by - American Mathematical Society
This book features the interplay of two main branches of mathematics: topology and real analysis. The text covers Lebesgue measurability, Baire classes of functions, differentiability, the Blumberg theorem, various theorems on Fourier series, etc.
(11141 views)
Book cover: Analysis Tools with ApplicationsAnalysis Tools with Applications
by - Springer
These are lecture notes from Real analysis and PDE: Basic Topological, Metric and Banach Space Notions; Riemann Integral and ODE; Lebesbgue Integration; Hilbert Spaces and Spectral Theory of Compact Operators; Complex Variable Theory; etc.
(11533 views)