The Real Numbers An Introduction to Set Theory and Analysis /

• Main Author: Stillwell, John. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2013.
• Series: Undergraduate Texts in Mathematics,
• Subjects: Mathematics.; Logic, Symbolic and mathematical.; Real Functions.; Mathematical Logic and Foundations.; History of Mathematical Sciences.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-319-01577-4

While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measu...

Table of Contents:

• The Fundamental Questions
• From Discrete to Continuous
• Infinite Sets
• Functions and Limits
• Open Sets and Continuity
• Ordinals
• The Axiom of Choice
• Borel Sets
• Measure Theory
• Reflections
• Bibliography
• Index.