Little C.H.C., Teo K.L., van Brunt B. The Number Systems of Analysis

Singapore: World Scientific Publishing Company, 2003. — 225 p. - ISBN: 9812386068.Although students of analysis are familiar with real and complex numbers, few treatments of analysis deal with the development of such numbers in any depth. An understanding of number systems at a fundamental level is necessary for a deeper grasp of analysis. Beginning with elementary concepts from logic and set theory, this book develops in turn the natural numbers, the integers and the rational, real and complex numbers. The development is motivated by the need to solve polynomial equations, and the book concludes by proving that such equations have solutions in the complex number system.Elements of Logic.
Sets.
Natural Numbers.
Integers.
Rational Numbers.
Sequences on Q.
The Real Number System.
Complex Numbers.
The Fundamental Theorem of Algebra.