#real-analysis

26. Real Functions

This volume studies functions of real variables with an emphasis on limits, continuity, differentiation, integration, and fine properties of functions. It builds the rigorous core of real analysis. Part I. Real Numbers and Limits Chapter 1. The Real Number System 1.1 Ordered fields 1.2 Completeness axiom 1.3 Suprema and infima 1.4 Sequences in ℝ 1.5 Convergence Chapter 2. Limits of Sequences 2.1 Definition of limit 2.2 Limit laws 2.3 Monotone...