Overview page for Introduction to Real Analysis, Volume I (Jiri Lebl, 2025).

This aggregation module imports the currently formalized sections in this book. Use the links below to jump directly into chapter and section overview pages.

Verso links:

• Book home
• Book overview

Directory:

Chapter 00

• Section 0.3 (Documentation) (Verso)

Chapter 01 -- Real Numbers

• 1.1 Basic Properties (Documentation) (Verso)
• 1.2 The Set of Real Numbers (Documentation) (Verso)
• 1.3 Absolute Value and Bounded Functions (Documentation) (Verso)
• 1.4 Intervals and the Size of R (Documentation) (Verso)
• 1.5 Decimal Representation of the Reals (Documentation) (Verso)

Chapter 02 -- Sequences and Series

• 2.1 Sequences and Limits (Documentation) (Verso)
• 2.2 Facts About Limits of Sequences (Documentation) (Verso)
• 2.3 Limit Superior, Limit Inferior, and Bolzano-Weierstrass (Documentation) (Verso)
• 2.4 Cauchy Sequences (Documentation) (Verso)
• 2.5 Series (Documentation) (Verso)
• 2.6 More on Series (Documentation) (Verso)

Chapter 03 -- Continuous Functions

• 3.1 Limits of Functions (Documentation) (Verso)
• 3.2 Continuous Functions (Documentation) (Verso)
• 3.3 Extreme and Intermediate Value Theorems (Documentation) (Verso)
• 3.4 Uniform Continuity (Documentation) (Verso)
• 3.5 Limits at Infinity (Documentation) (Verso)
• 3.6 Monotone Functions and Continuity (Documentation) (Verso)

Chapter 04 -- The Derivative

• 4.1 The Derivative (Documentation) (Verso)
• 4.2 Mean Value Theorem (Documentation) (Verso)
• 4.3 Taylor's Theorem (Documentation) (Verso)
• 4.4 Inverse Function Theorem (Documentation) (Verso)

Chapter 05 -- The Riemann Integral

• 5.1 The Riemann Integral (Documentation) (Verso)
• 5.2 Properties of the Integral (Documentation) (Verso)
• 5.3 Fundamental Theorem of Calculus (Documentation) (Verso)
• 5.4 The Logarithm and the Exponential (Documentation) (Verso)
• 5.5 Improper Integrals (Documentation) (Verso)

Chapter 06 -- Sequences of Functions

• 6.1 Pointwise and Uniform Convergence (Documentation) (Verso)
• 6.2 Interchange of Limits (Documentation) (Verso)
• 6.3 Picard's Theorem (Documentation) (Verso)

Chapter 07 -- Metric Spaces

• 7.1 Metric Spaces (Documentation) (Verso)
• 7.2 Open and Closed Sets (Documentation) (Verso)
• 7.3 Sequences and Convergence (Documentation) (Verso)
• 7.4 Completeness and Compactness (Documentation) (Verso)
• 7.5 Continuous Functions (Documentation) (Verso)
• 7.6 Fixed Point Theorem and Picard's Theorem Again (Documentation) (Verso)