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Analysis
Show table of contents
Table of contents
Preface
1
Starting at the begining: the natural numbers
2
Set theory
3
Integers and rationals
4
The real numbers
5
Limits of sequences
6
Series
7
Infinite sets
8
Continuous functions on \(\mathbb{R}\)
9
Differentiation of functions
10
The Riemann integral
11
Appendix: the basics of mathematical logic
12
Appendix: the decimal system
References
8
Continuous functions on
\(\mathbb{R}\)
8.1
Subsets of the real line
8.2
The algebra of real-valued functions
8.3
Limiting values of functions
8.4
Continuous functions
8.5
Left and right limits
8.6
The maximum principle
8.7
The intermediate value theorem
8.8
Monotonic functions
8.9
Uniform continuity
8.10
Limits at infinity
7
Infinite sets
9
Differentiation of functions
On this page
8
Continuous functions on \(\mathbb{R}\)
8.1
Subsets of the real line
8.2
The algebra of real-valued functions
8.3
Limiting values of functions
8.4
Continuous functions
8.5
Left and right limits
8.6
The maximum principle
8.7
The intermediate value theorem
8.8
Monotonic functions
8.9
Uniform continuity
8.10
Limits at infinity