Middle Down (1)

____________________ END CHAPTER EIGHT

Uniqueness of the Real Number System :
Periodic Infinite b-mals :
Every Infinite b-mal Represents a Real Number :
b-mal Expansions of Real Numbers :
The Fixed Point Theorem :
VIII. The Method of Successive Approximations ( ita - chapter 8 )

____________________ END CHAPTER FOUR

Uniform Continuity Implies Continuity :
Uniform Continuity :
Continuous Functions and Convergent Sequences :
Continuity on a Set :
Continuity at a Point :
IV. Continuous Functions ( ita - chapter 4 )

____________________ END CHAPTER THREE

Completeness :
Cauchy Sequences :
Bounded Monotonic Sequences :
Definition of Monotonic Sequences :
Limit of a Product Sequence :
Theorem on Sequences and Closed Sets :
Convergent Sequences are Bounded :
Definition of a Bounded Sequence :
Convergence of Subsequences :
Definition of Subsequences :
The Limit of a Sequence is Unique :
The Constant Sequence :
Convergence of a Sequence :
Bounded Sets :
Combinations of Closed Sets :
Combinations of Open Sets :
Examples with Real Numbers :
Closed Sets in a Metric Space :
Open Sets in a Metric Space :
Open and Closed Balls in a Metric Space :
The Real Numbers as a Metric Space :
Definition of a Metric Space :
III. Metric Spaces ( ita - chapter 3 )

____________________ END CHAPTER ONE

The Compliment of an Intersection :
The Compliment of a Union :
The Compliment of a Set :
I. Notions from Set Theory ( ita - chapter 1 )

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