This text forms a bridge between courses in calculus and real
analysis. It focuses on the construction of mathematical proofs as
well as their final content. Suitable for upper-level
undergraduates and graduate students of real analysis, it also
provides a vital reference book for advanced courses in
mathematics.The four-part treatment begins with an introduction to
basic logical structures and techniques of proof, including
discussions of the cardinality concept and the algebraic and order
structures of the real and rational number systems. Part Two
presents in-depth examinations of the completeness of the real
number system and its topological structure. Part Three reviews and
extends the previous explorations of the real number system, and
the final part features a selection of topics in real function
theory. Numerous and varied exercises range from articulating the
steps omitted from examples and observing mechanical results at
work to the completion of partial proofs within the text.
General
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