Analysis Zero - O'Farrell, Anthony G.
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This book leads up to the starting-point of a rigorous course in basic real analysis. It is designed to satisfy a student who wants to start 'further back' than the axioms of a complete ordered field. Typically, such a student will be in the second or higher year at University, and will have attained some level of mathematical maturity. The book presents a foundation in set theory, and builds up through the natural numbers, integers, and rational numbers to the real and complex numbers, and establishes their properties on the basis of some more basic axioms.

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This book leads up to the starting-point of a rigorous course in basic real analysis. It is designed to satisfy a student who wants to start 'further back' than the axioms of a complete ordered field. Typically, such a student will be in the second or higher year at University, and will have attained some level of mathematical maturity. The book presents a foundation in set theory, and builds up through the natural numbers, integers, and rational numbers to the real and complex numbers, and establishes their properties on the basis of some more basic axioms.