Abstract
Chapter 2 discusses different systems of numbers, emphasizing on reasons making them so important. It starts with the system of natural numbers and presents its existence as a natural consequence from the axiom of infinity. Next, the systems of integers and rational numbers are constructed over the system of natural numbers. The least upper bound property and its lack in the system of rational numbers are emphasized. The system of real numbers is introduced as an ordered field with least upper bound property, which improves the system of rational numbers. For completeness of the whole picture on numbers, brief information about the systems of extended real, complex and hyperreal numbers is also given. The chapter ends with a discussion of cardinality, emphasizing on finite, countable and continuum cardinalities.
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