Abstract
In elementary calculus courses, a large number of basic properties concerning numbers are assumed, and probably no explicit list of them is ever given. The purpose of this chapter is to make the basic list, so as to lay firm foundations for what follows. The purpose is not to minimize the number of these axioms, but rather to take some set of axioms which is neither too large, nor so small as to cause undue difficulty at the basic level. We don’t intend to waste time on these foundations. The axioms essentially summarize the properties of addition, multiplication, division, and ordering which are used constantly later.
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© 1997 Springer Science+Business Media New York
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Lang, S. (1997). Real Numbers. In: Undergraduate Analysis. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2698-5_2
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DOI: https://doi.org/10.1007/978-1-4757-2698-5_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2853-5
Online ISBN: 978-1-4757-2698-5
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