Abstract
This chapter consists of reference material with which the reader should be familiar. We present it here both to refresh the reader’s memory and to have them available for reference. In Section 1.1, we begin by recalling elementary properties of sets, in particular the set of rational numbers and their decimal representations. Then we proceed to introduce the irrational numbers. In Section 1.2, we briefly discuss the notion of supremum and infimum and state the completeness axiom for the set of real numbers. We introduce the concept of one-to-one, onto, and bijective mappings, as well as that of equivalent sets.
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Notes
- 1.
The symbol ⇔ and the word “iff” both mean “if and only if.”
- 2.
The terms mapping, function, and transformation are frequently used synonymously.
- 3.
The terms “one-to-one,” “onto,”, and “one-to-one correspondence” are sometimes referred as “injective,” “surjective,” and “bijective” mappings, respectively.
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Ponnusamy, S. (2012). The Real Number System. In: Foundations of Mathematical Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8292-7_1
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DOI: https://doi.org/10.1007/978-0-8176-8292-7_1
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Publisher Name: Birkhäuser, Boston, MA
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Online ISBN: 978-0-8176-8292-7
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