Abstract
Different sizes of infinity are defined in terms of cardinality. The Schroder–Bernstein theorem is stated and proven. Examples of infinite sets of the same cardinality are given. The diagonal trick is used to show that the cardinality of the real numbers is greater than that of the natural numbers. It is also shown that the power set of any set is of greater cardinality than it. It is demonstrated that the set of transcendental numbers is uncountable and the set of algebraic numbers is countable.
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© 2015 Springer International Publishing Switzerland
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Joshi, M. (2015). Diagonal Tricks and Cardinality. In: Proof Patterns. Springer, Cham. https://doi.org/10.1007/978-3-319-16250-8_13
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DOI: https://doi.org/10.1007/978-3-319-16250-8_13
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-16249-2
Online ISBN: 978-3-319-16250-8
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