Sets and Ordered Structures

Indexed in: Scopus, Zentralblatt MATH, EBSCO

This e-book presents several basic methods and results of order theory that are currently used in various branches of mathematics. It presents topics that require a broad explanation in a concise and ...
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Transfinite Algebra

Pp. 83-106 (24)

DOI: 10.2174/978160805338411201010083

Author(s): Sergiu Rudeanu


The theory of ordinal numbers is a natural and very powerful generalization of the order-theoretical properties of natural numbers. In particular it furnishes transfinite induction, a method for constructing rather complicated mathematical concepts and for proving properties valid beyond the natural numbers. Ordinal numbers can also serve as a basis for introducing cardinal numbers. The latter evaluate “how many elements” a set possesses, being thus a kind of “quantitative” generalization of natural numbers, widely used in mathematics.