Sets and Ordered Structures

Indexed in: Scopus, 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 ...
[view complete introduction]

US $
15

*(Excluding Mailing and Handling)



Transfinite Algebra

Pp. 83-106 (24)

Sergiu Rudeanu

Abstract

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.

Affiliation:

University of Bucharest, Romania