Introduction to Numbers and Set Theory

E. Mahmudov ()
Additional contact information
E. Mahmudov: Istanbul Technical University

Chapter Chapter 1 in Single Variable Differential and Integral Calculus, 2013, pp 1-30 from Springer

Abstract: Abstract Here we will give the main definitions and concepts of sets, the concepts of surjective, injective, and bijective functions, countability and uncountability of sets, cardinal number, and the cardinality of the continuum. These are very important in mathematical analysis and in other fields of the mathematical sciences. For this reason, different theorems connected with the concepts of countability and uncountability of sets are proved and it is shown that the cardinality of the set of functions defined on a closed interval is greater than the cardinality of the continuum. Furthermore, the Dedekind completeness theorem for the set of real numbers is proved. Finally, some of the topological properties of metric spaces are treated.

Date: 2013
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-91216-86-2_1

Ordering information: This item can be ordered from
http://www.springer.com/9789491216862

DOI: 10.2991/978-94-91216-86-2_1

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().