Author: Brian RotmanPublisher:
ISBN:
Category : Set theory
Languages : en
Pages :
Book Description
The theory of sets and transfinite numbers, by B.Rotman and G.T.Kneebone
Author: Brian RotmanThe Theory of Sets and Transfinite Numbers
Author: Brian RotmanPublisher:
ISBN:
Category : Numbers, Transfnite
Languages : en
Pages : 166
Book Description
Sets and Transfinite Numbers
Author: Martin M. ZuckermanPublisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 450
Book Description
Basic Set Theory
Author: Nikolai Konstantinovich VereshchaginPublisher: American Mathematical Soc.
ISBN: 0821827316
Category : Mathematics
Languages : en
Pages : 130
Book Description
The main notions of set theory (cardinals, ordinals, transfinite induction) are fundamental to all mathematicians, not only to those who specialize in mathematical logic or set-theoretic topology. Basic set theory is generally given a brief overview in courses on analysis, algebra, or topology, even though it is sufficiently important, interesting, and simple to merit its own leisurely treatment. This book provides just that: a leisurely exposition for a diversified audience. It is suitable for a broad range of readers, from undergraduate students to professional mathematicians who want to finally find out what transfinite induction is and why it is always replaced by Zorn's Lemma. The text introduces all main subjects of ``naive'' (nonaxiomatic) set theory: functions, cardinalities, ordered and well-ordered sets, transfinite induction and its applications, ordinals, and operations on ordinals. Included are discussions and proofs of the Cantor-Bernstein Theorem, Cantor's diagonal method, Zorn's Lemma, Zermelo's Theorem, and Hamel bases. With over 150 problems, the book is a complete and accessible introduction to the subject.
The Theory of Sets and Transfinite Numbers
Author: Saint Euphrasia PowderlyPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Contributions to the Founding of the Theory of Transfinite Numbers
Author: Georg CantorPublisher:
ISBN: 9781891396533
Category : Set theory
Languages : en
Pages : 222
Book Description
2010 Reprint of 1915 Edition. Georg Ferdinand Ludwig Philipp Cantor was a German mathematician, best known as the inventor of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between sets, defined infinite and well-ordered sets, and proved that the real numbers are "more numerous" than the natural numbers. In fact, Cantor's theorem implies the existence of an "infinity of infinities". He defined the cardinal and ordinal numbers and their arithmetic. Cantor's work is of great philosophical interest, a fact of which he was well aware. In 1895-97 Cantor fully propounded his view of continuity and the infinite, including infinite ordinals and cardinals, in his best known work, Contributions to the Founding of the Theory of Transfinite Numbers . This work contains his conception of transfinite numbers, to which he was led by his demonstration that an infinite set may be placed in a one-to-one correspondence with one of its subsets.