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Autore: | Faticoni Theodore G (Theodore Gerard), <1954-> |
Titolo: | The mathematics of infinity [[electronic resource] ] : a guide to great ideas / / Theodore G. Faticoni |
Pubblicazione: | Hoboken, N.J., : John Wiley & Sons, c2012 |
Edizione: | 2nd ed. |
Descrizione fisica: | 1 online resource (360 p.) |
Disciplina: | 511.3/22 |
Soggetto topico: | Cardinal numbers |
Infinite | |
Set theory | |
Classificazione: | MAT016000 |
Note generali: | Description based upon print version of record. |
Nota di bibliografia: | Includes bibliographical references and index. |
Nota di contenuto: | The Mathematics of Infinity: A Guide to Great Ideas; Contents; Preface for the Second Edition; 1 Logic; 1.1 Axiomatic Method; 1.2 Tabular Logic; 1.3 Tautology; 1.4 Logical Strategies; 1.5 Implications From Implications; 1.6 Universal Quantifiers; 1.7 Fun With Language and Logic; 2 Sets; 2.1 Elements and Predicates; 2.2 Equality; 2.3 Cartesian Products; 2.4 Power Sets; 2.5 Something From Nothing; 2.6 Indexed Families of Sets; 3 Functions; 3.1 Functional Preliminaries; 3.2 Images and Preimages; 3.3 One-to-One and Onto Functions; 3.4 Bijections; 3.5 Inverse Functions; 4 Counting Infinite Sets |
4.1 Finite Sets 4.2 Hilbert's Infinite Hotel; 4.3 Equivalent Sets and Cardinality; 5 Infinite Cardinals; 5.1 Countable Sets; 5.2 Uncountable Sets; 5.3 Two Infinities; 5.4 Power Sets; 5.5 The Arithmetic of Cardinals; 6 Well-Ordered Sets; 6.1 Successors of Elements; 6.2 Constructing Well Ordered Sets; 6.3 Cardinals as Ordinals; 6.4 Magnitude versus Cardinality; 7 Inductions and Numbers; 7.1 Mathematical Induction; 7.2 Sums of Powers of Integers; 7.3 Transfinite Induction; 7.4 Mathematical Recursion; 7.5 Number Theory; 7.6 The Fundamental Theorem of Arithmetic; 7.7 Perfect Numbers | |
8 Prime Numbers 8.1 Prime Number Generators; 8.2 The Prime Number Theorem; 8.3 Products of Geometric Series; 8.4 The Riemann Zeta Function; 8.5 Real Numbers; 9 Logic and Meta-Mathematics; 9.1 The Collection of All Sets; 9.2 Other Than True or False; 9.3 The Logic of A Theory of Everything; 9.3.1 Gödel's Incompleteness Theorem; 9.3.2 Logically Closed Sets; 9.3.3 Applications; Bibliography; Index | |
Sommario/riassunto: | Praise for the First Edition "". . . an enchanting book for those people in computer science or mathematics who are fascinated by the concept of infinity.""-Computing Reviews "". . . a very well written introduction to set theory . . . easy to read and well suited for self-study . . . highly recommended.""-Choice The concept of infinity has fascinated and confused mankind for centuries with theories and ideas that cause even seasoned mathematicians to wonder. The Mathematics of Infinity: A Guide to Great Ideas, Second Edition uniquely explores how we can manipulate these idea |
Titolo autorizzato: | The mathematics of infinity |
ISBN: | 1-280-59255-9 |
9786613622389 | |
1-118-24385-4 | |
1-118-24387-0 | |
1-118-24382-X | |
Formato: | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione: | Inglese |
Record Nr.: | 9910141257703321 |
Lo trovi qui: | Univ. Federico II |
Opac: | Controlla la disponibilità qui |