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The mathematics of infinity [[electronic resource] ] : a guide to great ideas / / Theodore G. Faticoni
| The mathematics of infinity [[electronic resource] ] : a guide to great ideas / / Theodore G. Faticoni |
| Autore | Faticoni Theodore G (Theodore Gerard), <1954-> |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Hoboken, N.J., : John Wiley & Sons, c2012 |
| Descrizione fisica | 1 online resource (360 p.) |
| Disciplina | 511.3/22 |
| Collana | Pure and applied mathematics |
| Soggetto topico |
Cardinal numbers
Infinite Set theory |
| ISBN |
1-280-59255-9
9786613622389 1-118-24385-4 1-118-24387-0 1-118-24382-X |
| Classificazione | MAT016000 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910141257703321 |
Faticoni Theodore G (Theodore Gerard), <1954->
|
||
| Hoboken, N.J., : John Wiley & Sons, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The mathematics of infinity : a guide to great ideas / / Theodore G. Faticoni
| The mathematics of infinity : a guide to great ideas / / Theodore G. Faticoni |
| Autore | Faticoni Theodore G (Theodore Gerard), <1954-> |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Hoboken, N.J., : John Wiley & Sons, c2012 |
| Descrizione fisica | 1 online resource (360 p.) |
| Disciplina | 511.3/22 |
| Collana | Pure and applied mathematics |
| Soggetto topico |
Cardinal numbers
Infinite Set theory |
| ISBN |
9786613622389
9781280592553 1280592559 9781118243855 1118243854 9781118243879 1118243870 9781118243824 111824382X |
| Classificazione | MAT016000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910825482203321 |
|
Faticoni Theodore G (Theodore Gerard), <1954->
|
||
| Hoboken, N.J., : John Wiley & Sons, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||