LEADER 04421nam 2200805Ia 450 001 9910825482203321 005 20200520144314.0 010 $a9786613622389 010 $a9781280592553 010 $a1280592559 010 $a9781118243855 010 $a1118243854 010 $a9781118243879 010 $a1118243870 010 $a9781118243824 010 $a111824382X 035 $a(CKB)2670000000177315 035 $a(EBL)818230 035 $a(SSID)ssj0000638366 035 $a(PQKBManifestationID)11432336 035 $a(PQKBTitleCode)TC0000638366 035 $a(PQKBWorkID)10708854 035 $a(PQKB)10747166 035 $a(Au-PeEL)EBL818230 035 $a(CaPaEBR)ebr10560609 035 $a(CaONFJC)MIL362238 035 $a(CaSebORM)9781118204481 035 $a(MiAaPQ)EBC818230 035 $a(OCoLC)795795376 035 $a(PPN)168380390 035 $a(OCoLC)824761418 035 $a(OCoLC)ocn824761418 035 $a(Perlego)2784786 035 $a(EXLCZ)992670000000177315 100 $a20111007d2012 uy 0 101 0 $aeng 135 $aurunu||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe mathematics of infinity $ea guide to great ideas /$fTheodore G. Faticoni 205 $a2nd ed. 210 $aHoboken, N.J. $cJohn Wiley & Sons$dc2012 215 $a1 online resource (360 p.) 225 0 $aPure and applied mathematics 300 $aDescription based upon print version of record. 311 08$a9781118204481 311 08$a1118204484 320 $aIncludes bibliographical references and index. 327 $aThe 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 327 $a4.1 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 327 $a8 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 Go?del's Incompleteness Theorem; 9.3.2 Logically Closed Sets; 9.3.3 Applications; Bibliography; Index 330 $aPraise for the First Edition "". . . an enchanting book for those people in computer science or mathematics who are fascinated by the concept of infinity.""-Computing Reviews "". . . a very well written introduction to set theory . . . easy to read and well suited for self-study . . . highly recommended.""-Choice The concept of infinity has fascinated and confused mankind for centuries with theories and ideas that cause even seasoned mathematicians to wonder. The Mathematics of Infinity: A Guide to Great Ideas, Second Edition uniquely explores how we can manipulate these idea 410 0$aPure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts 606 $aCardinal numbers 606 $aInfinite 606 $aSet theory 615 0$aCardinal numbers. 615 0$aInfinite. 615 0$aSet theory. 676 $a511.3/22 686 $aMAT016000$2bisacsh 700 $aFaticoni$b Theodore G$g(Theodore Gerard),$f1954-$0502645 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910825482203321 996 $aThe mathematics of infinity$93963781 997 $aUNINA