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| Cantor G. — Contributions to the Founding of the Theory of Transfinite Numbers |
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| Предметный указатель |
Abel, Niels Henrike 10
Abelian functions 10 11
Absolute Infinity 62 63
Actuality of numbers 67
Addition of cardinal numbers 80 91
Addition of ordinal types 81 119
Addition of transfinite numbers 63 66 153 175 206
Adherences 73
Aggregate of bindings 92
Aggregate of union 50 91
Aggregate, definition of 46 47 54 74 85
Alembert, Jean Lerond d’ 4
Algebraic numbers 38 ff. 127
Aquinas, Thomas 70
Araela 73
Aristotle 55 70
Arithmetic, foundations of, with Frege and Russell 202 203
Arithmetic, foundations of, with Weierstrass 12
Associative law with transfinite numbers 92 93 119 121 154 155
Baire, Rene 73
Bendixson, Ivar 73
Berkeley, George 55
Bernoulli, Daniel 4
Bernstein, Felix 204
Bois-Reymond, Pauldu 22
Bolzano, Bernard 13 14 17 21 41 55 72
Borel, Emile 73
Bouquet 7
Briot 7
Broden 73
Brouwer 208
Burali-Forti, Cesare 205 206
Cantor, Georg v vi vii 3 10 13 18 22 24 25 26 28 29 30 32 33 34 35 36 37 38 41 42 45 46 47 48 49 51 52 S3 54 55 56 57 59 60 62 63 64 68 69 70 72 73 74 76 77 79 80 8l 82 202 204 205 206 208
cardinal number 74 79 85 202 see
Cardinal number, finite 97 ff.
Cardinal number, smallest transfinite 103 ff.
Cardinal numbers, operations with 204
Cardinal numbers, series of transfinite 109
Cauchy, Augustin Louis 2 3 4 6 8 12 14 15 16 17 24
Class of types 114
Closed aggregates 132
Closed aggregates, types 133
Coherences 73
Coherent series 129 130
Commutative law with transfinite numbers 66 92 93 119 190
Condensation of singularities 3 9 48 49
Connected aggregates 72
Content of aggregates 73
Content-less 51
Continuity of a function 1
Continuous motion in discontinuous space 37
Continuum 33 37 41 47 48 64 70 96 205
Contradiction, Russell's 206 207
Convergence of series 1 15 16 17 20 24
Cords, vibrating, problem of 4
D'Alembert see "Alembert J.L.
de Morgan, Augustus 41
Dedekind axiom 30
Dedekind, Richard vii 23 41 47 49 73
Definition of aggregate 37
Democritus 70
Density in itself 132
Derivatives of point-aggregates 3 30 37
Descartes, Rene 55
Dirichlet, Peter Gustav Lejeune 2 3 5 7 8 9 22 35
Discrete aggregates 51
Distributive law with transfinite numbers 66 93 121 155
Enumerability 32 38ff. 47 50 62
Enumeral 52 62
Epicurus 70
Epimenides 207
Equivalence of aggregates 40 75 86
Euler, Leonhard 4 5 9 10
Everywhere-dense aggregates 33 35. 123-
Everywhere-dense aggregates, types 133
Exponentiation of transfinite numbers 82 94 207
Fontenelle 118
Formalism in mathematics 70 81
Fourier, Jean Baptiste Joseph i 2 6 8 24
Freedom in mathematics 67 ff.
Frege, Gottlob 23 70 202
Function, conception of 1
Functions, arbitrary 4 6 34
Functions, theory of analytic 2 6 7 10 11 12 13 22 73
Functions, theory of real 2 8 9 73
Fundamental series 20 128
Gauss, Carl Friedrich 6 12 14
Generation, principles of 56 57
Gudermann 10
Hahn, H. 203
Haller, Albrecht von 62
Hankel, Hermann 3 7 8 9 17 49 70
Hardy, G.H. 205 206
Harnack, Axel 51 73
Hausdorff, Felix 207 208
Heine, H.E. 3 26 69
Hessenberg, Gerhard 207
| Hobbes, Thomas 55
Imaginaries 6
Induction, mathematical 207
Infinite, definition of 41 61 62
Infinitesimals 64 81
Infinity, proper and improper 55 79
Integrability, Riemann’s conditions of 8
Integrable aggregates 51
Inverse-types 114
Irrational numbers 3 14 26
Irrational numbers, analogy of transfinite numbers with 77 ff.
Isolated aggregate 49
Isolated point 30
Jacobi, C.G.T. 10
Jordan, Camille 73
Jourdain, Philip E.B. 4 6 20 32 52 205 206 207 208
Killing, W. 118
Kind of a point-aggregate 32
Kirchhoff, G. 69
Koenig, Julius 207
Kronecker, L. 70 81
Kummer, E.E. 69
Lagrange, J.L. 5 14
Leucippus 70
Limit-point 30
Limitation, principle of 60
Limiting element of an aggregate 131
Limits with transfinite numbers 77 ff. 131 58
Liouville, L 40
Lipschitz, R. 6
Locke, J. 55
Lucretius 70
Mach, Ernst 69
Maximum of a function 22
Mittag-Leffler, Gosta 11
Mutliplication of cardinal numbers 80 91
Mutliplication of ordinal types 81 119 ff 154
Mutliplication of transfinite numbers 63 64 66 176
Newton, Sir Isaac 15
Nominalism, Cantor’s 69 70
Number-concept, logical definition of 202 203
Ordinal number 75 151 see
Ordinal numbers, finite 113 158 159
Ordinal type 75 79 110
Ordinal type of aggregate of rational numbers 122 ff. 202
Ordinal types of multiply ordered aggregates 81 208
Osgood, W.F. 73
Peano, G. 23
Perfect aggregates 72 132
Perfect types 133
Philosophical revolution brought about by Cantons work vi.
Physical conceptions and modem mathematics i.
Point-aggregates, Cantor’s early work on v vi.
Point-aggregates, theory of 3 20 30 64 73
Potential, theory of 7
Power of an aggregate 32 37 40 52 60 62
Power, second 64 ff. 169
Prime numbers, transfinite 64
Principal element of an aggregate 131
Puiseux, V. 7
Reducible aggregates 71
Relation numbers 203
Riemann, G.F.B. 3 7 8 9 10 T2 25 42
Riess, F. 208
Russell, Bertrand 20 23 53 202 203 204 206 207
Schepp, A. 117
Schmidt, E. 204
Schoenflies, A. 73 203 207
Schwarz 8 12
Second number-class, cardinal number of 169 ff.
Second number-class, epsilon-numbers of the 195 ff.
Second number-class, exponentiation in 178 ff.
Second number-class, normal form of numbers of 183 ff.
Second number-class, numbers of 160 ff.
Segment of a series 60 103 141
selections 204 ff.
Similarity 76 112
Species of a point-aggregate 31
Spinoza, B. 55
Steiner, J. 40
Stolz, O. 17 73-
Subtraction of transfinite numbers 66 I5S 156
Teubner, B.G. vii.
Transfinite numbers 4 32 36 50 52
Trigonometrical developments 2 3 4 5 6 7 8 24 31
Unextended aggregates 51
Upper limit 21
Veronese, G. 117 118
von Helmholtz, H. 42 70 81
von Leibniz, G.W. 55
Weierstiass, Karl vi vii 2 3 10 11 12 13 14 17 18 19 20 21 22 23 24 26 30
Well-ordered aggregates 60 61 75 137
Well-ordering 204 ff
Whitehead, A.N. 203 204
Zeno 15
Zermelo, E. 204 206 207 208
Zermelo’s axiom 204 ff.
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