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Cantor G. — Contributions to the Founding of the Theory of Transfinite Numbers
Cantor G. — Contributions to the Founding of the Theory of Transfinite Numbers

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Название: Contributions to the Founding of the Theory of Transfinite Numbers

Автор: Cantor G.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1915

Количество страниц: 211

Добавлена в каталог: 23.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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