10 books for « cantor georg »Edit

‎Collection of 13 fundamental papers by Cantor (of which 12 are the first translations into French). 1. Sur une propriété du systeme de tous les nombrés algébriques réels (translation of ""Über eine Eigenschaft des Inbegriffes aller reellen algebraisc...‎

‎Stockholm, F. & G. Beijer, 1883, 1884, 1885. 4to. Contained in 3 issues from ""Acta Mathematica"", Vol. 2:4, vol. 4:4 a. vol. 7:2. All 3 issues with orig. printed wrappers, no backstrip.Vol. 2:4: pp. 305-310, 311-328, 329-335, 336-348, 349-380, 381-408, 409-414. - Vol. 4:4: pp. 381-392 - Vol. 7:2: pp.105-124.‎

‎First appearance in French of Cantor's main, groundbreaking papers, the foundations of Set-Theory, Denumerability, Reals, Algebraic Number Theory, Infinite Point Sets, Transfinite Set Theory, Transfinite Numbers, The Continuum Hypothesis, Theory of Content (volume) for Finite and Transfinite Point Sets, etc.The last paper ""Zweite Mittheilung), the paper offered here as no. 12, finished the series devoted to the ""Punktmannigfaltigkeiten"" is the first printing, as Cantor agreed to add half a dozen or so paragraphs to his ""Grundlagen"" (no. 9 offered here) in order to clarify how his theories could add to the progress of other departments of the sciences. These paragraphs contains Cantor's ""World Hypothesis"". The first paper on algebraic numbers proves that the set of all algebraic numbers has the same power as the set of natural numbers, that is, that it is not ""denumerable"" or ""countable"", but the set of real numbers not only exist but are nondenumerably infinite. This paper is considered the first formal publication on set theory.""Having demonstrated the existence of sets with the same power and different powers, Cantor pursued this concept of the power of a set and introduced a theory of cardinal and ordinal numbers in which the transfinite cardinals and ordinals are the striking elements. Cantor developed this work in a series of papers in the ""Mathematische Annalen"" from 1879-1884...In the fifth paper on linear aggregates Cantor opens with the observation ""The description of my investigations in the theory of aggregates has reached a stage where their continuation has become dependent on a generalization of real positive integers beyond the present limits"" a generalization which takes a direction in which, as far as I know, nobody has yet looked..."" (Morris Kline).Hilbert spread Cantor's ideas in Germany and said ""No one shall expel us from the paradise which Cantor created for us"". He praised Cantor's transfinite arithmetic as ""the most astonishing product of mathematical thought, one of the most beautiful realizations of human activity in the domain of the purely intelligible"". Betrand Russel described Cantor's work as ""probably the greatest of which the age can boast"".""These discoveries of Cantor were a continuation of the infinite, and Cantor was well aware of it. He defended St. Augustine's full acceptance of the actually infinite, but had to defend himself against the opposition of many mathematicians who refused to accept the infinite except as a process expressed by [the symbol of infinity]... Cantor finally won full acceptance when the enormous importance of his theory for the foundation of real function theory and of topology became more and more obvious - this especially after Ebesque in 1901 had enriched the theory of aggregates with his theory of measure."" (Dirk J. Struik).‎

‎Über unendliche, lineare Punktmannichfaltigkeiten. - [THE THEORY OF SETS AND INFINITE SETS - THE SECOND PAPER]‎

‎Leipzig, B.G. Teubner, 1880. 8vo. Bound in a nice contemporary half calf with five raised gilt bands. Red leather title label with gilt lettering to spine. All edged gilt. In ""Mathematische Annalen"", Band 17, 1880. Entire volume offered. Corners with wear, otherwise a very fine and clean copy. Pp. 355-358. [Entire volume: IV, 576 pp.].‎

‎First printing of Cantor's important second paper of the landmark series consisting of a total of six papers which together constitute the foundation Theory of Sets (Mengenlehre) and Transfinite Set Theory. Cantor here introduces his new Set Theory with which he created an entirely new field of mathematical research and is widely regarded as being one of the most important mathematical conquests in the 19th century. ""Cantor's second paper of 1880 was brief. It continued the bricklaying work of the article of 1879, and it too sought to reformulate old ideas in the context of linear point sets. It also introduced for the first time an embryonic form of Cantor's boldest and most original discovery: the transfinite numbers. As a preliminary to their description, however, Cantor introduced several definitions. He also pointed out that first species sets could be completely characterized by their derived sets."" (Dauben, P. 80)Hilbert spread Cantor's ideas in Germany and praised Cantor's transfinite arithmetic as ""the most astonishing product of mathematical thought, one of the most beautiful realizations of human activity in the domain of the purely intelligible"". He is famously quoted for saying ""No one shall expel us from the paradise which Cantor created for us"". Bertrand Russel described Cantor's work as ""probably the greatest of which the age can boast"".""The major achievement of the ""Grundlagen"" was its presentation of the transfinite ordinal numbers as a direct extension of the real numbers. Cantor admitted that his new ideas might seem strange, even controversial, but he had reached a point in his study of the continuum where the new numbers were indispensable for further progress. Cantor had finally come to the realization that his 'infinite symbols' were not just indices for derived sets of the second species, but could be regarded as actual transfinite numbers that were just as real mathematically as the finite natural numbers."" (Grattan-Guinness, Landmark Writings in Western Mathematics, Pp. 604-5).Dauben: (Cantor)1880d. ‎

‎Über unendliche, lineare Punktmannichfaltigkeiten. - [THE THEORY OF SETS AND INFINITE SETS - THE FINAL PAPER]‎

‎Leipzig, B.G. Teubner, 1884. 8vo. Bound in a nice contemporary half calf with five raised gilt bands. Red leather title label with gilt lettering to spine. All edged gilt. In ""Mathematische Annalen"", Band 23, 1884. Entire volume offered. Corners with wear, otherwise a very fine and clean copy. Pp. 453-488. [Entire volume: IV, 598, (2) pp.].‎

‎First printing of Cantor's seminal sixth paper in the landmark series consisting of a total of six papers which together constitute the foundation Theory of Sets (Mengenlehre) and Transfinite Set Theory. Cantor here introduces his new Set Theory with which he created an entirely new field of mathematical research and is widely regarded as being one of the most important mathematical conquests in the 19th century. ""Cantor published a sequel in the following year as a sixth in the series of papers on the Punktmannigfaltigkeitslehre (The present paper). Though it did not bear the title of its predecessor, its sections were continuously numbered, 15 through 19"" it was clearly meant to be taken as a continuation of the earlier 14 sections of the ""Grundlagen"" itself. In searching for a still more comprehensive analysis of continuity, and in the hope of establishing his continuum hypothesis, he focused chiefly upon the properties of perfect sets and introduced as well an accompanying theory of content"" (Dauben, P. 111)Hilbert spread Cantor's ideas in Germany and praised Cantor's transfinite arithmetic as ""the most astonishing product of mathematical thought, one of the most beautiful realizations of human activity in the domain of the purely intelligible"". He is famously quoted for saying ""No one shall expel us from the paradise which Cantor created for us"". Bertrand Russel described Cantor's work as ""probably the greatest of which the age can boast"".""The major achievement of the ""Grundlagen"" was its presentation of the transfinite ordinal numbers as a direct extension of the real numbers. Cantor admitted that his new ideas might seem strange, even controversial, but he had reached a point in his study of the continuum where the new numbers were indispensable for further progress. Cantor had finally come to the realization that his 'infinite symbols' were not just indices for derived sets of the second species, but could be regarded as actual transfinite numbers that were just as real mathematically as the finite natural numbers."" (Grattan-Guinness, Landmark Writings in Western Mathematics, Pp. 604-5).Dauben: (Cantor)1884a. ‎

‎Über unendliche, lineare Punktmannichfaltigkeiten. - [THE THEORY OF SETS AND INFINITE SETS - THE FIRST PAPER]‎

‎Leipzig, B.G. Teubner, 1879. 8vo. Bound in a nice contemporary half calf with five raised gilt bands. Red leather title label with gilt lettering to spine. All edged gilt. In ""Mathematische Annalen"", Band 15, 1879. Entire volume offered. Corners with wear, otherwise a very fine and clean copy. Pp. 1-7. [Entire volume: IV, 576 pp.].‎

‎First printing of Cantor's seminal exceedingly important first paper in his landmark series of six papers which together constitute the foundation Theory of Sets (Mengenlehre) and Transfinite Set Theory. Cantor here introduces his new Set Theory with which he created an entirely new field of mathematical research and is widely regarded as being one of the most important mathematical conquests in the 19th century. Hilbert spread Cantor's ideas in Germany and praised Cantor's transfinite arithmetic as ""the most astonishing product of mathematical thought, one of the most beautiful realizations of human activity in the domain of the purely intelligible"". He is famously quoted for saying ""No one shall expel us from the paradise which Cantor created for us"". Bertrand Russel described Cantor's work as ""probably the greatest of which the age can boast"".""The major achievement of the ""Grundlagen"" was its presentation of the transfinite ordinal numbers as a direct extension of the real numbers. Cantor admitted that his new ideas might seem strange, even controversial, but he had reached a point in his study of the continuum where the new numbers were indispensable for further progress. Cantor had finally come to the realization that his 'infinite symbols' were not just indices for derived sets of the second species, but could be regarded as actual transfinite numbers that were just as real mathematically as the finite natural numbers."" (Grattan-Guinness, Landmark Writings in Western Mathematics, Pp. 604-5).Dauben: (Cantor)1879b. ‎

‎Bemerkung mit Bezug auf den Aufsatz: Zur Weierstrass'-Cantor'schen Theorie der Irrationalzahlen in Math. Annalen. Bd. XXXIII, p. 154. - [CANTOR ON NUMBER THEORY]‎

‎Leipzig, B.G. Teubner, 1889. 8vo. Original printed wrappers, no backstrip and a small nick to front wrapper. In ""Mathematische Annalen. Begründet 1889 durch Rudolf Friedrich Alfred Clebsch. XXXIII.[33] Band. 3. Heft."" Entire issue offered. Internally very fine and clean. [Cantor:] P. 476. [Entire issue: Pp. (1), 318-476, (1)].‎

‎First printing of Cantor's important comment to Illigens paper from the same year: ""Zur Weierstrass'-Cantor'schen Theorie der Irrationalzahlen"". He states that: ""The squareroot of 3 is thus only a symbol for number which has yet to to be found, but is not its definition. The definitions is, however, satisfactorily given by my method as, say (1.7, 1.73, 1.732, ...). [From the present paper]. Cantor is famous for his work on infinite numbers. ‎

‎La théorie Bacon-Shakespeare. Le drame sujectif d'un savant. Textes réunis et présentés par Erik Porge.‎

‎Paris GREC 1996 In-12 (h. 21 cm.) 175 pp. couverture souple. Première publication française de trois opuscules écrits par le mathématicien Georg Cantor. Confession de foi de Francis Bacon; Résurrection du divin Quirinus Francis Bacon. Recueil de Rawley des trente-deux élégies sur Francis Bacon. Un témoignage en faveur de la théorie Bacon-Shakespeare ; Ex oriente lux. Vie et travaux de Cantor, bibliographie. ‎

‎Bon état. Libraire membre du S.L.A.M. (Syndicat national de la Librairie Ancienne et Moderne) et de la L.I.L.A. (Ligue Internationale de la Librairie Ancienne). N'hésitez pas à prendre contact par mail pour des photographies et des détails supplémentaires, pour des recherches ou des estimations de livres anciens et rares.‎

‎Bemerkung mit Bezug auf den Aufsatz: Zur Weierstrass'-Cantor'schen Theorie der Irrationalzahlen (+) Die Zusammensetzung der stetigen endlichen Transformationsgruppen.‎

‎Leipzig, B. G. Teubner, 1889. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 33., 1889. Entire volume offered. Library label pasted on to pasted down front free end-paper. Small library stamp to lower part of title title page and verso of title page. Very fine and clean. P. 476"" Pp. 1-48. [Entire volume: IV, 604 pp.].‎

‎First printing of CANTOR'S important comment to Illigens paper from the same year: ""Zur Weierstrass'-Cantor'schen Theorie der Irrationalzahlen"". He states that: ""The squareroot of 3 is thus only a symbol for number which has yet to to be found, but is not its definition. The definitions is, however, satisfactorily given by my method as, say (1.7, 1.73, 1.732, ...). [From the present paper]. First publication of KILLING'S important second paper (of a total of four) in which he laid the foundation of a structure theory for Lie algebras.""In particular he classified all the simple Lie algebras. His method was to associate with each simple Lie algebra a geometric structure known as a root system. He used linear transformation, to study and classify root systems, and then derived the structure of the corresponding Lie algebra from that of the root system.""(Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences)Unfortunately for Killing a myth arose that his work was riddled with error, which later has been proved untrue. ""As a result, many key concepts that are actually due to Killing bear names of later mathematicians, including ""Cartan subalgebra"", ""Cartan matrix"" and ""Weyl group"". As mathematician A. J. Coleman says, ""He exhibited the characteristic equation of the Weyl group when Weyl was 3 years old and listed the orders of the Coxeter transformation 19 years before Coxeter was born.""The theory of Lie groups, after the Norwegian mathematician Sophus Lie, is a structure having both algebraic and topological properties, the two being related.‎

‎Georg Cantor Gesammelte Abhandlungen Mathematischen un Philosophischen Inhalts. Mit erläuternden Anmerkungen sowir mit Ergänzungen aus dem Briefwechsel Cantor-Dedekind.‎

‎ Hildesheim, Olms Verlag, 1966, (facsimile edition of the Berlin 1932 edition), softcover.‎

‎La Théorie Bacon-Shakespeare. Le drame subjectif d'un savant‎

‎Clichy, G.R.E.C., 1996, 14,5 x 21, 175 pages cousues sous couverture illustrée. Traduction de l'anglais par Madeleine Drouin, Christine Knoll-Froissart et Jacques de Maussion. Textes réunis et présentés par Eric Porge.‎

‎Sur les Fonctions Uniformes qui se reproduisent par des Substitutions Linéaires (+) Ueber ein neues und allgemeines Condensationsprincip der Singularitäten von Functionen.‎

‎Leipzig, B.G. Teubner, 1882. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 37, 1890. Entire volume offered. Library label pasted on to pasted down front free end-paper. Small library stamp to lower part of title title page and verso of title page. Fine and clean. Pp. 182-228. [Entire volume: IV, 604 pp.].‎

‎First printing of Poincaré's paper on his comprehensive theory of complex-valued functions which remain invariant under the infinite, discontinuous group of linear transformations. In 1881 Poincaré had published a few short papers with some initial work on the topic, and in the 1881, Klein invited Poincaré to write a longer exposition of his results to Mathematische Annalen which became the present paper. This, however, turned out to be an invitation to at mathematical dispute:""Before the article went to press, Klein forewarned Poincaré that he had appended a note to it in which he registered his objections to the terminology employed therein. In particular, Klein disputed Poincaré's decision to name the important class of functions possessing a natural boundary circle after Fuch's, a leading exponent of the Berlin school. The importance he attached to this matter, however, went far beyond the bounds of conventional priority dispute. True, Klein was concerned that his own work received sufficient acclaim, but the overriding issue hinged on whether the mathematical community would regard the burgeoning research in this field as an outgrowth of Weierstrassian analysis or the Riemannian tradition."" Parshall. The Emergence of the American Mathematical Research Community. Pp. 184-5.The issue contains the following important contributions by seminal mathematicians:1. Klein, Felix. Ueber eindeutige Functionen mit linearen Transformationen in sich. Pp. 565-68.2. Picard, Emile. Sur un théorème relatif aux surfaces pour lesquelles les coordnnées d´un point quelconque s´experiment par des fonctions abéliennes de deux paramètres. Pp. 578-87.‎