Georg Cantor Gesammelte Abhandlungen: Mathematischen und philosophischen Inhalts mit erläuternden Anmerkungen sowie mit Ergänzungen aus dem Briefwechsel Cantor-Dedekind

Abstract

“INFINITY,” wrote the schoolboy, “is the place where things happen that don't.” Similar opinions concerning the paradoxes which arise from the consideration of the infinite and the infinitesimal have been expressed for more than two thousand years. About 450 B.C., Zeno put forward four such paradoxes, of which the best known is “Achilles and the Tortoise”. In the seventeenth and eighteenth centuries infinity and the infinitesimal were used very recklessly, and when at last mathematicians sought to return to the Greek standard of accuracy, they were unanimous in rejecting the use of infinity as some thing completed. But what all had rejected Cantor chose as his foundation stone. Georg Cantor Gesammelte Abhandlungen: Mathematischen und philosophischen Inhalts mit erlauternden Anmerkungen sowie mit Erganzungen aus dem Briefwechsel Cantor-Dedekind. Heraus-gegeben von Ernst Zermelo. Nebst einem Lebenslauf Cantors von Adolf Fraenkel. Pp. vii + 486. (Berlin: Julius Springer, 1932.) 48 gold marks.