相关论文: Georg Cantor and his heritage

This article was written on the occasion of Hans Grauert receiving the Cantor Medallion of the Deutsche Mathematische Vereinigung. It is a brief overview of his mathematical contributions and attempts to convey the author's great respect…

This text tries to give an elementary introduction to the mathematical properties of infinite sets. The aim is to keep the approach as simple as possible. Advanced knowledge of mathematics is not necessary for a proper understanding, and…

Georg Cantor was the genuine discoverer of the Mathematical Infinity, and whatever he claimed, suggested, or even surmised should be taken seriously -- albeit not necessary at its face value. Because alongside his exquisite in beauty…

Georg Cantor (1845-1918) was born, and spent the first 11 years of his life in St. Petersburg. The present lecture is devoted to his childhood and his family. Most of these documents were not available before and are now published for the…

I present some reminiscences, both personal and scientific, over a lifetime of admiration of, and friendship with, one of the Grandmasters of our subject.

Discussions surrounding the nature of the infinite in mathematics have been underway for two millennia. Mathematicians, philosophers, and theologians have all taken part. The basic question has been whether the infinite exists only in…

The present article is devoted to representations of rational numbers in terms sign-variable Cantor expansions. The main attention is given to one of the discussions given by J. Galambos in [4].

This paper is an investigation into Cantor works about representing a function with trigonometric series, and his proofs about its uniqueness. These works are important, because they cause invention of point-set topology, and foundation of…

I discuss some general aspects of the creation, interpretation, and reception of mathematics as a part of civilization and culture.

A small and unsystematic selection of my favorite appearances of mathematicians and mathematics in German literature. It includes classic and romantic (Lessing, Goethe, Wezel, F. Schlegel, Kleist, Novalis, Grillparzer, Heine), modern…

Laudation delivered at the International Congress of Mathematicians in Berlin following the award of the Fields Medal to Richard Borcherds.

Cantor's algebraic calculation of the power of the continuum contains an easily repairable error related to Cantor own way of defining the addition of cardinal numbers. The appropriate correction is suggested.

Cantor sets of integers have a rich set of arithmetic combinatorial properties. We consider classical Cantor sets, with a base and a fixed set of allowed digits. For such sets, we (a) give examples of such sets that satisfy the intersective…

This paper is based on the talk given by the author after he received the International Bolyai Prize in Mathematics (on November 4, 2000 in Budapest, Hungary).

These informal notes briefly discuss various aspects of Cantor sets.

The purpose of this project is to outline various philosophies on the metaphysics of mathematics that have been prominent since the time of Cantor, highlighting some biographical aspects that have influenced these ideas as well. The main…

From 1873 to 1897, Georg Cantor worked on developing set theory, and despite a strong initial resistance, it rapidly became accepted as the foundation of mathematics. In this work, however, we'll demonstrate that Cantor's use of infinity is…

Generalizing a geometric idea due to J. Sondow, we give a geometric proof for the Cantor's Theorem. Moreover, it is given an irrationality measure for some Cantor series.

A mathematical framework is proposed for the "big bang". It starts with some Cantor set and assumes the existence of a transformation from that set to the continuum set used in conventional physical theories like general relativity and…

In the present article, modeling certain rational numbers, that are represented in terms of Cantor series, are described. The statements on relations between digits in the representations of rational numbers by Cantor series (for the case…