• Journal for History of Mathematics
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• v.24 no.3
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• pp.13-21
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• 2011

This mathematico-theological study addresses the Cantor's mathematics and theology of the infinite. From the scientific perspective, Cantor's landmark works opened the definition and logic of infinity in concreto, in abstracto, and in Deo. According to Cantor, the absolute infinite ${\Omega}$ could imply God's property beyond the actual infinite in physical and mathematical worlds.

• Journal for History of Mathematics
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• v.3 no.1
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• pp.71-79
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• 1986

• Journal for History of Mathematics
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• v.11 no.1
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• pp.47-51
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• 1998

We consider how the speculation of infinity has been established through Cantor's idea. Also this paper deals with a problem of infinity in view of the application of our real life, as well as the theoretical meaning.

• Communications of the Korean Mathematical Society
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• v.21 no.3
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• pp.409-417
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• 2006

자연현상의 복잡한 대상의 연구에서 출발한 프랙탈의 연구는 물리학에서 특히 열역학에서의 기법을 활용한 다중프랙탈의 연구로까지 그 영역이 확대되었다. 이 논문에서는 프랙탈과 다중프랙탈의 여러 가지 성질과 그 응용에 대한 최근 결과를 소개한다

• Journal for History of Mathematics
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• v.22 no.3
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• pp.1-30
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• 2009

Frege's logicism has been frequently regarded as a development in number theory which succeeded to the so called arithmetization of analysis in the late 19th century. But it is not easy for us to accept this opinion if we carefully examine his actual works on real analysis. So it has been often argued that his logicism was just a philosophical program which had not contact with any contemporary mathematical practices. In this paper I will show that these two opinions are all ill-founded ones which are due to the misunderstanding of the theoretical place of Frege's logicism in the context of contemporary mathematical practices. Firstly, I will carefully examine Cantorian definition of real numbers and Frege's critiques of it. On the basis of this, I will show that Frege's aim was to produce the purely logical definition of ratios of quantities. Secondly, I will consider the mathematical background of Frege's logicism. On the basis of this, I will show that his standpoint in real analysis was much subtler than what we used to expect. On the one hand, unlike Weierstrass and Cantor, Frege wanted to get such real analysis that could be universally applicable. On the other hand, unlike most mathematicians who insisted on the traditional conceptions, he would not depend upon any geometrical considerations in establishing real analysis. Thirdly, I will argue that Frege regarded these two aspects - the independence from geometry and the universal applicability - as those which characterized logic itself and, by logicism, arithmetic itself. And I will show that his conception of real numbers as ratios of quantities stemmed from his methodological maxim according to which the nature of numbers should be explained by the common roles they played in various contexts to which they applied, and that he thought that the universal applicability of numbers could not be adequately explicated without such an explanation.

• East Asian mathematical journal
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• v.25 no.3
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• pp.229-245
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• 2009

G. Cantor gave a deep influence to the society of mathematics in many ways, especially in the set theory. It is important for gifted and talented high school students in mathematics to understand the Euler constant and the fractal dimension of the Cantor set in a heuristic sense. On the historic basis of mathematics and the standard of high school students, we give the teaching method for the talented high school student to understand them better. Further we introduce the Riesz-N$\acute{a}$gy-Tak$\acute{a}$cs distribution and its first moment. We hope that from these topics, the gifted and talented students in mathematics will have insight in the analysis of mathematics.

• Journal of Korean Theatre Studies Association
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• no.49
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• pp.75-100
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• 2013

An on-going creative process was the major principle of Kantor's artistic endeavors. Kantor's emphasis on process grew out of his frustration with the experience of creation being isolated from the audience in the present time, during the moments of encounter. At the same time, however, Kantor was always aware of the fact that the first night of each and every performance that he made was the last point of his creative intervention. Despite being performed live in the present time, Kantor saw theatre essentially as an end product. This does not mean that Kantor abandoned the concept of on-going process, for process was for the artist a means to reject the idea of a finished work of art and to denounce the feeling of satisfaction derived from the traditional denouement in representational theatre. For him, theatre that dominated his time isolated the audience from the art work and the artist, and from this perspective his continual emphasis on process should be understood as an aesthetic principle in order to open up and expand the dimension of art into the realm of the spectator so that the experiences of both the artist and spectator may coexist. The heaviest barrier that separated the artist and his work from its audience was the creative structure that governed Western art. In theatre it was the dramatic structure that was the main object of his series of severe challenges. Not only did it fail to represent reality but it distorted reality, creating nothing but artificial illusion. Under this condition, all that was permitted to the audience was mirages. However, Kantor never completely discarded illusion from his theatre. The point for him was always to created a circumstance where the illusory reality of drama comes to exist within the dimensions of our reality. It was Kantor's belief that instead of a total denial of illusion, his theatre should strategically accommodate illusion which comes from reality. And, the aim of Kantor's theatrical experiments was to invite the audience into this ambience and transform the experience of his audience into a much more participatory one. This paper traces the ways in which Kantor transgressed the dominating conventions of representational, literary theatre, and how such attempts induced an alternative mode of spectatorship. The study will begin from an investigation into Kantor's attitude towards illusion and reality, and then move onto a closer inspection of how he spatially and dramaturgically materialized his concepts on stage, giving special focus on Wielopole, Wielopole.