• Title/Summary/Keyword: 무한수학

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Cantor's Theology and Mathematics of the Infinite (칸토르의 수학 속의 신학)

  • Hyun, Woo-Sik
    • 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.

The Histories of the Mathematical Concepts of Infinity and Limit in a Three-fold Role (세 가지 역할과 관련된 무한과 극한의 수학사)

  • Kim, Dong-Joong
    • Journal of Educational Research in Mathematics
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    • v.20 no.3
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    • pp.293-303
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    • 2010
  • The purpose of this study is to classify a three-fold role of the history of mathematics through epistemological analysis. Based on the history of infinity and limit, the "potential infinity" and "actual infinity" discourses are described using four different historical epistemologies. The interdependence between the mathematical concepts is also addressed. By using these analyses, three different uses of the history of mathematical concepts, infinity and limit, are discussed: past, present, and future use.

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Leibniz's concept of infinite and infinitely small and arithmetic of infinite (라이프니츠의 무한과 무한소의 개념과 무한의 연산)

  • Lee, Jin-Ho
    • Journal for History of Mathematics
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    • v.18 no.3
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    • pp.67-78
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    • 2005
  • In this paper we deals with Leibniz's definition of infinite and infinitely small quantities, infinite quantities and theory of quantified indivisibles in comparison with Galileo's concept of indivisibles. Leibniz developed 'method of indivisible' in order to introduce the integrability of continuous functions. also we deals with this demonstration, with Leibniz's rules of arithmetic of infinitely small and infinite quantities.

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Cantor의 무한관

  • 박창균
    • Journal for History of Mathematics
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    • v.10 no.1
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    • pp.33-38
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    • 1997
  • 본고는 수학적으로 취급된 Cantor의 무한을 소개하기보다는 그가 가졌던 무한에 대한 태도는 매우 종교적이었고 철학적으로는 실재론적인 입장에 있다는 것을 보이려고 한다. 이를 위해 먼저 Cantor의 초한수론과 무한의 역사를 약술하고 그의 무한관이 기독교 신앙과 중세 철학에 근거해 있음을 제시한다. 또한 Cantor의 초한수론은 당시의 세계관과 시대정신에 도전하고 있음을 밝히려 한다.

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A Qualitative Case Study about Mathematics Pre-Service Teachers' Ways of Dealing with Math and Linguistic Expressions on Infinity (중등 수학 예비교사의 수학을 다루는 방식과 무한에 관한 언어적 표현 양상에 대한 질적 사례 연구)

  • Jun, Youngcook;Shin, Hyangkeun
    • School Mathematics
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    • v.15 no.3
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    • pp.633-650
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    • 2013
  • The aim of this paper is to explore and understand, using in-depth interviews, the participant's interests and discourse analytic expressions in studying the notion of infinity and limit. In addition we tried to understand how the participant's ways of dealing with math and thinking patterns on the polygons whose boundary is infinite but area is finite as they brought up such examples. Further follow-up questions are posed on the infinite sum of a smallest number close to 0 and the sum of infinite sets of different smallest numbers close to 0. Larger aspects of two pre-service teachers' subjective thinking patterns and colloquial discourses were sketched by contrasting the three posed tasks. Cross case discussions are provided with several suggestions for the future research directions.

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Mathematical Infinite Concepts in Arts (미술에 표현된 수학의 무한사상)

  • Kye, Young-Hee
    • Journal for History of Mathematics
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    • v.22 no.2
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    • pp.53-68
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    • 2009
  • From ancient Greek times, the infinite concepts had debated, and then they had been influenced by Hebrew's tradition Kabbalab. Next, those infinite thoughts had been developed by Roman Catholic theologists in the medieval ages. After Renaissance movement, the mathematical infinite thoughts had been described by the vanishing point in Renaissance paintings. In the end of 1800s, the infinite thoughts had been concreted by Cantor such as Set Theory. At that time, the set theoretical trend had been appeared by pointillism of Seurat and Signac. After 20 century, mathematician $M\ddot{o}bius$ invented <$M\ddot{o}bius$ band> which dimension was more 3-dimensional space. While mathematicians were pursuing about infinite dimensional space, artists invented new paradigm, surrealism. That was not real world's images. So, it is called by surrealism. In contemporary arts, a lot of artists has made their works by mathematical material such as Mo?bius band, non-Euclidean space, hypercube, and so on.

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A study on understanding of infinite series (무한급수의 이해에 대한 연구)

  • Oh, Hye-Young
    • Communications of Mathematical Education
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    • v.34 no.3
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    • pp.355-372
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    • 2020
  • The concept of infinite series is an important subject of major mathematics curriculum in college. For several centuries it has provided learners not only counter-intuitive obstacles but also central role of analysis study. As the understanding in concept on infinite series became foundation of development of calculus in history of mathematics, it is essential to present students to study higher mathematics. Most students having concept of infinite sum have no difficulty in mathematical contents such as convergence test of infinite series. But they have difficulty in organizing concept of infinite series of partial sum. Thus, in this study we try to analyze construct the concept of infinite series in terms of APOS theory and genetic decomposition. By checking to construct concept of infinite series, we try to get an useful educational implication on teaching of infinite series.

무한개념의 이해와 반성적 추상

  • Jeon, Myeong-Nam
    • Communications of Mathematical Education
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    • v.13 no.2
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    • pp.655-691
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    • 2002
  • 16개의 무한개념 문제를 가지고 47명의 대학생에게 개별 검사하여 무한개념의 이해 과정을 설명하고자 시도했다. 전문가-초심자의 조망에서 미시발생적 방법을 사용하여 2명의 사례를 비교 ${\cdot}$ 분석하였다. Cifarelli(1988)'의 반성적 추상과 Robert(1982)와 Sierpinska(1985)의 무한개념의 3단계를 설명의 틀로 사용하였다. 실무한 개념 수준으로 이행한 사례 P는 그렇게 하지 못한 L보다 높은 수준의 반성적 추상을 보여 주었다. 따라서 반성적 추상은 무한개념의 이해에 결정적인 사고의 메카니즘으로 볼 수 있다.

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배중률에 관한 소고

  • 김성수
    • Journal for History of Mathematics
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    • v.9 no.2
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    • pp.10-14
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    • 1996
  • 논리법칙은 유한집합에서 성립하는 수학의 정리들을 최대한 일반화시킨 것에 불과하다. 따라서 우리는 이들 논리법칙들이 아무런 고려없이 무한집합의 수학에서도 성립할 것으로 단정해서는 안된다. 집합론에서 역리가 발생하는 것은 논리학의 한 원리인 배중률이 무한집합의 수학에서는 성립하지 않음을 보여주는 것이다.

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The Infinite Decimal Representation: Its Opaqueness and Transparency (무한소수 기호: 불투명성과 투명성)

  • Lee, Jihyun
    • Journal of Educational Research in Mathematics
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    • v.24 no.4
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    • pp.595-605
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    • 2014
  • Infinite decimals have an infinite number of digits, chosen arbitrary and independently, to the right side of the decimal point. Since infinite decimals are ambiguous numbers impossible to write them down completely, the infinite decimal representation accompanies unavoidable opaqueness. This article focused the transparent aspect of infinite decimal representation with respect to the completeness axiom of real numbers. Long before the formalization of real number concept in $19^{th}$ century, many mathematicians were able to deal with real numbers relying on this transparency of infinite decimal representations. This analysis will contribute to overcome the double discontinuity caused by the different conceptualizations of real numbers in school and academic mathematics.

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