• Communications of Mathematical Education
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• v.19 no.1 s.21
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• pp.45-55
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• 2005

대학수학 1학년 과정(미분적분학)에서 정리, 정의 등 개념의 이해를 도와주기 위해 학생들이 갖는 어려움을 그들이 자주 겪는 실수를 통해 찾아내어 분석하고 올바른 이해의 길로 안내한다. 실수를 탓하기보다 학생의 편에 서서 이해하고 도움을 주도록 한다. 흔히 부딪칠 수 있는 예제 문제를 풀어보게 하고 공통으로 저지르는 실수를 제시하여 개념의 이해나 문제풀이를 바르게 하도록 이끌어 준다.

• Journal for History of Mathematics
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• v.18 no.3
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• pp.55-66
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• 2005

In our school mathmatics, the irrational numbers and the real numbers are defined and instructed on the basis of decimal fractions. In relation to this fact, we identified the essences of the real number and the irrational number defined by the decimal fractions through the historical analysis. It is revealed that the formation of real numbers means the numerical measurements of all magnitudes and the formation of irrational numbers means the numerical measurements of incommensurable magnitudes. Finally, we suggest instructional plan for the meaninful understanding of the real number concept.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1996.10a
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• pp.115-118
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• 1996

연관규칙(Association Rule)은 데이터 베이스에 존재하는 속성들 사이의 관계를 기술하는 것으로, 간단하면서도 사용자에게 많은 정보를 줄 수 있다. 그러나, 지금까지는 이진 데이터베이스에 존재하는 연관규칙의 발견에 대해서 주로 연구되어 왔으며, 실수값 속성을 갖는 데이터에 관한 연구는 미비하였다. 본 논문에서는 퍼지집합을 이용하여 실수값 사이에 존재하는 연관규칙을 기술하고, 그것을 찾아내는 방법을 제시한다. 제시하는 방법은 사용자에 의해서 정의된 언어항을 이용하여, 실수값 속성을 가진 데이터를 이진 데이터로 재구성한다. 그리고 재구성된 이진 데이터에 기존의 연관규칙 발견 방법을 이용하여 연관규칙을 찾아내고, 찾아진 연관규칙을 정의된 언어항을 이용하여 다시 기술한다.

• Journal of Educational Research in Mathematics
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• v.26 no.2
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• pp.159-172
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• 2016

This study examines the approach of introduction of the real numbers through the infinite decimal, which is suggested by Lee Ji-Hyun(2014; 2015) in the aspect of the overcoming the double discontinuity, and analyses Li(2011), which is the mathematical background of the foregoing Lee's. Also, this study compares these construction methods given by Lee and Li with the traditional method using the nested intervals. As a result of analysis, this study shows that Lee Ji-Hyun(2014; 2015) and Li(2011) face the risk of the circulation logic in making the infinite decimal corresponding each point on the geometrical line, and need the steps not using the 'limit to a real number' in order to compensate the mathematical and educational defect. Accordingly, this study raises the opinion that the traditional method of defining the infinite decimal as a sequence by using the geometrical nested intervals axiom would be a appropriate supplementation.

• Korean Journal of Logic
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• v.14 no.3
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• pp.137-176
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• 2011

Bob Hale recently proposed a theory of real numbers based on abstraction principles. In his theory, real numbers are regarded as ratios of quantities and the criteria of identities of ratios of quantities are given by an Eudoxan ratio principle. The reason why Hale defines real numbers as ratios of quantities is that he wants to satisfy Frege's requirement that arithmetical concepts should be defined to be adequate for their universal applicability. In this paper I show why Hale's explanation of applications of real numbers fails to satisfy Frege's requirement, and I propose an alternative explanation. At first I show that there are some gaps between his explanation of the concept of quantity and his stipulation of domains of quantities, and that those gaps give rise to some difficulties in his explanation of applications of real numbers. Secondly I introduce a new ratio principle which can be applied to any kinds of quantities, and I argue that it allows us an adequate explanation of the reason why real numbers as ratios of quantities can be universally applicable. Finally I enquire into some procedures of the measurement of quantities, and I propose some principles which we should presuppose in order to successfully apply real numbers to the measurement of quantities.

• Korean Journal of Logic
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• v.10 no.2
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• pp.47-107
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• 2007

나는 이 글에서 프레게 제한에 대한 라이트의 해석이 옳지 않다는 것을 보인다. 우선 나는 그가 산수 개념의 적용에 대한 반성을 통해 그 개념에 대한 선천적 지식을 얻을 수 있다고 여긴 사례를 검토한다. 이 검토를 기초로 나는 산수 개념의 적용을 지배하는 원리가 있고, 프레게 제한은 바로 그런 원리가 성립하도록 해당 개념을 정의하라는 요구임을 보인다. 둘째로 나는 라이트의 해석은 수학의 적용에 대한 아주 좁은 견해에 의존한다는 것을 보인다. 나는 산수의 적용에 대한 프레게의 견해를 살펴본 후에 실수가 적용될 수 있는 양을 산수량, 순수 공간량 및 물리량 세 부류로 나눈다. 나는 실수 적용 원리는 순수 공간량만 아니라 물리량에 대해서도 성립한다는 것을 보인다. 이에 근거해서 나는 실수 이론을 확립하는 데에도 여전히 프레게 제한은 유효하다고 결론짓는다.

• School Mathematics
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• v.17 no.2
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• pp.309-329
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• 2015

This study is to provide didactical implications for teaching and learning of radian through a analysis of investigation result about pre-service teachers' understanding of radian. The results of this study are as follows. First, pre-service teachers understood the radian as ${\frac{180^{\circ}}{\pi}}$, rather than as the definition. Secondly, the definition style of radian affected the problem solving strategy for the measurement of the angle. Thirdly, pre-service teachers had insufficient content knowledge about properties of measurement as a pure number of radian. Lastly, They failed to describe the usefulness of circular measure. We suggested the definition of radian in textbooks should be changed from ${\frac{180^{\circ}}{\pi}}$ to mathematical definition of radian. And the general angle should be stated as the reason why the domain of trigonometric function is real numbers.

• Journal of the Korea Computer Graphics Society
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• v.16 no.4
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• pp.17-23
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• 2010

Effective visualizing is an important issue when one processing real number domain volume data such as distance fields, or volume texture. In this paper, we introduce a framework for inspecting, magnifying, cross-section viewing of real number domain volume data from an implementation of a simple interface. The interface can be freely implemented from any kind of existing algorithm, so that we can easily view the result and evaluate the algorithm.

• Journal for History of Mathematics
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• v.22 no.3
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• pp.131-152
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• 2009

The Eudoxean theory of Proportion is correlated with 'Dedekind cut' with which Dedekind defined the real number system in modern usage. Dedekind established a firm foundation for the real number system by retracing some of Eudoxus' steps of over two thousand years earlier. Thus it should be quite worthy that we separate Greek inheritance from the definition of Dedekind, However, there is a fundamental difference between Eudoxean theory of proportion and Dedekind cut. Basically, it seems impossible for Greeks to distinguish between the distinction between number and magnitude. In this paper, we will consider how the Eudoxean theory of proportion was related to Dedekind cut introduced to prove the Dedekind's real number completion and how it influenced Dedekind cut by looking at the relation between Eudoxos's explication of the notion of ratio and Dedekind's well-known construction of the real numbers.

• Journal of the Korean School Mathematics Society
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• v.20 no.4
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• pp.495-519
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• 2017

The purpose of this study is to analyze the concept of the real number e and to investigate the understanding of pre-service teachers about the real number e. 28 pre-service teachers were asked to take a test based on the various ideas of the real number e and 8 pre-service teachers were interviewed. The results of this study are as follows. First, a large number of pre-service teachers couldn't recognize relation between the formal definition and the representations of the real number e. Secondly, pre-service teachers judged appropriately for the irrationality and the construction impossibility of the real number e, but they couldn't provide reasonable evidence. Lastly, pre-service teachers understood the continuous compounding context and exponential function context of the real number e, but they had a difficulty in understanding the geometric context and natural logarithm context of the real number e.