• The Mathematical Education
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• v.49 no.4
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• pp.437-462
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• 2010

The purpose of this research is to analyze the textbook contents about the natural number concepts in the Korean National Elementary Mathematics Curriculum. Understanding a concept of natural number is crucial in school mathematics curriculum planning, since elementary students start their basic learning with natural number system. The concepts of natural number have various meaning from the perspectives of pedagogical research, and the philosophy of mathematics. The natural number concepts in the elementary math curriculum consist of four aspects; counting numbers, cardinal numbers, ordinal numbers, and measuring numbers. Two research questions are addressed; (1) How are the natural number concepts focusing on counting, cardinal, ordinal, measuring numbers are covered in the national math curriculum? ; (2) What suggestions can be made to enhance the teaching and learning about the natural number concepts? Findings reveal that (1) the national mathematics curriculum properly reflects four aspects of natural number concepts, as the curriculum covers 50% of the cardinal number system; (2) In the aspect of the counting number, we hope to add the meaning about 'one, two, three, ......, and so on' in the Korean Mathematics curriculum. In the ordinal number, we want to be rich the related meaning in a set. Further suggestions are made for future research to include them ensuing number in the curriculum.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.403-409
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• 1999

In this paper we introduce the notions of expansive homeomorphism and its properties, and study the relation between countable compacta and ordinal numbers. Our results extend and improve those of T.Kimura and others.

• Journal of the Korean Mathematical Society
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• v.59 no.1
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• pp.105-127
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• 2022

It is known that the maximal invariant set of a continuous iterative dynamical system in a compact Hausdorff space is equal to the intersection of its forward image sets, which we will call the first minimal image set. In this article, we investigate the corresponding relation for a class of discontinuous self maps that are on the verge of continuity, or topologically almost continuous endomorphisms. We prove that the iterative dynamics of a topologically almost continuous endomorphisms yields a chain of minimal image sets that attains a unique transfinite length, which we call the maximal invariance order, as it stabilizes itself at the maximal invariant set. We prove the converse, too. Given ordinal number ξ, there exists a topologically almost continuous endomorphism f on a compact Hausdorff space X with the maximal invariance order ξ. We also discuss some further results regarding the maximal invariance order as more layers of topological restrictions are added.

• School Mathematics
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• v.15 no.1
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• pp.137-158
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• 2013

In this paper we compared waldorf education with korean public education in the area of teaching the numbers form 0 to 10. We took several characters of both. The korean education style has the characters like separation of 0~9 and 10, teaching of the meaning of ordinal numbers and cardinal numbers, use of storytelling. The waldorf education style has the characters like teaching of the qualitive meaning of numbers, use of storytelling, meeting numners in rhythm, teaching from whole to part.

• Communications for Statistical Applications and Methods
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• v.15 no.4
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• pp.517-530
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• 2008

In this paper we introduce a time series model using the triangle fuzzy numbers in order to construct a statistical relation for the data which is a sequence of observations which are ordered in time. To estimate the proposed fuzzy model we split of a universal set includes all observation into closed intervals and determine a number and length of the closed interval by the frequency of events belong to the interval. Also we forecast the data by using a difference between observations when the fuzzified numbers equal at successive times. To investigate the efficiency of the proposed model we compare the ordinal and the fuzzy time series model using examples.

• Journal for History of Mathematics
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• v.12 no.1
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• pp.32-44
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• 1999

This paper is a sequel to [8]. Development of modern logic was initiated by Boole and Morgan. Boolean logic is one of their completed works. Cantor created the set theory along with cardinal and ordinal numbers. His theory on infinite sets brought about a remarkable development on modern mathematical theory, but generated many paradoxes (e.g. Russell Paradox) that in turn motivated mathematicians to solve them. Further, mathematicians attempted to construct sound foundations for Mathematics. As a result three important schools of thought were formed in relation to fundamentals of mathematics for the resolution of paradoxes of set theory, namely logicism developed by Russell and Whitehead, intuitionism lead by Brouwer and formalism contended by Hilbert and Bernays. In this paper, we examine the logic for intuitionism which is originated by Brouwer in 1908 and study Heyting algebra.

• Journal of the Korean Society for Library and Information Science
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• v.23
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• pp.33-62
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• 1992

The purpose of this is to evaluate the contents through the anal us is of the merits and demerits, and its special quality of the Cutter-Sanborn Three-figure Author Table. table. The abstract of this study is as follows : With the results of the analysis of Cutter-Sanborn's Tabls, several advent-age were found in the area of enumerative-ordinal numbering system, mixed notation, and information retrieval. A defect is that each corporate author and serials and reference book's titles are difficult to be numbered, and there is serious diviation in percentages of the numbers assigned to each letter because each letter apportion rate was applied without any criteria. Such phenomenon decrease the effectiveness as author notation in several letters. The separation of headings are seriously unbalanced because the separation of heading is not consistent with actual publishing trends. This phenomenon made difficult individualization of materials in several letters.

• Journal of Korean Academy of Nursing
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• v.52 no.2
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• pp.144-156
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• 2022

Purpose: This study aimed to investigate the influence of social capital on the depression of older adults living in rural areas. Methods: Data sets were obtained from the 2019 Korea Community Health Survey. The participants were 39,390 older adults over 65 years old living in rural areas. Indicators of social capital included trust, reciprocity, network, and social participation. Depression-the dependent variable-was measured using the Patient Health Questionnaire-9 (PHQ-9). Hierarchical ordinal logistic regression was conducted to identify factors associated with depression after adjusting the data numbers to 102,601 by applying the Synthetic Minority Oversampling Technique (SMOTE). Results: The independent variables-indicators of social capital-exhibited significant association with the depression of older adults. The odds ratios of depression were higher in groups without social capital variables. Conclusion: To reduce depression, we recommend increasing social capital. Factors identified in this study need to be considered in older adult depression intervention programs and policies.