• Journal of Educational Research in Mathematics
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• v.12 no.4
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• pp.557-579
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• 2002

The purpose of this study is to find out the problems which are caused when the limit concept of sequences is learned through an intuitive definition and to suggest a way of solving those problems. Students in Korea study the limit concept of sequences through an intuitive definition. They fail to apply the intuitive definition properly to the problems and they are apt to have misconception even though the Intuitive definition is applied properly. To solve these problems, this study examined the develop- mental process of the limit concept of sequences from the Intuitive definition to the formal definition, and looked into the way of students' internalization of the process through a field study. In this study, the levels of the limit concept of sequences possessed by the students at ZPD are as follows; level 0 : Students understand the limit concept of sequences through the intuitive definition. level 1 : Students understand the limit concept of sequences as 'The difference between $\alpha$$_{n}$ and $\alpha$ approaches 0' rather than 'The sequence approaches $\alpha$ infinitely.' level 2 : Students understand the limit concept of sequences through the formal definition. The levels of students' limit concept development were analysed by those criteria. Almost of the students who studied the limit concept of sequences through the intuitive defition stayed at level 0, whereas almost of the students who studied through the formal definition stayed at level 1. Through the study, I found that it was difficult for the students to develop the higher level of understanding for themselves but the teachers and peers could help the students to progress to the higher level. Students' learning ability was one of major factors that make the students progress to the higher level of understanding as the concept was developed hierarchically from Level 0 to Level 2. If you want to see your students get to the higher level of understanding in the limit concept, you need to facilitate them to fully develop understanding in lower levels through enough experiences so that they can be promoted to the highest level.

• Korean Journal of Mathematics
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• v.22 no.1
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• pp.169-180
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• 2014

In this study, we consider the informal and formal definition of limit on the basis of middle and high school curriculum, and then analyze the reason of difficulties experienced when sophomores learn the formal definition(${\epsilon}-{\delta}$ procedure) of limit. We conducted teaching of the formal definition of limit with sophomores and analyzed their errors which were appeared when they applied to limits problems. In addition, we try to improve the understanding of ${\epsilon}-{\delta}$ procedure of the limit taught in analysis.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.675-686
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• 2011

The aim of this paper is two fold: One of them is to introduce a formal definition of ordinals which is equivalent to Neumann's definition without assuming the axiom of regularity. The other is to introduce the weak transfinite set and show that the weak transfinite set is a transfinite limit ordinal.

• East Asian mathematical journal
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• v.35 no.2
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• pp.239-257
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• 2019

The purpose of this study is to show that the topology is closely related to some subjects learned in school mathematics and then to give motivations for learning of the topology. To do this, it is showed that the topology is an abstracted device that deal with structure of limit and continuity introduced in school mathematics. This study took a literature study. The results of this study are as follows. First, the formal definition of general topology to structure open sets was examined. The nearness relation together with the closure operation was introduced and used to characterize for construction of general topology. Second, as definitions for continuity of function, we considered the intuitive definition, definition, structured definitions using open intervals and definition using open sets and then we investigated their roles. We also examined equivalent definition using the nearness relation which is helpful to understand continuity of function. Third, the sequence and its limit are treated in terms of continuous functions having the set of natural numbers and its extended set as domains. From these, it can be concluded that the convergence of sequence and the continuity of function are identified as functions that preserve the nearness relation and that the topology is a specialized tool for dealing with convergence and continuity.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.11
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• pp.1777-1784
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• 2001

This paper provides d simplified engineering J estimation method fur semi-e1liptical surface cracked plates in tension, based on the reference stress approach. Note that the essential element of the reference stress approach is the plastic limit lead in the definition of the reference stress. However, for surface cracks, the definition of the limit load is ambiguous ("local" or "global"limit lead), and thus the most relevant limit load (and thus reference stress) for the J estimation should be determined. In the present work, such limit load solution is found by comparing reference stress bated J results with those from extensive 3-D finite element analyses. Validation of the proposed equation against FF J results based on tactual experimental tensile data of a 304 stainless steel shows excellent agreements not only far the J values at the deepest point but also for those at an arbitrary paint along the crack front, including at the surface point. Thus the present results provide a good engineering tool for elastic-plastic fracture analyses of surface cracked plates in tension.

• Korean Chemical Engineering Research
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• v.43 no.6
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• pp.696-703
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• 2005

The definition of cake is not established for cake filtration, and especially the definition was impossible for the filtration of the floc already sedimented. The definition is proposed with the experimental method named 'filtration-permeation'. The limit of water content which can be achieved with cake filtration of floc was established with the definition of cake. The expression operation of which the purpose is to reduce the water content of pre-formed filter cake is calculated with our 'unified theory on solid-liquid separation' and compared with the experimental results. The importance of expression is analyzed by the calculated whole procedure of cake filtration and expression. The method determining the most effective operational conditions of filter press including the cake discharge and washing time is proposed.

• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.301-314
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• 1992

In this paper, motivated by [1] and [7] we give a sequential definition of conditional Wiener integral and then use this definition to evaluate conditional Wiener integral of several functions on C [0, T]. The sequential definition is defined as the limit of a sequence of finite dimensional Lebesgue integrals. Thus the evaluation of conditional Wiener integrals involves no integrals in function space [cf, 5].

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.383-399
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• 2020

Following Matsumoto's definition of continuous orbit equivalence for one-sided subshifts of finite type, we introduce the notion of orbit equivalence to canonically associated dynamical systems, called the limit dynamical systems, of self-similar groups. We show that the limit dynamical systems of two self-similar groups are orbit equivalent if and only if their associated Deaconu groupoids are isomorphic as topological groupoids. We also show that the equivalence class of Cuntz-Pimsner groupoids and the stably isomorphism class of Cuntz-Pimsner algebras of self-similar groups are invariants for orbit equivalence of limit dynamical systems.

• The Mathematical Education
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• v.57 no.2
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• pp.157-177
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• 2018

The students in secondary schools have been taught calculus as an important subject in mathematics. The order of chapters-the limit of a sequence followed by limit of a function, and differentiation and integration- is because the limit of a function and the limit of a sequence are required as prerequisites of differentiation and integration. Specifically, the limit of a sequence is used to define definite integral as the limit of the Riemann Sum. However, many researchers identified that students had difficulty in understanding the concept of definite integral defined as the limit of the Riemann Sum. Consequently, they suggested alternative ways to introduce definite integral. Based on these researches, the definition of definite integral in the 2015-Revised Curriculum is not a concept of the limit of the Riemann Sum, which was the definition of definite integral in the previous curriculum, but "F(b)-F(a)" for an indefinite integral F(x) of a function f(x) and real numbers a and b. This change gives rise to differences among ways of introducing definite integral and explaining the relationship between definite integral and area in each textbook. As a result of this study, we have identified that there are a variety of ways of introducing definite integral in each textbook and that ways of explaining the relationship between definite integral and area are affected by ways of introducing definite integral. We expect that this change can reduce the difficulties students face when learning the concept of definite integral.

• Structural Engineering and Mechanics
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• v.26 no.1
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• pp.15-30
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• 2007

In the paper, one focuses on the problem of duality in non-linear programming, applied to the solution of no-tension problems by means of Limit Analysis (LA) theorems for Not Resisting Tension (NRT) models. In details, one demonstrates that, starting from the application of the duality theory to the non-linear program defined by the static theorem approach for a discrete NRT model, this procedure results in the definition of a dual problem that has a significant physical meaning: the formulation of the kinematic theorem.