• 제목/요약/키워드: infinite set

검색결과 169건 처리시간 0.019초

극한과 무한집합의 상호작용과 그 교육적 시사점에 대한 역사적 연구 (A Historical Study on the Interaction of the Limit-the Infinite Set and Its Educational Implications)

  • 박선용
    • 한국수학사학회지
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    • 제31권2호
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    • pp.73-91
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    • 2018
  • This study begins with the awareness of problem that the education of mathematics teachers has failed to link the limit and the infinite set conceptually. Thus, this study analyzes the historical and reciprocal development of the limit and the infinite set, and discusses how to improve the education of these concepts and their relation based on the outcome of this analysis. The results of the study confirm that the infinite set is the historical tool of linking the limit and the real numbers. Also, the result shows that the premise of 'the component of the straight line is a point.' had the fundamental role in the construction of the real numbers as an arithmetical continuum and that the moral certainty of this premise would be obtained through a thought experiment using an infinite set. Based on these findings, several proposals have been made regarding the teacher education of awakening someone to the fact that 'the theoretical foundation of the limit is the real numbers, and it is required to introduce an infinite set for dealing with the real numbers.' in this study. In particular, by presenting one method of constructing the real numbers as an arithmetical continuum based on a thought experiment about the component of the straight line, this study opens up the possibility of an education that could get the limit values psychologically connected to the infinite set in overcoming the epistemological obstacle related to the continuum concept.

미술에 표현된 수학의 무한사상 (Mathematical Infinite Concepts in Arts)

  • 계영희
    • 한국수학사학회지
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    • 제22권2호
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    • pp.53-68
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    • 2009
  • 고대 그리스에서 발현된 수학의 무한 개념은 헤브라이인의 유대교 전통인 카발라의 영향을 받아 중세 기독교 교부 철학자들에 의해 보다 성숙되어져 갔으며, 그 후 기독교의 무한사상이 르네상스 시대에는 화가들에 의해 원근법으로 구체화되었다. 본 논문에서는 그리스 시대부터 발전된 무한 개념의 경로를 살펴보고, 근대와 19세기 이후 무한수학이 발달될 때 당시 미술에서는 무한 개념이 어떻게 표현되었는지 그 시대정신을 고찰한다.

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BOUNDEDNESS AND CONTINUITY OF SOLUTIONS FOR STOCHASTIC DIFFERENTIAL INCLUSIONS ON INFINITE DIMENSIONAL SPACE

  • Yun, Yong-Sik;Ryu, Sang-Uk
    • 대한수학회보
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    • 제44권4호
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    • pp.807-816
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    • 2007
  • For the stochastic differential inclusion on infinite dimensional space of the form $dX_t{\in}\sigma(X_t)dW_t+b(X_t)dt$, where ${\sigma}$, b are set-valued maps, W is an infinite dimensional Hilbert space valued Q-Wiener process, we prove the boundedness and continuity of solutions under the assumption that ${\sigma}$ and b are closed convex set-valued satisfying the Lipschitz property using approximation.

SUFFICIENT CONDITION FOR THE DIFFERENTIABILITY OF THE RIESZ-NÁGY-TAKÁCS SINGULAR FUNCTION

  • Baek, In-Soo
    • 대한수학회보
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    • 제54권4호
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    • pp.1173-1183
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    • 2017
  • We give some sufficient conditions for the null and infinite derivatives of the $Riesz-N{\acute{a}}gy-Tak{\acute{a}}cs$ (RNT) singular function. Using these conditions, we show that the Hausdorff dimension of the set of the infinite derivative points of the RNT singular function coincides with its packing dimension which is positive and less than 1 while the Hausdorff dimension of the non-differentiability set of the RNT singular function does not coincide with its packing dimension 1.

SOLVING A CLASS OF GENERALIZED SEMI-INFINITE PROGRAMMING VIA AUGMENTED LAGRANGIANS

  • Zhang, Haiyan;Liu, Fang;Wang, Changyu
    • Journal of applied mathematics & informatics
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    • 제27권1_2호
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    • pp.365-374
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    • 2009
  • Under certain conditions, we use augmented Lagrangians to transform a class of generalized semi-infinite min-max problems into common semi-infinite min-max problems, with the same set of local and global solutions. We give two conditions for the transformation. One is a necessary and sufficient condition, the other is a sufficient condition which can be verified easily in practice. From the transformation, we obtain a new first-order optimality condition for this class of generalized semi-infinite min-max problems.

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On Generalized Absolute Riesz Summability Factor of Infinite Series

  • Sonker, Smita;Munjal, Alka
    • Kyungpook Mathematical Journal
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    • 제58권1호
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    • pp.37-46
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    • 2018
  • The objective of the present manuscript is to obtain a moderated theorem proceeding with absolute Riesz summability ${\mid}{\bar{N}},p_n,{\gamma};{\delta}{\mid}_k$ by applying almost increasing sequence for infinite series. Also, a set of reduced and well-known factor theorems have been obtained under suitable conditions.

SLOW VISCOUS FLOW PAST A CAVITY WITH INFINITE DEPTH

  • Kim, D.W;Kim, S.B;Chu, J.H
    • Journal of applied mathematics & informatics
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    • 제7권3호
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    • pp.801-812
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    • 2000
  • Two-dimensional slow viscous flow on infinite half-plane past a perpendicular infinite cavity is considered on the basis of the Stokes approximation. Using complex representation of the two-dimensional Stokes flow, the problem is reduced to solving a set of Fredholm integral equations of the second kind. The streamlines and the pressure and vorticity distribution on the wall are numerically determined.

DERIVATIONS OF MV-ALGEBRAS FROM HYPER MV-ALGEBRAS

  • Hamidi, M.;Borzooei, R.A.
    • 호남수학학술지
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    • 제38권3호
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    • pp.643-659
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    • 2016
  • In this paper, we investigate some new results in MV-algebras and (strong) hyper MV-algebras. We show that for any infinite countable set M, we can construct an MV-algebra and a strong hyper MV-algebra on M. Specially, for any infinite totally bounded set, we can construct a strong hyper MV-algebra on it. Then by considering the concept of fundamental relation on hyper MV-algebras, we define the notion of fundamental MV-algebra and prove that any MV-algebra is a fundamental MV-algebra. In practical, we show that any infinite countable MV-algebra is a fundamental MV-algebra of itself, but it is not correct for finite MV-algebras.

ON CANTOR SETS AND PACKING MEASURES

  • WEI, CHUN;WEN, SHENG-YOU
    • 대한수학회보
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    • 제52권5호
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    • pp.1737-1751
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    • 2015
  • For every doubling gauge g, we prove that there is a Cantor set of positive finite $H^g$-measure, $P^g$-measure, and $P^g_0$-premeasure. Also, we show that every compact metric space of infinite $P^g_0$-premeasure has a compact countable subset of infinite $P^g_0$-premeasure. In addition, we obtain a class of uniform Cantor sets and prove that, for every set E in this class, there exists a countable set F, with $\bar{F}=E{\cup}F$, and a doubling gauge g such that $E{\cup}F$ has different positive finite $P^g$-measure and $P^g_0$-premeasure.

SOFT SOMEWHERE DENSE SETS ON SOFT TOPOLOGICAL SPACES

  • Al-shami, Tareq M.
    • 대한수학회논문집
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    • 제33권4호
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    • pp.1341-1356
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    • 2018
  • The author devotes this paper to defining a new class of generalized soft open sets, namely soft somewhere dense sets and to investigating its main features. With the help of examples, we illustrate the relationships between soft somewhere dense sets and some celebrated generalizations of soft open sets, and point out that the soft somewhere dense subsets of a soft hyperconnected space coincide with the non-null soft ${\beta}$-open sets. Also, we give an equivalent condition for the soft csdense sets and verify that every soft set is soft somewhere dense or soft cs-dense. We show that a collection of all soft somewhere dense subsets of a strongly soft hyperconnected space forms a soft filter on the universe set, and this collection with a non-null soft set form a soft topology on the universe set as well. Moreover, we derive some important results such as the property of being a soft somewhere dense set is a soft topological property and the finite product of soft somewhere dense sets is soft somewhere dense. In the end, we point out that the number of soft somewhere dense subsets of infinite soft topological space is infinite, and we present some results which associate soft somewhere dense sets with some soft topological concepts such as soft compact spaces and soft subspaces.