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http://dx.doi.org/10.7468/jksmee.2021.35.4.413

The Empty Set as a Mathematical Object  

Ryou, Miyeong (Banpo high school)
Choi, Younggi (Department of Mathematics Education, Seoul National University)
Publication Information
Communications of Mathematical Education / v.35, no.4, 2021 , pp. 413-423 More about this Journal
Abstract
This study investigated the empty set which is one of the mathematical objects. We inquired some misconceptions about empty set and the background of imposing empty set. Also we studied historical background of the introduction of empty set and the axiomatic system of Set theory. We investigated the nature of mathematical object through studying empty set, pure conceptual entity. In this study we study about the existence of empty set by investigating Alian Badiou's ontology known as based on the axiomatic set theory. we attempted to explain the relation between simultaneous equations and sets. Thus we pondered the meaning of the existence of empty set. Finally we commented about the thoughts of sets from a different standpoint and presented the meaning of axiomatic and philosophical aspect of mathematics.
Keywords
empty set; existence; Badiou;
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  • Reference
1 Devlin, K. (2012). The joy of sets: fundamentals of contemporary set theory. Springer Science & Business Media.
2 Chang, T. S. (2017b). Zero, one, many - Alain Badiou's conception of multiple, Korean Journal of Philosophy. 131, 151-170.   DOI
3 Kim, W. K. et al. (2018). (High school) Mathematics. Seoul: Visang.
4 Seo, B. (2017). The Analytical study of the historical process of mathematics curriculum in Korea. BD18070008. Korea foundation for the advancement of science & creativity.
5 Go, S. E. et al. (2018). (High school) Mathematics. Seoul: Sinsago.
6 Kwon, O. N. et al. (2018). (High school) Mathematics. Seoul: Kyohaksa.
7 Lew, H. C. et al. (2018). (High school) Mathematics. Seoul: Chunjae.
8 Park, K. S. et al. (2018a). (Middle school) Mathematics 1. Seoul: Dong-a.
9 Park, S. (2006) Invitation to the world of mathematics. Seoul: SNUPress.
10 Seo, Y. S. (2011). Etre, verite et sujet dans la philosophie d'Alain Badiou: autour de L'etre et l'evenement, Sogang Journal of Philosophy, 27, 79-115.   DOI
11 Ryou, M., & Choi, Y. (2015). The diorism in proposition I-22 of 「Euclid Elements」 and the existence of mathematical objects, Journal of Educational Research in Mathematics, 25(3), 367-379.
12 Lee, K., Park, K. & Yim, J.(2002). A Critical review on the concept of set as a school mathematics topic. Journal of Educational Research in Mathematics, 12(1), 125-143.
13 Lee, J. W. (1998). Historical background and development of geometry. Seoul: Kyungmoonsa.
14 Badiou, Alain. (1988). L'etre et l'evenement. Paris: Seuil, 조형준 역(2013), 존재와 사건 : 사랑과 예술과 과학과 정치 속에서, 서울 : 새물결.
15 Im, J. D. (1992). The basis of set theory. Seoul:
16 Hong, K. S. (2006). Letre comme multiple pur et la verite comme un. Korean Society for Social Philosophy, (12), 241-262.
17 Hong, S. et al. (2018). (High school) Mathematics. Seoul: Jihaksa.
18 Eves, H. (1994). 수학의 위대한 순간들. (허민, 오혜영 역), 서울: 경문사. (영어 원작은 1980년 출판).
19 Lin, Y., & Lin, S. (1974). Set Theory - An intuitive approach. Boston : Houbhton Mifflin Company.
20 Fischbein, & Baltsan (1998). The mathematical concept of set and the collection model, Educational Studies in Mathematics, 37(1), 1-22.   DOI
21 Pinter, C. (1986). Set theory. (Addison - Wesley series in mathematics). 서울: 연합출판.
22 Tiles, M. (2004). The philosophy of set theory: an historical introduction to Cantor's paradise. Courier Corporation.
23 Wegner, S. A. (2014). A Workshop for High School Students on Naive Set Theory. European Journal of Science and Mathematics Education, 2(4), 193-201.   DOI
24 Zazkis, R., & Gunn, C. (1997). Sets, subsets, and the empty set: students' constructions and mathematical conventions. Journal of Computers in Mathematics and Science Teaching, 16, 133-169.
25 Nam, K. H. (2013). Platon. Seoul: Acanet.
26 Paek, D. H., & Yi, J. (2011). Symbol statements in middle school mathematics textbooks : how to read and understand them? Journal of Educational Research in Mathematics, 21(2), 165-180.
27 Chang, T. S. (2017a). Deleuze and Badiou's Concept of Multiplicity : From the Dispute of the Two Philosophers, Journal of The Society of philosophical studies. 117, 169-189.   DOI
28 Hwang, S. et al. (2018). (High school) Mathematics. Seoul: Mirae N.
29 Park, K. S. et al. (2019). (Middle school) Mathematics 2. Seoul: Dong-a.
30 Ministry of Education. (2015). Mathematics curriculum. Seoul: Author.
31 Park, K. S. et al. (2018b). (High school) Mathematics. Seoul: Dong-a.
32 Bae, J. S. et al. (2018). (High school) Mathematics. Seoul: Kumsung.
33 Jeong, J. H. (2012) Proofmood, a computer logic system. Seoul: Kyungmoonsa.
34 Seo, Y. S. (2006). The problem of the void in philosophy of Badiou. The Journal of Contemporary Psychoanalysis, 8(2), 95-114.
35 Yoo, Y. J. (2012). Secondary Mathematics Textbook Research. Seoul: Kyungmoonsa.
36 Lee, J. Y. et al. (2018). (High school) Mathematics. Seoul: Chunjae.
37 Bagni, T. (2006). Some cognitive difficulties related to the representations of two major concepts of set theory. Educational Studies in Mathematics, 62(3), 259-280.   DOI
38 Kolitsoe Moru, E., & Qhobela, M. (2013). Secondary school teachers' pedagogical content knowledge of some common student errors and misconceptions in sets. African Journal of Research in Mathematics, Science and Technology Education, 17(3), 220-230.   DOI