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실수의 구성 방법에 관한 연구

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Author(s)
김인경
Issued Date
2008
Abstract
The study about Mathematics is started from the study for the number system. In particular, it is important to grasp properly the substance of a real number system, because all contents in analytics are established on the feature of real line .
Introducing irrational numbers with rational numbers, we expand the real number system. The typical methods of constructy real numbers are as follows; Dedekind's method using the notion of the cut in rational numbers, Cauchy's method using the limit notion of Cauchy's sequence in rational numbers, and the least upperbound property-method using the existence of the supremum.
In this study, introducing Cauchy's method that uses the Cauchy's sequence in rational numbers, we prove the existence of the supremum for the bounded subset of real numbers.
Alternative Title
A study on the construction method of real numbers
Alternative Author(s)
kim inkyung
Affiliation
교육대학원 수학교육전공
Department
교육대학원 수학교육
Advisor
정윤태
Awarded Date
2009. 2
Table Of Contents
- 목 차-

ABSTRACT


Ⅰ. 서 론 1

Ⅱ. 정수에서 유리수로의 확장 2

Ⅲ. 유리수에서 실수로의 확장 4
A. 실수의 구성 4
B. 실수의 대수적 구조 7
C. 실수에서의 순서 17

Ⅳ. 실수의 완비성 21



참고문헌 34
Degree
Master
Publisher
조선대학교
Citation
김인경. (2008). 실수의 구성 방법에 관한 연구
Type
Dissertation
URI
https://oak.chosun.ac.kr/handle/2020.oak/4944
http://chosun.dcollection.net/common/orgView/200000237664
Appears in Collections:
Education > Theses(Master)(교육대학원)
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