실수의 구성 방법에 관한 연구

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.