B. Bolzano's Infinity and Sets in the Mathematics (The study of the history of mathematics 2016)

"The study of the history of mathematics 2016". August 29～September 1, 2016. edited by Shigeru Jochi. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.In the field of computer science, it has been often discussed that formalization of Matehematics. In spite of the concern over sets has risen, little attention has been given B.Bolzano's infity and sets. What is to be noted is 'eine unendliche Vielheit' which regarded as 'infinity of finitery sets' in the mathematics. R.Dedekind holds the same atitude that in the in this aspects. Inaddition, it should also be emphasized that compactness. It is based on Model Theory. Compactness is one of the real number products. It can be said B.Bolzano's infinity clarifies essence of real number. The same sets is true for mathematics. This study make contribution to a better understanding of sets in the computer science