Ito, Mika B. Bolzano’s infinity and sets in the mathematics. (Japanese. English summary) Zbl 1433.01006 RIMS Kôkyûroku Bessatsu B69, 201-208 (2018). Summary: In the field of computer science, the formalization of mathematics has been often discussed. In spite of the concern over sets has risen, little attention has been given to B. Bolzano’s infinity and sets. What is to be noted is ‘eine unendliche Vielheit’ which is regarded as an ‘infinity of finite sets’ in mathematics. R. Dedekind holds the same atitude in this aspect. In addition, compactness should also be emphasized. It is based on model theory. Compactness is one of the real number products. It can be said that B. Bolzano’s infinity clarifies the essence of real numbers. The same is true for mathematics. This study contributes to a better understanding of sets in computer science. MSC: 01A50 History of mathematics in the 18th century 01A55 History of mathematics in the 19th century 01A67 Future perspectives in mathematics Keywords:infinity sets; real number; compactness; homotopy-type theory; computability theory; proof theory; model theory Biographic References: Bolzano, Bernard PDFBibTeX XMLCite \textit{M. Ito}, RIMS Kôkyûroku Bessatsu B69, 201--208 (2018; Zbl 1433.01006)