×

B. Bolzano’s infinity and sets in the mathematics. (Japanese. English summary) Zbl 1433.01006

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

Biographic References:

Bolzano, Bernard
PDFBibTeX XMLCite