数の定義に関する内容学的考察 : K-Theoryと数の構成的定義

抄録

The purpose of this paper is to show the importance of the constructive definitions. I compare the constructive definitions of numbers with those of the K-groups. Just as the integers are constructed from pairs of the natural numbers, the K-groups are constructed from pairs of vector bundles, and the K-groups give some profound results because there are the virtual vector bundles in the K-groups which play the role of integers. I assert that the instruction of such constructive definition in the school mathematics is important for students to understand the mathematical concepts correctly and also to recognize mathematics as always developed.