Lexicon of Arguments

 

I 21
Extension/Waismann: e.g. the law a^m x aⁿ = a^{m + n} would lose its validity for n = 0.
Through the convention a° = 1 the existing laws not only remain in force, they are also extended to a larger area.
The maintenance of the laws thus regulates conceptual formation.
I 44
Caution: rational numbers are not an extension of the integers. The system of the integers can be mapped to a part of the rational numbers such that the four types of arithmetic are preserved: one-to-one, similar, isomorphic.