STRUCTURING OF NUMBER SYSTEMS

In this short book, the operative properties, i.e., the properties of operations and the order relation of number systems, are exposed in terms of the ordered semi-fields. Thus, from Chapter II on, starting from natural numbers with zero, number systems are described having better and better operative properties what culminates in Chapter VI with the field of rational numbers.

For a student of mathematics, who is acquainted with basics of abstract algebra, this book will be the one where the number systems are exposed to a precise investigation and the concept of ordered semi-fields enable such investigation.