## ABSTRACT

The set of integer numbers is a mathematical ring in the sense that the addition operation is reversible: adding m can be reversed by adding −m. In this chapter, we extend it into a yet more complete set: the set of rational numbers. This set is not only a mathematical ring but also a mathematical ﬁeld, in which not only the addition operation but also the multiplication operation is reversible: multiplying by m = 0 can be reversed by multiplying by 1/m.