Chapter 3
Definition of computer arithmetic
In all branches of mathematics one is interested in gaining insight into the
structures that can occur. We have established in the preceding chapter
that the spaces listed in the leftmost element of every row in Figure 1 are
ringoids and vectoids with certain order properties such as being weakly
ordered or ordered or inclusion-isotonally ordered. We are now going to
show that these structures recur in the subsets on the right-hand side of
Figure 1 provided that the arithmetic and mapping properties are prop-
erly defined. In Section 3.1 of this chapter we give a heuristic approach to
the mapping concept of a semimorphism. In Section 3.2 we derive some
fundamental properties of semimorphisms and certain other ...