Hyperreal Line

This section develops some theory that will be needed for integration in Chapter 4. We begin with a new concept, that of a hyperinteger. The hyperintegers are to the integers as the hyperreal numbers are to the real numbers. The hyperintegers consist of the ordinary finite integers, the positive infinite hyperintegers, and the negative infinite hyperintegers. The hyperintegers have the same algebraic properties as the integers and are spaced one apart all along the hyperreal line as in Figure 3.8.1.

Figure 3.8.1 The Set of Hyperintegers