2.12.3 Systems

For each property there is a compact syntax which states that the constructed number system tracks that property.

• The system enhances by tracking with .
• The system enhances by tracking with .
• The system enhances by tracking with .

The description can be placed above the number system, as was done previously:

The exact number system used to track properties can also be specified:

Conjuctive descriptions are also described as before:

Properties may be combined if they share the same underlying number system:

A similar notation is used in describing intervals; for example, is an interval with value j, whose continuity is described by d.  

  In the next subsection, interval sets will be introduced. For any interval arithmetic , there is an associated interval set arithmetic . and are likely implementations, both of which have been carried out by the author, for k=1, 2, 3.

Jeff Tupper

March 1996