All of the results of the previous sections are valid for the
familiar domain of the real numbers. However, when we work in
any fixed-precision
system, we have two difficulties:
- Not all numbers are even representable in the system, and
- Arithmetic doesn't have the properties we are used to.

For example, defining ** u** as the smallest machine representable
number which when added to **1** gives a number different from **1**
when stored, we see that is computed as **0**, whenever
is any number between **0** and ** u**. This effectively
limits the power of the singularity of the Gauss map.