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