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Re: inexactness vs. exactness
The problem with this assumption is that after doing inexact
mathematics of more than a few steps, you run the risk of
getting accumulated errors. When you have accumulated
errors from several roundoffs, you get an approximate
answer, and you *CANNOT* claim that there is no representable
inexact number closer to the correct answer; after as little
as four inexact operations, it is unlikely to be true.
The answers in inexact math, other than trivially simple
single operations, are not "the closest representable
inexact number" to the answer, which in your opinion
is the key feature that transforms them into neighborhoods;
they are simply answers which are known to be wrong, but
which we hope are reasonably close.