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Re: Table 4 proposal version 0.2...



Lee Winter wrote:
> But I'll bite.  Does the term "exact Infinite result" that you quoted
> refer to a 754-standard "infinity", which I would describe as an
> overflow, or does it refer to a mathematical infinity such as Cantor's
> aleph-one?

It refers to one of the ends of the affine completion (two-point
compactification) of the Reals -- ONE of the many different mathematical
infinities.  Cantor's infinite Ordinal and Cardinal numbers are some of
the others; the projective (one-point) compactification (most useful for
Complex numbers) is another, and more closely related -- and there are
others still.  Besides, Aleph-one might not be the one relevant to the
Reals anyway, or rather, it depends on whether your axioms include the
Continuum Hypothesis or not.

The problem here is that the 754 representations of Zero, Infinity
(and also NaN) are overloaded.  For results, the flags can be used
to distinguish the meanings, but inputs are considered exact by
definition.

That was precisely the motivation for my IFP exploration mentioned
in my earlier posts today.

Michel.
---Sent: 2012-03-22 21:30:40 UTC