Happy Happy Joy Joy (was: On to Hydro)

[Jonathan S. Shapiro]

> >The space of floating point values is a tumbler space, I'm not sure that
> >*any* floating point value should properly be considered a number.
>
> I am boggled.  Please expand.

I was picking a nit. The question is: "What is a number?" The answer, in the
limit, is "something that responds to zero test and summation in a
well-defined way." Floating point values do not. The sum of two
representable floating point values is not always a representable floating
point value. Further, multiplication does not always result in the obvious
iterated summation. This is because of roundoff issues in the
representation.

This is in contrast to fixed-precision integer arithmetic, where all of
these operations generate results within the representation (provided you
use a ring-structured arithmetic).

Thus, I'ld say that the space of IEEE floating point values can be projected
into the space of real numbers, but when viewed as floating point values
they aren't numbers.

Like I say, I was picking a nit.

shap