On 4/27/07, Jan Grant firstname.lastname@example.org wrote:
On Thu, 26 Apr 2007, Dan Christensen wrote:
Note also that double-precision reals are a subset of the rationals, since each double precision real is exactly representable as a rational number, but many rational numbers are not exactly representable as double precision reals. Not sure if this means that reals should be a subclass of the rationals.
Not quite all: the space of doubles include a small number of things that aren't representable by a rational (+/- inf, for instance).
This suddenly makes me think of a new idea -- perhaps we could changes the type of Inf and NaNs to some *other* numeric type? We could then reserve a place in the numeric hierarchy for its abstract base class. Though I don't know if this extends to complex numbers with one or both parts NaN/Inf or not.