On 4/27/07, Guido van Rossum <[EMAIL PROTECTED]> wrote: > On 4/27/07, Jan Grant <[EMAIL PROTECTED]> 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.
From the Fortress spec: "The trait Q ( QQ ) encompasses all finite rational numbers, the results of dividing any integer by any nonzero integer. The trait Q∗ ( QQ_star ) is Q with two extra elements, + ∞ and −∞ . The trait Q# ( QQ_splat ) is Q∗ with one additional element, the indefinite rational (written 0/0 ), which is used as the result of dividing zero by zero or of adding −∞ to +∞." So separating Inf and NaN into other types has some precedent. I'd also point out that A being a subset of B doesn't make it a subtype also. If operations on A behave differently than the specification of the operations on B, then As aren't substitutable for Bs and A isn't a subtype. Because doubles have finite precision and rationals don't, I don't think doubles are a subtype of the rationals, even if you juggle Nan/Inf to make them a subset. Then again, doubles aren't a group either because of this imprecision, and I'm suggesting claiming they're a subclass of that, so maybe there's room in a practical language to make them a subclass of the rationals too. -- Namasté, Jeffrey Yasskin _______________________________________________ Python-3000 mailing list Python-3000@python.org http://mail.python.org/mailman/listinfo/python-3000 Unsubscribe: http://mail.python.org/mailman/options/python-3000/archive%40mail-archive.com
