Re: int2interval, frac2interval, rat2interval
On 2012-04-22 10:22:21 +0100, N.M. Maclaren wrote:
> On Apr 22 2012, Vincent Lefevre wrote:
> >
> >>While there are conventions that define extend the reals to include
> >>1/0, none are widely used, unlike the usual extension.
> >
> >You don't extend the reals by including 1/0. You include either a
> >single (unsigned) infinity or you include two (signed) infinities.
> >These are the usual conventions. Then IEEE 754 has its own rules
> >to define 1/+0, 1/-0 and so on.
>
> If you extend with a single 'unsigned infinity' (actually a NaN),
> one common convention is to define that x/0 delivers it. It's not
> commonly used in mathematics, but it is used.
Yes.
> >Though this could also be done, I've never seen a similar convention
> >on the integers (probably because it isn't much useful).
>
> I have seen and used the usual extended integers, and have seen the
> NaN (single 'infinity') form used.
>
>
> This is getting ridiculous, however. My point wasn't that it is worth
> adding complication to support such extensions but that, if the integer
> arithmetic includes infinities or NaNs, there shouldn't be a gratuitous
> restriction to exclude them. In mathematics, they are exactly as well-
> defined as for reals - no more, no less.
I'm not excluded them. I'm just saying that there is no point to
consider them as exact integers (or rationals) in the context of
int2interval, frac2interval and rat2interval. Said otherwise,
int2interval(+oo) does not describe a singleton interval and
should return some form of NaI.
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
100% accessible validated (X)HTML - Blog: <http://www.vinc17.net/blog/>
Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)
- References:
- Re: int2interval, frac2interval, rat2interval
- Re: int2interval, frac2interval, rat2interval
- Re: int2interval, frac2interval, rat2interval
- Re: int2interval, frac2interval, rat2interval
- Re: int2interval, frac2interval, rat2interval
- Re: int2interval, frac2interval, rat2interval
- Re: int2interval, frac2interval, rat2interval
- Re: int2interval, frac2interval, rat2interval
- Re: int2interval, frac2interval, rat2interval
- Re: int2interval, frac2interval, rat2interval