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Re: int2interval, frac2interval, rat2interval

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.


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 have no interest in any standard that copies the defects of IEEE 754's
model, as I regard those aspects as almost unusable for mathematical
analysis.


Regards,
Nick Maclaren.