RE: Oops, restatement Motion P1788/M0037.01:MidAndRadSpecs:
Rad(Empty) = NaN is good too, let us go with Michel's suggestion
-----Original Message-----
From: stds-1788@xxxxxxxx [mailto:stds-1788@xxxxxxxx] On Behalf Of Michel Hack
Sent: Sunday, October 21, 2012 2:17 PM
To: stds-1788
Subject: RE: Oops, restatement Motion P1788/M0037.01:MidAndRadSpecs:
Vladik wrote:
> I would suggest mid(Empty) = NaN, since we want mid to be an element
> of the original interval.
I agree. However:
> If we define radius as the smallest non-negative real F-number for
> which [mid - rad, mid + rad] contains the original interval, then,
> since an empty set is contained in everything, we naturally get rad(Empty) = 0.
Well, vacuously true perhaps, but [NaN,NaN] is not a set, so it cannot even contain the Empty set! (it's a domain error).
rad=0 is more useful in identifying singletons, so I would suggest that
rad(Empty) also be NaN.
The following is NOT a proposal, but a curiosity worth mentioning. If we defined mid() and rad() to return an interval, either singleton or empty, we could avoid these problems! Well, they would just kick the can down the road, because one would take nummid = inf(mid) = up(mid), relying on how the nonexistent bounds of Empty are to be reported (as NaN, of course).
Michel.
---Sent: 2012-10-21 20:31:11 UTC