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