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Re: Discussion paper: what are the level 2 datums?

Vincent Lefevre wrote:

On 2010-10-09 12:41:42 +0200, Arnold Neumaier wrote:

The only reasonable alternative I can see (but do not propose to use)
is the treatment of Empty, where (at the expence of more complex
executing formulas) one could sensibly argue to take
  inf(Empty)=+inf, sup(Empty)=+inf, mid(Empty)=0,  rad(Empty)=-inf
in place of NaN for all four results.


I suppose you meant sup(Empty)=-inf.


Yes.



Concerning mid(Empty), I don't like 0, because it would be an
arbitrary choice (just like +inf + -inf is not 0). IMHO it should
be undefined at Level 1 and NaN at Level 2.

Concernant rad(Empty), -inf makes sense if we regard rad(x) as
(sup(x) - inf(x)) / 2. But NaN would be fine too.


Yes, the above was only meant to be arguable, not that I want this.
Indded, in the text I suggested to use the version in the Vienna proposal, which has mid=rad=NaN for Empty.