Re: Comparisons and decorations
Nate
On 24 Sep 2010, at 11:48, Arnold Neumaier wrote:
> Nate Hayes wrote:
>> special cases for
>> A \interior B
>> such as when A and B are both Entire or A=[1,Infnity] and B=[0,Infinity]. In these cases, the interior operator would need to return a different result than when A and B are compact intervals, such as A=[1,100] and B=[0,200].
>
> ??? There is a uniform formula in 754:
>
> [al,au] interior [bl,bu] iff ~(bl-al>=0) and ~(au-bu>=0).
Looking at 754-2008 §5.3.1, I think
(nextDown(al) >= bl) and (nextUp(au) <= bu)
also works, since nextDown(-oo) = -oo and nextUp(+oo) = +oo.
John Pryce