Re: Containment-only Interval Standard

[Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>]

On 08/04/2011 05:56 PM, Lee Winter wrote:
> > > On Wed, Aug 3, 2011 at 2:56 PM, Michel Hack<hack@xxxxxxxxxxxxxx>  wrote:
> > >
> > > > (1)  Intervals as imprecise single values.
> > > >
> > > > (2)  Intervals as bounded (or semibounded) ranges of separate values.
>
> I disagree.  The above-described intervals do not specify collections
> of values all of which are "active".  Instead they represent a single
> value,


In all applications I know of, intervals represent bounds on the value 
of an unknown quantity.


The difference between (1) and (2) is that in (1) the bounds are 
supposed to be narrow (high relative accuracy), as they represent a 
quantity that in reality has a particular value, whereas in (ii) the 
bounds are usually wide, as they represent a quantity that in reality 
ranges over very different possibilities, and one is interested in 
selecting a particular, ''good'' one.


Arnold Neumaier