between and among: worth Phobosization?

[Ola Fosheim Grøstad" <ola.fosheim.grostad+dlang at gmail.com>]

On Wednesday, 18 December 2013 at 17:29:19 UTC, Andrei 
Alexandrescu wrote:
> Within the tolerance allowed, they are equal.

No, "a != a" is only false for singeltons ([3,3] etc)

>> [0,5] < [6,10] => true
>> [0,5] < [2,10] => uncertain
>
> That would be false.

Interval-arithmetic is used for approximate calculations with 
upper-lower bounds, so it should not be false because then you 
make the wrong approximation. If the approximation is uncertain 
you need to track that or throw an exception when intervals 
overlap.

> The whole trick is to define primitives such that they have the 
> fundamental properties (transitivity, (anti-)symmetry etc).

The trick is to make the algebra useful for the domain it is used 
in. Some properties we are used to from regular real numbers will 
almost always break, so you have to decide based on usefulness.

Ola.