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.
