Re: "Disjoint" relation
Nate Hayes wrote:
Arnold Neumaier wrote:
Vacuous truth is a hard concept even for experts and mathemeticans.
If you really believe that, you'd also promote the abolishion of the
empty set (a vacuous collection of objects)
Actually, I _would_ advocate abolishment of the empty set from IEEE 1788!
I my opinion and personal experience, empty set is totally unnecessary.
We don't have empty set in our Kaucher interval arithmetic library now
for five years. It makes the code fast and simpler due to less special
cases.
In a sense, Kaucher arithmetic has infinitely many empty sets, but the
operations on them are not consistent with those for Moore intervals.
But Kaucher arithmetic is completely different. It is not based on a
model of intervals as sets, as Moore's arithmetic, but on a model of
intervals as elements of R^2.
Therefore in Kaucher arithmetic many decisions are done differently
than in Moore arithmetic.
For example, there the most relevant comparisons are <= and <, not
subset and interior. This is also why I want to leave the latter
optional in the standard, so that one can have a single conforming
implementation catering for both.