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Interval functions: comment on conceptual problem

There seems to me to be, not so much a bug, as a conceptual error in the
implementation of the Interval functions. For instance, if we define A and B
and ask if 100 is contained in each of the intervals, the answers are
IntervalMemberQ[A, 100]  is True
IntervalMemberQ[B, 100]  is True
indicating that, in general, Intervals are closed on both the left and the
But if we ask about intersection, we get
IntervalIntersection[A,B], we get
suggesting that there were no shared points between A and B, and hence that
the intervals are open on left and right ... in contradiction of the
previous result.

Now I realize that a purist might argue that the answer Interval[] simple
indicates that there was not shared "Interval" rather than shared
single-point, but it seems to me to lead to an inconsistent set of functions
and definitions.
Better, I think, would be for
IntervalIntersection[A,B] to return
No example appears in the documentation of an interval with equal left and
right end-points, but it operates just fine with the other functions, and
makes for consistentency in that
Interval[{x,y}] can now be considered to be a closed interval.

It might also be desirable to have a way of indicating open intervals,
either at one or both ends.


Mark R. Diamond
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