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MathGroup Archive 2002

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Interval functions: comment on conceptual problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg33723] Interval functions: comment on conceptual problem
  • From: "DIAMOND Mark R." <dot at dot.dot>
  • Date: Wed, 10 Apr 2002 00:49:03 -0400 (EDT)
  • Organization: The University of Western Australia
  • Sender: owner-wri-mathgroup at wolfram.com

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
as
A=Interval[{99,100}];
B=Interval[{100,101}];
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
right.
But if we ask about intersection, we get
IntervalIntersection[A,B], we get
Interval[]
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
Interval[{100,100}]
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.

Cheers,

Mark
--
Mark R. Diamond
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