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On 05/09/2012 05:22 PM, Nate Hayes wrote:
One may even argue that to justify midpoint([1,+Inf]) = REALMAX at Level 2 is due to implicit reasoning of overflow.
The right definition of the midpoint of an empty or unbounded interval is 'undefined' on level 1 and NaN on level 2. Any other definition is mathematically artificially and hence misleading some users.
Also, one of the recurring arguments in favor of unbounded intervals is they supposedly make it easier to design interval algorithms at Level 1. However, many interval algorithms can't be designed (or proven) at Level 1 in the current model if midpoint is not defined.
Interval algorithms that use the midpoint of an unbounded interval are unsound at any level, and would be inefficient anyway. We do not need to provide support for stuff that is never useful.
Arnold Neumaier