| Thread Links | Date Links | ||||
|---|---|---|---|---|---|
| Thread Prev | Thread Next | Thread Index | Date Prev | Date Next | Date Index |
Alexandre Goldsztejn wrote:
On Wed, May 9, 2012 at 4:32 PM, Nate Hayes <nh@xxxxxxxxxxxxxxxxx> wrote:Alexandre Goldsztejn wrote:So, what is the point? Why introducing families of bounded intervals to model one unbounded interval? Only for being able to justify at Level 1a a definition of the midpoint? Anyway, the definition of the midpoint of an unbounded interval is arbitrary, so your proposal tries to justify something arbitrary, which is dangerous with many regards.The proposal does not define the midpoint of an unbounded interval; it allows the midpoint of an overflow family at Level 1a to be defined in the same manner and for the same reasons that P1788 has already discussed defining midpoint of an unbounded interval at Level 2. If such an idea is really so dangerous, P1788 should not define midpoint for unbounded intervals at Level 2 in the current model, either.As I said previously, I personally see no problem if the midpoint is undefined at Level 1 for unbounded intervals, but defined arbitrarily at Level 2 after discussing the right choice (which could be Fmax or anything else). What I think is dangerous is to give an artificial mathematical definition of the midpoint at Level 1a, because such a definition would look non arbitrary while it is actually arbitrary.
The motion does not define midpoint for an unbounded interval at any level; it allows the midpoint of an overflow family at Level 1a and Level 2 to be defined the same way you suggest midpoint for an unbounded interval may be arbitrarily defined at Level 2 (but not Level 1) in the current model. One may even argue that to justify midpoint([1,+Inf]) = REALMAX at Level 2 is due to implicit reasoning of overflow. So technically I think overflow is more correct because in that model the midpoint of an unbounded interval is never defined at ANY level, but the midpoint of overflow may be given safe and reasonable definitions at ALL levels. 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. These are reasons why I continue to believe the current model is not adequate; and reasons why I continue to believe overflow is a safe, reasonable and viable alternative. Others may disagree, but we shall all have an opportunity to cast a vote accordingly. Nate