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Vincent Lefevre wrote:
On 2012-04-05 15:35:18 -0500, Nate Hayes wrote:Vincent Lefevere wrote: >I agree. But there will be no "overflown" intervals at Level 2. >AFAIK, the Level 2 choice for the midpoint on unbounded intervals >has been done for practical reasons, not because of some notion >of "overflown" intervals (if this is what you meant). Nope. That's not what I meant. What I meant is that at Level 1 there is no definition of midpoint for unbounded intervals. So why include unbounded intervals in the Level 1 model?because the midpoint is not the only function. For instance: 1 / [0,1] = [1,+oo] at Level 1 and Level 2 (+ some decorations).
We don't actually perform arithmetic in a computer at Level 1, and at Level 2 with overflow one has 1 / [0,1] = [1,+OVR]
Especially when a similar treatment at Level 2 of "overflown" intervals can provide the same practical benefits? IMO the Level 1 model is then cleaner and simpler.I disagree: without unbounded intervals, you wouldn't have a closed arithmetic
It seems academic to me: we don't perform arithmetic in a computer at Level 1, (and the overflown arithmetic is closed at Level 2, btw). When restricted to bounded intervals, the Level 1 arithmetic is closed and cancellative for addition, subtraction, multiplication and division with 0 not in the denominator. This is the oldest interval arithmetic of RamonMoore, etc. and has withstood the test of time already. IMO this is better than the current P1788 model with unbounded intervals.
Nate