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Vincent Lefevere wrote:
On 2010-10-13 08:55:32 -0500, Nate Hayes wrote:This is important: you just agreed that NaI should not be convertible to empty set, or vice-versa.What you call NaI is a bare decoration. So, you're meaning that a bare decoration should not be convertible to an interval (either a bare interval or a decorated interval); I think this is fine.
Great.
But if you have a decorated interval X where bare(X) is the empty set, then dec(X) still makes sense.
Correct.
So, why vice-versa?
If you are referring to the "vice-versa" above in my original comment, I meant to speak only about conversions directly between bare intervals and bare decorations. Let me clarify:
-- As you mention above, if one has decorated interval X where bare(X) is the empty set, then dec(X) still can be used to obtain NaI. I fully agree with this.
-- If one has a bare interval xx (either empty or non-empty) and one also has a bare decoration (NaI), then it should not be possible to directly perform any conversion between xx and NaI.
-- In an arithmetic operation, the bare decoration (NaI) must always take precedence over the bare interval, e.g., xx + NaI = NaI (c.f. subclause 2.3 of Motion 8.02). I also believe this should be the case for set-theoretic operations as well, such as xx \union NaI = NaI.
Sincerely, Nate Hayes
-- Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/> 100% accessible validated (X)HTML - Blog: <http://www.vinc17.net/blog/> Work: CR INRIA - computer arithmetic / Arénaire project (LIP, ENS-Lyon)