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Re: Motion P1788/M0013.02:ComparisonOperations : NO

John Pryce wrote:

  aa  strictLess  bb <==> a1 <  b1 && a2 <  b2

 I shall use the analogue of "lessEqual":
  for all b in bb, there exists a in aa such that a < b
 and
  for all a in aa, there exists b in bb such that a < b.
 This agrees with the level 3 definition for bounded intervals, I
  think. But not for unbounded ones, e.g. ([-oo,0] strictLess
 [-oo,1]), and (Entire strictLess Entire) are true in my definition
 but not in the level 3 one. Comments please.
IMHO, unbounded and empty intervals continue to be the source of unwanted difficulties and semantics. It may be better to restrict our Level 1 mathematical model to compact non-empty intervals, i.e., IR, in conjunction with properly defined tetrits for exception handling (current motion 15 does not do this, btw). At Level 2, this would also include overflow semantics described by Ian McIntosh.
This appears to alleveiate much of the problems while also giving the desired semantics, e.g., as Vincent points out, X <= Empty is true, although we really would like the semantics X <= NaI, which is false. Same for his comments on glb and gub: 




On 30 Apr 2010, at 15:14, Vincent Lefevre wrote:
The motion says:

 The greatest lower bound and the least upper bound of an interval
 with the empty set are both the empty set.

So, this would mean that X <= Empty and Empty <= X for any X, but
with the consequence that <= would no longer be an order relation
(since no antisymmetric).

I think that X <= Empty and Empty <= X should be false for any
non-empty X. If defined as operations of P1788, glb and lub
should return NaI on (X,Empty).