Re: a < b < c revisited

[gudeman@cs.arizona.edu (David Gudeman)]

In article  <3195@enea.se> Erland Sommarskog writes:
]
](4)     IF a /= b /= c THEN
]
]But, wait, is that really the same thing? Well, with the definition
]above it is the same thing, but would we expect it to be the same
]thing? No. (3) is true if a = c, but we would expect (4) to say
]false in this case.

I wouldn't expect (4) to say false.  Frankly, I wouldn't know what to
think of such an expression unless I had a clear definition like the
one you gave -- which strikes me as a perfectly sound one.

The definition

  a <op1> b <op2> c   ==>   a <op1> b & b <op2> c

gives the correct meaning for transitive relations and a consistent
(but otherwise arbitrary) meaning for non-transitive relations.  Since
I can't think of any non-arbitrary meaning for that construct for
non-transitive relations, I see no problem with the def above.
--
					David Gudeman
gudeman@cs.arizona.edu
noao!arizona!gudeman