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Michel Hack wrote:
Nate Hayes wrote:the comparison of "overflown" intervals [7,+OVR] \interior [1,+OVR] is necessarily false.I disagree -- if we had the concept of +OVR, this comparison would be UNORDERED, neither TRUE nor FALSE.
Thanks Michel. That was part of the conversation way back when, too, which I omitted for the sake of brevity in my last e-mail.
Arnold's conclusion that the comparision would be false was based on the assumption at that point of the discussion (as I recall) that we wanted all coparisons to be boolean (as opposed to, say, a tetrit or something).
I'm not sure if that assumption I still true or not, but if not then as you note UNORDERD might be relevant.
(Btw, "overflown" may be cute, but "overflowed" would be the correct English word. We can of course always define "overflown" as a new technical term!)
Well, I like the cuteness factor; but it probably is not good idea to start inventing new technical terms. So I will try to break my bad habit and use term "overflowed".
Nate