AA with complex keytype?
Joel C. Salomon
JoelCSalomon at Gmail.com
Wed Feb 14 06:24:05 PST 2007
Charles D Hixson wrote:
> Stewart Gordon wrote:
>> So if x != y, then both x < y and y < x? That wouldn't make sense at
>> all.
>>
>
> Actually, there are many cases where modular arithmetic to various bases
> is the desired behavior, and in such a system "both x < y and y < x"
> makes perfect sense. You can reach ANY number by repeatedly
> incrementing and also by repeatedly decrementing.
Mathematically speaking, a group like ℤ₃ is unordered, precisely for the
reason given. If we need to impose an ordering for array purposes (I
don’t understand that bit, just (mis)repeating something I°ve seen said
on the subject), then give the ordering lexicographic properties.
(x < y) && (y < x)
should not ever return true.
--Joel
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