On Jun 10, 2006, at 23:51 , Michael Glaesemann wrote:
A range can be formed for any point type, where a point type is
any type that's well-ordered:
* the range of values is bounded (the number of values in the type
is finite)
* comparisons are well-defined for any two values, and
* for any point p, the next point can be found using a successor
function
It was pointed out to me off list that I got my definition of well-
ordered wrong. I was confusing the definition of well-ordered with
the overall requirements that I was using to define ranges.
Well-ordered is just that for any two values a and b of a given type,
a < b is defined. That's what I was attempting to get at in the
second point above. The added requirements of having the type bounded
(which is going to happen on a computer anyway) and having a
successor function are still required for the range definition, but
not part of the definition of well-orderedness per se.
Michael Glaesemann
grzm seespotcode net
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