Re: Ranges for well-ordered types

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