Re: The horse race

"Marshall Spight" <marshall.spight_at_gmail.com> wrote:

>Mark Johnson wrote:

>> But as I understand it, relations are not supposed to be sorted.

>Relations have no implicit order. This is part of the definition.

That's how I understood it. It was considered an advantage not to allow sorting.

>> So I
>> wondered that if a relation includes a horse's ranking, as a 'thing'
>> intrinsic, that one is trying to say that relations can be sorted?

>It depends on what you mean by "sorted." If you mean, can
>we change the definition of relation to include the idea that
>it has implicit order, then the answer is "no." If you mean,
>can we pass the relation to a sort function that will examine
>the attributes of the relation and return an ***ordered set***
>that has the same elements as the original set, then the
>answer is "yes."

>Reviewing the fundamentals of set theory might be in order;
>this is a very basic question.

It really is. It suggests almost mere semantics. In other words, if a relation is sorted, one simply claims that it is something - else - rather than use the word, sorted. Therefore, it is neither sorted, nor unsorted, neither ordered nor unordered. Received on Tue Feb 21 2006 - 22:49:06 CET