Re: The horse race

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

>Mark Johnson wrote:

>> But the use terms ought to be. That's the subject, not "Math".

>When you're asking about the essential characteristics of
>relations

Then the example of a simple relation ought to be discussed. I've proposed many, many examples, which you seemed to suggest confused you no end in another message.

>> Not even a hierarchy, necessarily. Just a sorted list, nothing more.
>> Fail to account, throw out that information, and what you have may
>> become useless, mathematically or otherwise.

>History has shown that sets are useful, so your hypothesis is
>incorrect.

My statement. I simply stated that if you have intrinsically ordered information then - Fail to account, throw out that information, and what you have may become useless, mathematically or otherwise.

>Anyway, set theory doesn't discount order

A simple relation is said to be unordered. If it represents ordered data - then what? It's not a relation? Or it must be divided into n-relations? And then what comes from that?

>> Perhaps for other purposes that set may be unordered.

>That's right.

You're saying it always is, by definition.

But, here, let's see:

>> If I give you page one, with story A in column left and story B
>> beginning over in column right, with A paragraph one following the
>> headlines and all falling below the banner, and A paragraph three
>> following two and preceding four, one might say the set of all
>> paragraphs is an unordered set. But there is an intrinsic order.

>Yes. But that order is not part of the set of paragraphs S.

They would be meaningless without it. It is intrinsic to both the semantics and the syntax of that group of paragraphs. They must appear in - proper order.

But:

>may capture that order in an order relation R.

An ordered relation?

>The pair (S, R)
>is called an ordered set.

And set that is ordered. But in the example, elements of R are inextricably part of the elements of S, and furthermore would be ordered by S-order, which supposedly can't be true in either case? It has to be one or the other.

>The set S is not called ordered;

But it is, nonetheless.

>is unordered. R is also unordered.

And:

>R and S are sets; they
>are unordered by definition.

Which seems to be the problem, once again. I don't know if I'm supposed to be Abbott or Costello in this. And information is not unordered. It must hold to its proper order. It means nothing without it.

>But R specifies a (not "the") order for set S.

There is only one order for that group of paragraphs, titles, footnotes, etc. Anything else would be characterized as computer error, a potential virus attack, somebody drunk on the job. The structure must be respected and retained with the text, links, markup and what have you. Without it, you have nothing but a 1000 unnumbered punch cards spilled onto the floor. Received on Thu Feb 23 2006 - 04:21:56 CET