Re: Database design

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

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

>> If something is said to be a set, the elements are unsorted.

>Correct!

And if in any way ordered, are not a set.

And:

>> They have no particular ranking with regard to any other element or member.

>Correct!

No tuple order, no entry/entity order.

Or:

>> Fine. There can never be something known as an ordered or partially
>> ordered set.

>(Annoyingly, standard mathematical terminology includes both the
>terms "ordered set" and "partially ordered set" but neither one is a
>set! They are both ordered pairs of sets. An ordered pair is not
>a set.)

A tuple is not a set, BECAUSE . . it is ordered, in other words?

In short, an n-tuple is simply never called, a set.

What if it is?

"An Ntuple is a set of events, where for each event"
"An ordered n-tuple is a set of n objects"
"a common-point n-tuple set"

Etc.

So - what if?

>> >> Let's say you have a roster of US Presidents.

>> >we move on to your US Presidents example.

>> Presidents is a great example.

>It's certainly great at sidestepping the issues

That was the original question.

>> Then you deny its a set, at all.

>It is the term "redefinition" I object to.

>Let's say you have a set. Then you make a list of the members
>of the set, putting them in some specific order.

A batting order selected from the active roster, let's say.

>Now you have a list.

You have a list, a sequence, an order.

>But you still have the original set!

But they're not playing, until a substitution is made. This is generally done in the pitcher's spot. But a faster man might be substituted for a runner, and so on, as well.

>> To become a set, we're saying that the
>> most important attribute, the most important bit of information, must
>> simply be discarded?

>> >We cannot "discard" an order attribute of a set, because
>> >by definition no set ever had intrinsic order in the first place.

>> So a list with an intrinsic ordering, which is basically most every
>> list of every thing one might imagine, is not a set,

>Yes!

So:

>> and perhaps is not even properly an object for the RM, if you took it that far?

>Well, that's not a very well-defined question. Set theory is
>foundational;
>it can be used as the basis for substantially all of mathematics.
>Including
>lists. But in set theory, instead of using lists as such, we instead
>have sets that represent the same information.

As in:

>Consider the list of the first three presidents
>[Washington, Adams, Jefferson]

>This structure is ordered. It is not a set. It could even be said
>to be intrinsically ordered, or to have a proper order, to use
>your terminology.

>But we can construct an isomorphic set value using ordered pairs:

>{ (1, Washington), (3, Jefferson), (2, Adams) }

>This is a set of three members. The three members are unordered.
>This set contains exactly the same information as the previous list.

This is simply to substitute a key for position. You've added a sort attribute, in short. Indeed, the ordinal is a unique key, while the name is not. What you have written is a set of 2-tuples forming a relation.

>Here is another way to write the *same* value:

>{ (3, Jefferson), (1, Washington), (2, Adams) }

Certainly, because of the introduction of the important sorting attribute. It could well be stored, this way.

>Here is a third way to write the *same* set:

>2 Adams
>1 Washington
>3 Jefferson

But this isn't being written, this way. It's being stored, this way. If it were written, this way, it would make no sense. It's not in the proper order. Washington, not Lincoln, say, was our first President. He even used to have a national holiday in his honor. So did Lincoln.

>That third way sometimes tricks people into thinking that relations
>are two-dimensional.

If you wrote it, that way, you'd be wrong. If you represented it that way and always wrote it in order, it would not matter.

>> >Thus it is not possible for order to be "the most important attribute."

>> Unless it is. Sequence, rank and time. Sequence is not necessarily
>> temporal but also spatial. But all can be termed - proper order.

>> It's the most important.

>I don't believe what you're describing has any mathematical validity.

You don't give "mathematical" enough credit, here. You can represent a sequence, mathematically. You can calculate sequences, mathematically. And so on.

>It is a psychological issue.

Apparently.

>> >Now, you might have a *list* of things; that *would* have an
>> >intrinsic order. You can make a set by taking the elements
>> >of the list and removing the intrinsic order, and discarding
>> >duplicates. The resulting set would not change the nature
>> >of the original list.

>> It would destroy it.

>Nope. The list value would be unchanged, just like 1 remains
>unchanged when you divide 1 by 2. You get a result

But you aren't going to say, in other words, that 2/1 is the same as 1/2. You aren't going to tell me that Lincoln was our first President.

>result is different than the original operands, but the operands
>themselves are unmodified.

But which is trivial to point out. It's not that one can store what is ordered in some jumble of papers on the desk. It's that when time comes, and the information is needed, the papers can be sorted and information reported in its proper order. You may have a jumble of punch cards, which was a previous example. But if you can't sort these, at some point, even manually, then you might even hang up the card reader (don't know, JCL or something) while still not producing much of a run, a result.

>> If you remove the ordering, what you read,
>> paragraph by paragraph, title by title, sidebar by sidebar, in the
>> daily newspaper, or online, would become gibberish.

>Well don't do that then.

But I'm not the one, here, that suggests that I would.

>> You'd have to try
>> to piece it together, yourself, as a puzze. And on the other hand, if
>> you necessarily retain the proper orde, then you have set of ordered
>> entities and relations.

>Not necessarily.

Sorry. A puzzle, then. I do commit typo, on occasion, as you know.

>You can capture the information contained in an
>order with yourself resorting to the use of order. So no information
>need be lost.

A much fun as a puzzle may be, in some particular mood, this is not how you allot time in the morning when you, if you, rustle open the morning's paper.

All I can say is that if the editors adopted this view of yours, their Sunday circulation would plummet, never mind whatever handful of weekday subscribers remain. There are pages within the paper specifically set aside for puzzles. While some decry the invasion of the front page with editorial content, I say similarly as the opinionists should stay in their section, and yellow journalism should be a thing of the historical past (who am I kidding, right?), so the puzzles should not intrude into the front section, either, unless it's an occasional object of a story. Received on Thu Feb 23 2006 - 22:46:24 CET