Re: Database design

Mark Johnson wrote:
> "Marshall Spight" <marshall.spight_at_gmail.com> wrote:
>
> >> Even if the set were so ordered?
>
> >Once you order a set, it's not a set any more.
>
> Because by definition, correct? Alright:

Yes, yes, yes. The *definition* of a set includes the fact that the members have no intrinsic order.

> >Let's say you have some integers: 1 and 2.
>
> Let's say you have a roster of US Presidents.

Let's say you respond to my 1 and 2 example before we move on to your US Presidents example.

1 is an integer. 2 is an integer. Divide the first by the second, you get 1/2. But this is not an integer! And yet, integer-ness is one of the fundamental properties of 1 and 2; how can we discard that property merely by applying definitions? Do you see the flaw?

> So a set cannot be ordered because to place it in any order is to
> redefine it as non-set?

It is not "redefinition" at all. A set is a value; you cannot do anything
to that value by using it as a parameter to a function. In exactly the same way, nothing happens to 1 when you divide it by 2.

> To become a set, the most important attribute of that set must be
> discarded?

Sets cannot "become" things; they exist platonically and cannot be altered. 1 cannot become anything other than 1; a set cannot become anything other than a set. You can perform operations that use 1 as an argument, but regardless of the result of the operation, 1 remains itself.

We cannot "discard" an order attribute of a set, because by definition no set ever had intrinsic order in the first place. Thus it is not possible for order to be "the most important attribute."

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. Likewise, you can take a set and an order, and construct a list (specifically, an ordered set) out of those two, but that won't affect either of them.

> But because someone kept saying, and confusing 'first responders' -
> fire, what fire? Building, what building?

These strawman analogies have no bearing on the topic.

Marshall Received on Wed Feb 22 2006 - 22:38:11 CET