Re: More on lists and sets

"x" <x_at_not-exists.org> wrote in message news:dvp23n$rk4$1_at_emma.aioe.org...
>
> "Brian Selzer" <brian_at_selzer-software.com> wrote in message
> news:2ISTf.3660$tN3.3129_at_newssvr27.news.prodigy.net...
>
>> A list of widgits cannot be converted to a set of widgits without losing
>> information. A list can be represented as a single path through a
> directed
>> graph where the set of verticies is the underlying domain for the list,
> for
>> example, widgits. The set of verticies is only one part of the graph,
> since
>> a graph not only includes the verticies, but also the edges, which are
> lost
>> in the process. A list can also be represented as a relation with a
> widgit
>> attribute and a sequence attribute, so the set of widgits can be thought
> of
>> as a projection on that relation. Any way you look at it, the operation
> is
>> definitely not lossless, and therefore, not reversible.
>
> Without any operators the operation is indeed not reversible.
> You forgot to mention the list as a set of links which include vertices
> AND
> edges.
>

I said that the list can be represented as a path through a directed graph. That implies both edges and verticies.

>> The value of the elements in a list or bag are augmented by their
>> presence
>> within the list or bag, and in a list, the value is augmented further by
> the
>> position of the element. This augmentation gives each element identity.
>> "It's the third element in the list." "It's one of the five apples in
> the
>> bag." That identity is lost when converting a list to a bag or a set or
>> when converting a bag to a set.
>
> The the elements in a relations are augmented by their presence
> within the relation, and in a relation, the value is augmented further by
> the
> position of the element. This augmentation gives each element identity.
> "It's the element of the domain 'bla' next to the element 'bla bla' in the
> domain 'bla bla bla'."
> That identity is lost when converting a relation to a list.
>
>
>

I disagree, at least as far as the Relational Model goes: the position of a value in a relation is undefined and unimportant. A relation is a uniform set of r-tuples. An r-tuple is a set of named values. Therefore, the relation {{x = 5, y = 6}, {x = 3, y = 8}} is equivalent to the relation {{y = 8, x = 3}, {x = 5, y = 6}}.

On the other hand, the juxtaposition of a value with all other values in a given r-tuple does augment its value, as does its membership in the set of all other values in the relation with the same attribute name.

I can't see how injecting order would cause a loss of identity or information. If anything, information would be gained as a result. Received on Thu Mar 23 2006 - 09:48:49 CET