Re: More on lists and sets

"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.

> 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. Received on Tue Mar 21 2006 - 15:20:38 CET