Re: Relation Definition

"Anith Sen" <anith_at_bizdatasolutions.com> wrote in message news:xAwSd.3039$873.584_at_newsread3.news.pas.earthlink.net...
>>> No, that cannot be right because it would allow the same attribute name
>>> to appear more than once.
>
> Why so? The header is a set -- so the elements i.e. the named typed
> attributes in a set are unique.

It was the way you said it (which I forget now) that would permit a Field named "Phone" with a numeric type and another with the same name and a string type.

> When one ignores the typed perspective, the header is simply a set of
> column names, again being a set, the elements must be distinct.

And then you are fine -- it is if/when you have a set of couples (column name, type) when you could have duplicated colum names.

> If the uniqueness of attribute names were not made explicit is your
> concern, the definition of the header in a relation is stated as: Given a
> collection of n types or domains Ti ( I = 1, 2, ...n ), not necessarily
> distinct, r is a relation on those types if it consists of two parts, a
> heading and a body, where the heading is a set of n attributes of the form
> Ai:Ti, where Ai ( which must all be distinct) are the attributes names of
> r and the Ti are corresponding type names ( i = 1,2,...n )
>
>>> http://mathworld.wolfram.com/n-Tuple.html
>
> That provides a possible vector interpretation of an n-Tuple. Nothing in
> that reference suggests the notion of n-dimensional tuple is usually
> reserved for ordered tuples and is inappropriate elsewhere.

Is there such a thing as an unordered tuple in mathematics? It seems that then you simply have a set or bag, although one where each element might map to a different set "from which it comes". We don't talk about the dimension of a set, but the cardinality. I'm pulling this out of my head without research, however, and we have already identified that there are gaps there. I just saw another report on the President of Harvard's remarks and it sounds feasible that my aptitude is simply lower than others on this list too, but that's my two cents, subject to change based on mood swings. smiles. --dawn

> --
> Anith
Received on Tue Feb 22 2005 - 04:36:51 CET