Re: MV Keys

Brian Selzer wrote:
> "Jon Heggland" <heggland_at_idi.ntnu.no> wrote in message
> news:MPG.1e7e1f4d25e871bb98979e_at_news.ntnu.no...
> > In article <1142006381.942511.18190_at_v46g2000cwv.googlegroups.com>,
> > marshall.spight_at_gmail.com says...
> >> And just for fun, here's an alternative semantics for the syntax
> >> above, in which the parentheses *do* mean the same thing.
> >>
> >> (1,b)
> >>
> >> Above, "(" means "introduce a new set, cardinality 1, with
> >> the following attributes."
> >
> > A set has attributes? No, a set with card 1 has one element. What is
> > that element? Not "an attributes". :)
> >
>
> A set has at least one attribute, though it can have more. I may be
> conflating terminology, but isn't the cardinality of a set an attribute? A
> uniform set is a set of something, so wouldn't the type (or domain) of its
> elements be an attribute?

Yes, a set absolutely has attributes (otherwise the concept is called a 'fusion'). It's most important property is that of membership (and so consequently no. of members or cardinality). This is a formal attribute, and is used by set theory to distinguish the set concept from an individual (or atom). Thinking about the properties of the empty set emphasises the importance of this notion.

A while back in the thread I also read talk of an individual being a set of one item, or x = {X}. This is actually an area that was explored most prominently by Quine early last century, but currently held in scant regard by contemporary mathematics.

(In set theory an individual is an item that has no membership property. With x ={x} this goes out the window and the definition of an individual becomes an item that contains itself - a definition wholly frowned upon as a contrived artifice).

All best, Jim. Received on Mon Mar 13 2006 - 04:20:31 CET