Date: Sun, 10 Jul 2005 12:08:32 +0100
>>> In some sense you might say that is is "too large" to be a set. The >>> collection of all relations has the same problem. >> >> I'm skeptical to this, but if it is too difficult to explain (or to >> give an example of a problem), I'll let it be for the moment.
> I'll give another hint. Since unary relations are similar to sets you
> can get Cantor's paradox.
Doesn't this only apply if you are considering the set of all relations over all domains? What if you restrict yourself to a finite set of domains? I can't see how Cantor's Paradox would apply in this case.
So rather than having a domain of "the set of all relations", which can't exist, you could have a domain of "the set of all relations over a specified finite set of domains". Or even an infinite set of domains, I suppose, providing it's still a well-defined set.
So the "size explosion" problem here is with the domains rather than the relations?
Paul. Received on Sun Jul 10 2005 - 13:08:32 CEST