Re: Columns without names

JOG wrote:
> While I have your attention perhaps you might also clarify a
> distinction that I previously had:
>
> I was under the impression that - given that the extension of a
> predicate is the set of true propositions that can be formed by
> substituting a term for each of its free variables

In the mathematical context, a predicate extension is a collection of things in some universe for which the predicate holds. In other words,  a predicate can be interpreted as a mathematical relation in some domain of interpretation, or one can say that a predicate defines a relation in some domain. The '<' predicate in the {1,2,3} domain defines the {(1,2), (1,3), (2,3)} relation which is the predicate extension.

• a predicate
  > /always/ has an extension.
  

It depend on your favorite set theory. In some, R = {x | not( x in x)}  does not exist, in others it does.

>In contrast a set defined such as { m/n :
> m,n E Z & n!=0 } (rational numbers) is infinite and cannot be
> enumerated.
>

This, I do not understand.

> Is this distinction incorrect?
Received on Wed Sep 20 2006 - 18:16:58 CEST