Re: Columns without names

JOG wrote:
[...]

> Either way I always viewed "not(x in x)" as the predicate, and the
> whole definition " x | not(x in x)" as the intension.

"x|P(x)" is syntactically incorrect without curly brackets. With the curly brackets (A = {x | P(x)} ), it's a shorthand for "forall(x) x in A iff P(x)".

>Similarly are you
> saying that for a definition of rational numbers { m/n | is_integer(m)
> & is_integer(n) & non_zero(n) } the whole statement is the predicate,
> as opposed to just the part after the | . I appreciate the time spent
> answering
> these questions.

See above.

>
> >
> > >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?
>
> Just to offer you a quote from the Potter book:
>
> "The idea of an extension of a property is standardly explained by
> examples
> such as the properties of 'having a heart' and 'having a kidney'. Logic
> textbooks assure us that although they are different properties they
> apply
> to the same objects (apart from pathological cases). Logicians express
> this
> by saying that the two predicates have different intensions but the
> same
> extension."

I do not know who those "logicians" are, just wondering why they could not just have said that "two different predicates have the same extension" (or better define the same set) without conjuring the ill-defined spirit of "intension" ? Received on Thu Sep 21 2006 - 16:30:18 CEST