Re: Columns without names
From: Bob Badour <bbadour_at_pei.sympatico.ca>
Date: Thu, 21 Sep 2006 00:37:26 GMT
Message-ID: <a9lQg.31700$9u.290740_at_ursa-nb00s0.nbnet.nb.ca>
>> paul c wrote:
>>
>>> vc wrote:
>>>
>>>> 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.
>>>> ...
>>>
>>> I'm having a hard time seeing this - in what set theory would R = {x |
>>> not( x in x)} exist?
>>
>> NBG.
>>
>>> thanks,
>>> p
Date: Thu, 21 Sep 2006 00:37:26 GMT
Message-ID: <a9lQg.31700$9u.290740_at_ursa-nb00s0.nbnet.nb.ca>
paul c wrote:
> vc wrote: >
>> paul c wrote:
>>
>>> vc wrote:
>>>
>>>> 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.
>>>> ...
>>>
>>> I'm having a hard time seeing this - in what set theory would R = {x |
>>> not( x in x)} exist?
>>
>> NBG.
>>
>>> thanks,
>>> p
> > thanks for that. now i'll try to figure out what NBG stands for. maybe > the plonk is slowing me down. if it's obvious to everybody else, then > the joke's on me.
It wasn't obvious to me, but google is our friend. Searching "set theory nbg" yields this page:
http://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Bernays%E2%80%93G%C3%B6del_set_theory Received on Thu Sep 21 2006 - 02:37:26 CEST