Date: Jan 29, 2013 1:50 PM
Author: fom
Subject: Re: Matheology § 203

On 1/29/2013 11:36 AM, fasnsto wrote:
> "WM" <mueckenh@rz.fh-augsburg.de> wrote in message
> news:f5702bc4-f905-4e60-94c5-a503f3d9d887@n2g2000yqg.googlegroups.com...

>> "All" and "every" in impredicative statements about infinite sets.
>>
>> Consider the following statements:
>>
>> A) For every natural number n, P(n) is true.
>> B) There does not exist a natural number n such that P(n) is false.
>> C) For all natural numbers P is true.
>>
>> A implies B but A does not imply C.

>
>
> P(n) notation means the function P with variable n
>
> P{n,...} notation typically means set P with elements n,...
>
> P notation usually is a constant, sometimes a variable, not a set unless
> you call it "set P"
>
>
> so please clean up your notation of above,


No. The notation is fine. In logical contexts,
P(n) means that "n has the property P." It is
the language of monadic relation.