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.