Date: Jan 29, 2013 12:36 PM
Author: Scott Berg
Subject: Re: Matheology � 203

"WM" <> wrote in message
> "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,

(also pick up a good book on sets and read{it} )

the set read has at least one element, it.

Bonus question;
is the null set a member of the set read ?