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Re: Matheology § 203
Posted:
Jan 29, 2013 1:21 PM
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On 29 Jan., 18:36, "fasnsto" <inva...@invalid.com> wrote:
> "WM" <mueck...@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) denotes a property of the argument n.
>
> P{n,...} notation typically means set P with elements n,...
But if necessary, you can also think without sets?
>
> P notation usually is a constant, sometimes a variable, not a set unless
> you call it "set P"
P is not a set but abbreviates a property that has to be defined
separately. Example: P stands for "is prime". The collection of
arguments has to be defined separately too, like above in C: All
natural numbers.
>
> so please clean up your notation of above,
Hope that helps.
>
> (also pick up a good book on sets and read{it} )
Done several times. Nevertheless logic and analysis can get along
without sets. And that better than with.
Regards, WM
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