Date: Jan 29, 2013 4:18 AM
Author: William Hughes
Subject: Re: Matheology § 203
On Jan 29, 10:09 am, WM <mueck...@rz.fh-augsburg.de> wrote:

> On 29 Jan., 09:54, William Hughes <wpihug...@gmail.com> wrote:

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> > On Jan 29, 9:33 am, WM <mueck...@rz.fh-augsburg.de> wrote:

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> > > "All" and "every" in impredicative statements about infinite sets.

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> > > Consider the following statements:

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> > > 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.

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> > > A implies B but A does not imply C.

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> > Which is the point. Even though A

> > does not imply C we still have

> > A implies B.

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> > Let L be a list

> > d the antidiagonal of L

> > P(n), d does not equal the nth line of L

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> > We have (A)

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> > For every natural number n, P(n) is true.

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> > This implies (B)

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> > There does not exist a natural number n

> > such that P(n) is false.

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> > In other words, there is no line of L that

> > is equal to d.

>

> And how can C be correct nevertheless? Because "For all" is

> contradictory.

B: There is no line of L that is equal to d

does not imply

C: For all n, line n is not equal to d.

B correct does not mean "C correct nevertheless"