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Re: Matheology § 203
Posted:
Jan 30, 2013 4:22 AM
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On 30 Jan., 10:05, William Hughes <wpihug...@gmail.com> wrote:
> On Jan 30, 9:57 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>
>
>
>
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> > On 30 Jan., 09:40, William Hughes <wpihug...@gmail.com> wrote:
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> > > On Jan 30, 9:28 am, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > > On 30 Jan., 00:16, William Hughes <wpihug...@gmail.com> wrote:
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> > > > > On Jan 29, 10:11 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > > > > On 29 Jan., 21:28, William Hughes <wpihug...@gmail.com> wrote:
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> > > > > <snip>
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> > > > > > > It does, however, imply that d in not one
> > > > > > > of the lines of the list L
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> > > > > > For that sake you must check all lines. Can you check what is not
> > > > > > existing?
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> > > > > So now your claim is
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> > > > > We can know
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> > > > > There does not exist a natural number n
> > > > > such that d is equal to the nth line
> > > > > of L
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> > > > > but we cannot know
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> > > > > d is not one of the lines of L
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> > > > You are trying hard to misunderstand!
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> > > Do you agree
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> > > i. There does not exist a natural number n
> > > such that d is equal to the nth line
> > > of L
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> > > and
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> > > ii. d is one of the lines of L
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> > > are mutually exclusive?-
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> > In existing finite sets this is true. In actually infinite sets it is
> > not true,
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> Does
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> ii. d is one of the lines of L
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> imply
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> iii. there is a natural number n such that
> d is equal to the nth line of L
In finite sets or potentially infinite sets this is true, of course.
Reason: Every line n can be checked since we can go to line n+1.
In actually infinite sets it is not true, since there must be more
lines than every number n can reach. Remember: Beyond every n there
follow more loines than can be reached by a natural number or can be
measured by a natural number or can be enumerated by natural numbers.
Regards, WM
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