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Re: Matheology § 092
Posted:
Aug 10, 2012 10:44 PM
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On Aug 10, 12:52 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 9 Aug., 23:19, William Hughes <wpihug...@gmail.com> wrote:
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> > On Jul 22, 6:51 am, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > Matheology § 092
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> > > My second best proof contradicting set theory
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> > > 1)
> > > Define a sequence of points p_n in the unit interval
> > > p_n = 1/n.
> > > These points define intervals
> > > A_k = [1/n, 1/(n+1)] for odd n
> > > and B_j = [1/n, 1/(n+1)] for even n.
> > > The intervals of sort A ==== and B ---- are alternating. If the points
> > > are denoted by n, we have something like the following configuration.
> > > ...7--6==5--4====3---------2===========1
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> > > Theorem: If two neighbouring points p_n and p_(n+1) are exchanged, the
> > > number of intervals remains the same.
> > > ...7--6==5--3====4---------2===========1
> > > The intervals remain alternating. And in particular the number of
> > > intervals cannot increase.
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> > From this Theorem we immediately get:
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> > If any finite set of the p_n are moved then the
> > number of intervals does not increase.
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> That means the increase of intervals can be put into a sequence:
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> 0, 0, 0, ....
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> that is 0 for every finite n.
Thus the limit of the number of changes is 0
Look! Over There! A Pink Elephant
Thus the number of changes of the limit is 0
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