Virgil
Posts:
4,479
Registered:
1/6/11
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Re: Matheology � 092
Posted:
Aug 12, 2012 7:01 PM
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In article
<233b3daa-ee40-4b6d-b949-b2f500fa71a4@h5g2000vbl.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 11 Aug., 19:46, William Hughes <wpihug...@gmail.com> wrote:
> > On Aug 11, 4:06 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> >
> >
> >
> >
> > > On 11 Aug., 04:44, William Hughes <wpihug...@gmail.com> wrote:
> >
> > > > On Aug 10, 12:52 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> > > > > That means the increase of intervals can be put into a sequence:
> >
> > > > > 0, 0, 0, ....
> >
> > > > > 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
> >
> > > There is no "change of limit".
> >
> > > There is the number of changes of the interval number for 1, 2,
> > > 3, ..., n, ... moving points.
> >
> > The phrase
> > "number of changes of the interval number" is nonsense.
>
> My construction has aleph_0 endpoints and aleph_0 intervals (of type A
> and B) between them.
>
> The number of changes of the number of intervals is zero for every
> move of every endpoint in every direction.
You are effectively arguing that all but one endpoint of one of the I_n
intervals must be an upper endpoint of exactly one interval and the
lower endpoint of another such interval, which is nonsense. or that
their order properties are irrelevant, which mis even ore nonsensical.
>
> > There are a number of possible things you might mean by
> > this ambiguous phrase.
>
> There is no number of things because every possible change is zero.
The no changes have occurred, and your argument is nothing.
>
> But your "Look over there is" is nonsense. If a sequences of sets
> could increase in another manner than its cardinality,
It is not that the NUMBER of I_n intervals differs from the NUMBER of
intervals A-B intervals, but that order properties of those two sets of
intervals differ and that difference is not destroyed by your
'bijection'.
> The limit oo of the sequence of cardinalities
There are only two equal cardinalities involved, but their equality is
irrelevant to other properties of the set of I_n intervals.
>
> You will stop with your silly "Look over there"
Wy should he stop when you are the one claiming that your argument
proves something else quite different and irrelevant to it.
> until you think that
> the serious objection against countability implied by your arguing
> will have been forgotten, and then you will start again with that
> nonsense.
Countability is NOT the issue. The isue is whether countability proves
anything else, and in this cans it does NOT prove that the set of I_n
intervals behaves as WM claims it behaves.
WM wishes to claim that after removing the countably many I_n intervals,
with I_n of length 1/10^n, from [0,1], one will have only countably many
points remaining.
But his maunderings prove no such thing.
--
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