Re: |N unitär

Marc Olschok schrieb:

> peter schurr <peter.schurr@xxxxxxxxxx> wrote:
> > Amicus schrieb:
> >
> > > On 13 Jan 2006 05:34:26 -0800, "albrecht" <albstorz@xxxxxx> wrote:
> > >
> > > >
> > > > Nicht nur jede endliche Auswahl oder Folge von x-en ist ein Name und
> > > > bezeichnet damit eine Zahl, sondern _jede_ Auswahl oder Folge.
> > > >
> > > Wie gesagt, das ist natürlich falsch.
> > >
> > > Es ist m. E. aber interessant, dass diese (falsche) Ansicht offenbar
> > > zum _Standardrepertoire_ der ML-Cranks gehört. (Es bleibt zu hoffen,
> > > dass D i r nichts daran liegt, Deinen Crank-Status zu prolongieren.)
> > >
> > > Im Wikipedia-Eintrag zu /Cantor's diagonal argument/ findet sich (wohl
> > > aus diesem Grunde) sogar eine kurze Anmerkung, die sich mit diesem
> > > Irrtum auseinander setzt:
> > >
> > > ---------------------------------------------------------
> > >
> > > Why this does not work on integers
> > >
> > > People sometimes think that the above proof can be adapted to the
> > > integers to show that they too are uncountable. They try to do this by
> > > dropping the decimal point in the expansions above. The trouble is
> > > that an infinite sequence of non-zero digits does not represent an
> > > integer. [...]
> > >
> > > ---------------------------------------------------------
> > >
> > > Source:
> > > http://en.wikipedia.org/wiki/Cantors_Diagonal_argument
> > >
> > >
> > > "The trouble is that an infinite sequence of non-zero digits does
> > > not represent an integer." Das nämliche gilt natürlich auch für die
> > > unitäre Darstellung der natürlichen Zahlen.
> > >
> > >
> > > A.
> > >
> > >
> > > --
> > >
> > > E-mail:
> > > amicus<at>simple<bindestrich>line<punkt>de
> >
> > "The trouble is that fools imagine that an infinite number of integers
> > may fit in a finite number of integers which we have to rely on by
> > allowing just finite numbers of digits each."
>
> The trouble is that ignorants fail to understand, that the set of all
> finite words over a finite alphabet may well be infinite.
>
> And others think, that the free semigroup on one generator is their own
> invention, because they do not know the concept.
>
> Marc

Neither off topic examples nor off topic concepts may not repair the
logical misfit due to the ignorance of the fact that an infinite number
of (all different) integers must not lead to a finite difference over
the infinite range. The problem in general is that there are no "real
infinite" sequences of numbers at all that could be relied on other
than in the meaning of "transcendent".

Peter Schurr

.

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