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Topic: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR:
THE REALS ARE UNCOUNTABLE!

Replies: 47   Last Post: Jan 12, 2013 11:33 AM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR: THE REALS ARE UNCOUNTABLE!
Posted: Jan 10, 2013 5:21 PM

In article
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 10 Jan., 12:11, Zuhair <zaljo...@gmail.com> wrote:
>

> > > The anti-diagonal up to digit n must have a double up to digit n.
> >
> > Of course, because the list is defined as the list of ALL terminating
> > decimal representations. That is correct and natural and Cantor's
> > arguments Agrees with that completely.

>
> Can you quote the relevant paragraph?

A competent mathematician would be aware that one can list the set of
all terminating proper decimals (truncating any terminating 0's):
shorter before longer, and for those of the same length, smaller before
larger.
> >
> > > Result: The diagonal cannot be an entry of the list.
> >
> > the list
> > ONLY contains TERMINATING decimal representations, while the diagonal
> > and the anti-diagonal are non terminating decimal representations

>
> I do not know what you worship .

Common sense, for a start, which we realize is never found in
Wolkenmuekenheim.

Every finite initial segment of the
> anti-diagonal is an entry of the list. I do not know what else can
> belong to the anti-diagonal. But certainly this additional thing
> cannot be used to distinguish it from anything.

All it takes to distinguish between any two functions from |N to {m,w},
say f and g, is some n in |N such that f{n) =/= g(n).

So f = g iff no such n exists and f =/= g if one or more such an n does
exist.
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