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Re: Simple Refutation of Cantor's Proof
Posted:
Dec 26, 2012 12:15 AM
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On Dec 26, 1:23 pm, Virgil <vir...@ligriv.com> wrote:
> In article
> <aa637598-f327-464f-954b-9cdbe4c87...@i2g2000pbi.googlegroups.com>,
> Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > > Since the constructed string must differ from each string listed in L in
> > > a way that gives it a different value from that listed string, how can
> > > it possibly still be among a set of values from which it is by
> > > construction excluded?
>
> > the size of the string is not fixed.
>
> The one to be constructed is constructed to be of the same length as
> the ones listed.
>
>
>
> > You construct a portion, you construct another portion, and you never
> > stop.
>
> One usually creates a rule which defines all the digits of the
> construction simultaneously.
>
Right but your rule is just applied to one digit at a time
and it equally applies to the whole plane.
+----->
| 0. 542..
| 0. 983..
| 0. 143..
| 0. 543..
| ...
v
AD = 0.656...
Transpose Plane
+----->
| 0. 666..
| 0. 556..
| 0. 666..
| 0. 666..
| ...
v
D = 0.656...
Just use the Transpose Plane intermediate step to see your error.
Herc
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