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Topic: CANTORS PROOF DEMO the Reals are UN-COUNTABLE
Replies: 1   Last Post: Jan 23, 2013 3:32 PM

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Graham Cooper

Posts: 4,250
Registered: 5/20/10
Re: CANTORS PROOF DEMO the Reals are UN-COUNTABLE
Posted: Jan 23, 2013 3:32 PM
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On Jan 23, 3:50 pm, George Greene <gree...@email.unc.edu> wrote:
> On Jan 9, 7:34 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:





A SUBLIST OF REALS IN [BASE 4]
R1 0.0000...
R2 0.3333...
R3 0.3210...
...

DIAGONAL = 0.031...
DEFINE
AD(d) = 2 IFF DIAGONAL(d) < 2
AD(d) = 1 IFF DIAGONAL(d) > 1

AD=0.212... is MISSING FROM THE LIST

PROOF
DIGIT 1 (2) IS DIFFERENT TO LIST[1,1] (0)
DIGIT 2 (1) IS DIFFERENT TO LIST[2,2] (3)
DIGIT 3 (2) IS DIFFERENT TO LIST[3,3] (1)
AND SO ON
So AD is DIFFERENT to EVERY ROW

since This Holds For Any Arbitrary List Of Reals
there is a missing Real for any List Of Reals
therefore Reals are Un-Countable!








>
> > So AD is DIFFERENT to EVERY ROW
>
> Different from every row.
>

> > since This Holds For Any Arbitrary List Of Reals
>
> Clearly.
>

> > there is a missing Real for any List Of Reals
>
> There is a real missing from anarbitrary list, therefore, there is  a
> real missing from EACH OR ANY list.
> Or,technically, from EVERY list.  Please note that in English, "every"
> IS SINGULAR
> and this IS NOT the same as "there is a real missing from ALL listS",
> PLURAL.
>

> > therefore Reals are Un-Countable!
>
> Well, they ARE CERTAINLY unLISTable.  That is what this proves.
> Do you still have a problem with the argument?


A SUBLIST OF REALS IN [BASE 4]
R1 0.0000...
R2 0.3333...
R3 0.3210...
...

0.100... is MISSING FROM THE LIST
0.200... is MISSING FROM THE LIST
0.300... is MISSING FROM THE LIST
0.110... is MISSING FROM THE LIST
0.210... is MISSING FROM THE LIST
0.310... is MISSING FROM THE LIST
0.120... is MISSING FROM THE LIST
0.220... is MISSING FROM THE LIST
0.320... is MISSING FROM THE LIST
0.102... is MISSING FROM THE LIST
0.202... is MISSING FROM THE LIST
0.302... is MISSING FROM THE LIST
0.112... is MISSING FROM THE LIST
0.212... is MISSING FROM THE LIST
0.312... is MISSING FROM THE LIST
0.122... is MISSING FROM THE LIST
0.222... is MISSING FROM THE LIST
0.322... is MISSING FROM THE LIST
0.103... is MISSING FROM THE LIST
0.203... is MISSING FROM THE LIST
0.303... is MISSING FROM THE LIST
0.113... is MISSING FROM THE LIST
0.213... is MISSING FROM THE LIST
0.313... is MISSING FROM THE LIST
0.123... is MISSING FROM THE LIST
0.223... is MISSING FROM THE LIST
0.323... is MISSING FROM THE LIST

**********************

HINT: DIGIT 1 IS DIFFERENT TO LIST[1,1]
HINT: DIGIT 2 IS DIFFERENT TO LIST[2,2]
HINT: DIGIT 3 IS DIFFERENT TO LIST[3,3]

TRUE OR FALSE YOU HYPER-INFINITE-DUMBASS ??

Herc




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