Date: Dec 25, 2012 6:00 PM
Author: Virgil
Subject: Re: Simple Refutation of Cantor's Proof
In article

<67261d2b-d57e-4174-af7b-921ac287e30d@r4g2000pbi.googlegroups.com>,

Graham Cooper <grahamcooper7@gmail.com> wrote:

> On Dec 25, 7:22 pm, Virgil <vir...@ligriv.com> wrote:

> > > > > [1] you change each digit ONE AT A TIME

> > > > > 0.694...

> > > > > but this process NEVER STOPS

> >

> > > > > [2] and you NEVER CONSTRUCT A NEW DIGIT SEQUENCE!

> >

> > > > Do you deny that f(x) = x^2 and g(x) = 2*x+3 define real functions,

> > > > i.e., functions taking arbirary real numbers as arguments and producing

> > > > from them appropriate real numbers as values?

> >

> > > > It you accept them as functions why balk at functions from |N to

> > > > the set of decimal digits, interpreted as reals in [0,1]?

> >

> > > the logical manipulations do not hold on AD(x) = D(x)+1 [mod 9]

> >

> > > This is what you are really doing.

> >

> > > +----->

> > > | 0. 542..

> > > | 0. 983..

> > > | 0. 143..

> > > | 0. 543..

> > > | ...

> > > v

> >

> > > T(x,y) = L(x,y)+1 [mod 9]

> >

> > > +----->

> > > | 0. 653..

> > > | 0. 004..

> > > | 0. 254..

> > > | 0. 654..

> > > | ...

> > > v

> >

> > > This plane exists as much as your altered string.

> >

> > > It's mere naivety to define any digit string from

> >

> > > 0 . T(1,_) T(2,_) T(3,_) ...

> >

> > > where the set of free values _ biject N

> > > and then conclude such strings are absent from L.

> >

> > > Herc

> >

> > Since that is not a rule used by anyone who knows what is needed, it is

> > irrelevant,

> >

> > A rule that actually works on decimals, or with any base larger than 7,

> > is to look at the nth digit of the nth element in the list and if it

> > less than a 6 make the nth digit of the "anti-diagonal a 6 but

> > otherwise make it a 5.

> >

>

> OK!

>

> +----->

> | 0. 542..

> | 0. 983..

> | 0. 143..

> | 0. 543..

> | ...

> v

>

> T(x,y) = 6 IFF L(x,y) < 6

> T(x,y) = 5 OTHERWISE

>

>

> +----->

> | 0. 666..

> | 0. 556..

> | 0. 666..

> | 0. 666..

> | ...

> v

>

> This plane exists as much as your altered string.

> It's mere naivety to define any digit string from

>

> 0 . T(1,_) T(2,_) T(3,_) ...

>

> where the set of free values _ biject N

> and then conclude such strings are absent from L.

>

> Herc

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?

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