CANTOR DISPROOF <<<<<<<<<<<<<<<< [Math]

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From: Graham Cooper on 23 Jun 2010 00:13

On Jun 23, 1:50 pm, Sylvia Else <syl...(a)not.here.invalid> wrote:
> On 23/06/2010 1:02 PM, Graham Cooper wrote:
>
>
>
>
>
> > On Jun 23, 12:56 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
> >> On 23/06/2010 12:45 PM, Graham Cooper wrote:
>
> >>> On Jun 23, 12:25 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
> >>>> On 23/06/2010 10:09 AM, Sylvia Else wrote:
>
> >>>>> On 22/06/2010 4:49 PM, Graham Cooper wrote:
>
> >>>>>> IN FACT
>
> >>>>>> 3 It takes 10^x reals to list every permutation of digits x digits
> >>>>>> wide
> >>>>>> So with infinite reals you can list Every permutation of digits
> >>>>>> infinite digits wide.
>
> >>>>> That's just an assertion. Let's see your proof. You might think it's
> >>>>> obvious, but in Maths, obvious doesn't count.
>
> >>>>> Sylvia.
>
> >>>> Are you going to ignore this Herc? Let's see the colour of your money.
> >>>> If you can prove it, do so.
>
> >>>> Sylvia.
>
> >>> You agreed the width of all permutations approached oo
> >>> since the list of reals is considered infinitely long
> >>> your claim is that the limit does not equal the infinite case
>
> >> The width is not in question. What you have failed to prove is that
> >> every permutation can be *listed*. Since that's the core issue in your
> >> entire attack on Cantor, you cannot be allowed to get away with merely
> >> asserting it. Prove it!
>
> >> Sylvia.
>
> > Consider the list of computable reals.
>
> > Let w = the digit width of the largest set
> > of complete permutations
>
> > assume w is finite
> > there are 10 computable copies of the
> > complete permutations of width w
> > each ending in each of digits 0..9
> > which generates a set larger than width w
> > so finite w cannot be the maximum size
>
> > therefore w is infinite
>
> That w is infinite is, as I said, not in dispute. You still haven't
> proved that the permutations can be *listed*. Not that they exist, not
> that there are inifinitely many of them, not that each number is
> infinitely long, not that zebras have stripes, but that the permutations
> can be *listed*. I'm empahsising the point as much as I can - the issue
> is whether they can be *listed*.
>
> Sylvia.

Read the proof again, beginning consider the list of computable reals

w is just a variable

Herc

From: Graham Cooper on 23 Jun 2010 00:15

On Jun 23, 2:13 pm, Graham Cooper <grahamcoop...(a)gmail.com> wrote:
> On Jun 23, 1:50 pm, Sylvia Else <syl...(a)not.here.invalid> wrote:
>
>
>
>
>
> > On 23/06/2010 1:02 PM, Graham Cooper wrote:
>
> > > On Jun 23, 12:56 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
> > >> On 23/06/2010 12:45 PM, Graham Cooper wrote:
>
> > >>> On Jun 23, 12:25 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
> > >>>> On 23/06/2010 10:09 AM, Sylvia Else wrote:
>
> > >>>>> On 22/06/2010 4:49 PM, Graham Cooper wrote:
>
> > >>>>>> IN FACT
>
> > >>>>>> 3 It takes 10^x reals to list every permutation of digits x digits
> > >>>>>> wide
> > >>>>>> So with infinite reals you can list Every permutation of digits
> > >>>>>> infinite digits wide.
>
> > >>>>> That's just an assertion. Let's see your proof. You might think it's
> > >>>>> obvious, but in Maths, obvious doesn't count.
>
> > >>>>> Sylvia.
>
> > >>>> Are you going to ignore this Herc? Let's see the colour of your money.
> > >>>> If you can prove it, do so.
>
> > >>>> Sylvia.
>
> > >>> You agreed the width of all permutations approached oo
> > >>> since the list of reals is considered infinitely long
> > >>> your claim is that the limit does not equal the infinite case
>
> > >> The width is not in question. What you have failed to prove is that
> > >> every permutation can be *listed*. Since that's the core issue in your
> > >> entire attack on Cantor, you cannot be allowed to get away with merely
> > >> asserting it. Prove it!
>
> > >> Sylvia.
>
> > > Consider the list of computable reals.
>
> > > Let w = the digit width of the largest set
> > > of complete permutations
>
> > > assume w is finite
> > > there are 10 computable copies of the
> > > complete permutations of width w
> > > each ending in each of digits 0..9
> > > which generates a set larger than width w
> > > so finite w cannot be the maximum size
>
> > > therefore w is infinite
>
> > That w is infinite is, as I said, not in dispute. You still haven't
> > proved that the permutations can be *listed*. Not that they exist, not
> > that there are inifinitely many of them, not that each number is
> > infinitely long, not that zebras have stripes, but that the permutations
> > can be *listed*. I'm empahsising the point as much as I can - the issue
> > is whether they can be *listed*.
>
> > Sylvia.
>
> Read the proof again, beginning consider the list of computable reals
>
> w is just a variable
>
> Herc

I gave the inductive step for listing permutations
the base step is trivial

Herc

From: Graham Cooper on 23 Jun 2010 00:30

On Jun 23, 1:02 pm, Graham Cooper <grahamcoop...(a)gmail.com> wrote:
> On Jun 23, 12:56 pm, Sylvia Else <syl...(a)not.here.invalid> wrote:
>
>
>
>
>
> > On 23/06/2010 12:45 PM, Graham Cooper wrote:
>
> > > On Jun 23, 12:25 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
> > >> On 23/06/2010 10:09 AM, Sylvia Else wrote:
>
> > >>> On 22/06/2010 4:49 PM, Graham Cooper wrote:
>
> > >>>> IN FACT
>
> > >>>> 3 It takes 10^x reals to list every permutation of digits x digits
> > >>>> wide
> > >>>> So with infinite reals you can list Every permutation of digits
> > >>>> infinite digits wide.
>
> > >>> That's just an assertion. Let's see your proof. You might think it's
> > >>> obvious, but in Maths, obvious doesn't count.
>
> > >>> Sylvia.
>
> > >> Are you going to ignore this Herc? Let's see the colour of your money.
> > >> If you can prove it, do so.
>
> > >> Sylvia.
>
> > > You agreed the width of all permutations approached oo
> > > since the list of reals is considered infinitely long
> > > your claim is that the limit does not equal the infinite case
>
> > The width is not in question. What you have failed to prove is that
> > every permutation can be *listed*. Since that's the core issue in your
> > entire attack on Cantor, you cannot be allowed to get away with merely
> > asserting it. Prove it!
>
> > Sylvia.
>
> Consider the list of computable reals.
>
> Let w = the digit width of the largest set
> of complete permutations
>
> assume w is finite
> there are 10 computable copies of the
> complete permutations of width w
> each ending in each of digits 0..9
> which generates a set larger than width w
> so finite w cannot be the maximum size
>
> therefore w is infinite
>
> Herc

Where I say a sequence ends in a new
digit I meant that new digit is at position w+1
appended to the sequence

Herc

From: Sylvia Else on 23 Jun 2010 00:37

On 23/06/2010 2:15 PM, Graham Cooper wrote:
> On Jun 23, 2:13 pm, Graham Cooper<grahamcoop...(a)gmail.com> wrote:
>> On Jun 23, 1:50 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
>>
>>
>>
>>
>>
>>> On 23/06/2010 1:02 PM, Graham Cooper wrote:
>>
>>>> On Jun 23, 12:56 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
>>>>> On 23/06/2010 12:45 PM, Graham Cooper wrote:
>>
>>>>>> On Jun 23, 12:25 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
>>>>>>> On 23/06/2010 10:09 AM, Sylvia Else wrote:
>>
>>>>>>>> On 22/06/2010 4:49 PM, Graham Cooper wrote:
>>
>>>>>>>>> IN FACT
>>
>>>>>>>>> 3 It takes 10^x reals to list every permutation of digits x digits
>>>>>>>>> wide
>>>>>>>>> So with infinite reals you can list Every permutation of digits
>>>>>>>>> infinite digits wide.
>>
>>>>>>>> That's just an assertion. Let's see your proof. You might think it's
>>>>>>>> obvious, but in Maths, obvious doesn't count.
>>
>>>>>>>> Sylvia.
>>
>>>>>>> Are you going to ignore this Herc? Let's see the colour of your money.
>>>>>>> If you can prove it, do so.
>>
>>>>>>> Sylvia.
>>
>>>>>> You agreed the width of all permutations approached oo
>>>>>> since the list of reals is considered infinitely long
>>>>>> your claim is that the limit does not equal the infinite case
>>
>>>>> The width is not in question. What you have failed to prove is that
>>>>> every permutation can be *listed*. Since that's the core issue in your
>>>>> entire attack on Cantor, you cannot be allowed to get away with merely
>>>>> asserting it. Prove it!
>>
>>>>> Sylvia.
>>
>>>> Consider the list of computable reals.
>>
>>>> Let w = the digit width of the largest set
>>>> of complete permutations
>>
>>>> assume w is finite
>>>> there are 10 computable copies of the
>>>> complete permutations of width w
>>>> each ending in each of digits 0..9
>>>> which generates a set larger than width w
>>>> so finite w cannot be the maximum size
>>
>>>> therefore w is infinite
>>
>>> That w is infinite is, as I said, not in dispute. You still haven't
>>> proved that the permutations can be *listed*. Not that they exist, not
>>> that there are inifinitely many of them, not that each number is
>>> infinitely long, not that zebras have stripes, but that the permutations
>>> can be *listed*. I'm empahsising the point as much as I can - the issue
>>> is whether they can be *listed*.
>>
>>> Sylvia.
>>
>> Read the proof again, beginning consider the list of computable reals
>>
>> w is just a variable
>>
>> Herc
>
> I gave the inductive step for listing permutations
> the base step is trivial

I can't find it. Perhaps you could give it again.

Sylvia.

From: Graham Cooper on 23 Jun 2010 00:45

On Jun 23, 2:37 pm, Sylvia Else <syl...(a)not.here.invalid> wrote:
> On 23/06/2010 2:15 PM, Graham Cooper wrote:
>
>
>
>
>
> > On Jun 23, 2:13 pm, Graham Cooper<grahamcoop...(a)gmail.com> wrote:
> >> On Jun 23, 1:50 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
>
> >>> On 23/06/2010 1:02 PM, Graham Cooper wrote:
>
> >>>> On Jun 23, 12:56 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
> >>>>> On 23/06/2010 12:45 PM, Graham Cooper wrote:
>
> >>>>>> On Jun 23, 12:25 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
> >>>>>>> On 23/06/2010 10:09 AM, Sylvia Else wrote:
>
> >>>>>>>> On 22/06/2010 4:49 PM, Graham Cooper wrote:
>
> >>>>>>>>> IN FACT
>
> >>>>>>>>> 3 It takes 10^x reals to list every permutation of digits x digits
> >>>>>>>>> wide
> >>>>>>>>> So with infinite reals you can list Every permutation of digits
> >>>>>>>>> infinite digits wide.
>
> >>>>>>>> That's just an assertion. Let's see your proof. You might think it's
> >>>>>>>> obvious, but in Maths, obvious doesn't count.
>
> >>>>>>>> Sylvia.
>
> >>>>>>> Are you going to ignore this Herc? Let's see the colour of your money.
> >>>>>>> If you can prove it, do so.
>
> >>>>>>> Sylvia.
>
> >>>>>> You agreed the width of all permutations approached oo
> >>>>>> since the list of reals is considered infinitely long
> >>>>>> your claim is that the limit does not equal the infinite case
>
> >>>>> The width is not in question. What you have failed to prove is that
> >>>>> every permutation can be *listed*. Since that's the core issue in your
> >>>>> entire attack on Cantor, you cannot be allowed to get away with merely
> >>>>> asserting it. Prove it!
>
> >>>>> Sylvia.
>
> >>>> Consider the list of computable reals.
>
> >>>> Let w = the digit width of the largest set
> >>>> of complete permutations
>
> >>>> assume w is finite
> >>>> there are 10 computable copies of the
> >>>> complete permutations of width w
> >>>> each ending in each of digits 0..9
> >>>> which generates a set larger than width w
> >>>> so finite w cannot be the maximum size
>
> >>>> therefore w is infinite
>
> >>> That w is infinite is, as I said, not in dispute. You still haven't
> >>> proved that the permutations can be *listed*. Not that they exist, not
> >>> that there are inifinitely many of them, not that each number is
> >>> infinitely long, not that zebras have stripes, but that the permutations
> >>> can be *listed*. I'm empahsising the point as much as I can - the issue
> >>> is whether they can be *listed*.
>
> >>> Sylvia.
>
> >> Read the proof again, beginning consider the list of computable reals
>
> >> w is just a variable
>
> >> Herc
>
> > I gave the inductive step for listing permutations
> > the base step is trivial
>
> I can't find it. Perhaps you could give it again.
>
> Sylvia.

Given a set of complete permutations w digits wide

eg

00
01
10
11

make 2 copies and append each of 0,1

00+0
01+0
10+0
11+0

00+1
01+1
10+1
11+1

therefore there is no max width of w

Herc