CANTOR DISPROOF <<<<<<<<<<<<<<<<
in [Logic]
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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 |