THE CANTOR ARGUMENT SO FAR
in [Logic]
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From: |-|ercules on 20 Jun 2010 03:03 "Sylvia Else" <sylvia(a)not.here.invalid> wrote ... > On 20/06/2010 12:42 PM, |-|ercules wrote: >> "George Greene" <greeneg(a)email.unc.edu> wrote >>>> Is it a *NEW DIGIT SEQUENCE* or not? >>> >>> YES, DUMBASS, IT IS A NEW DIGIT-SEQUENCE because it was >>> NOT ON THE LIST of (allegedly "all") THE OLD digit-sequences! >> >> >> But you keep saying the anti-diagonal is NEW and ignoring me when >> I say it's not a new digit sequence. >> >> Then you repeat Cantor's proof again and again that it's NEW. >> >> You use terms NEW and NOT ON THE LIST, but evade me when I challenge >> whether it contains any new digit sequence. > > And you just ignore the point that it must be new because it > demonstrably isn't in the list. > > Sylvia. All you demonstrated was An AD(n) =/= L(n,n) -> An AD(n) =/= L(n,n) You don't like axioms stating a fact, but you use a definition as a proof. Herc
From: Sylvia Else on 20 Jun 2010 04:49 On 20/06/2010 5:03 PM, |-|ercules wrote: > "Sylvia Else" <sylvia(a)not.here.invalid> wrote ... >> On 20/06/2010 12:42 PM, |-|ercules wrote: >>> "George Greene" <greeneg(a)email.unc.edu> wrote >>>>> Is it a *NEW DIGIT SEQUENCE* or not? >>>> >>>> YES, DUMBASS, IT IS A NEW DIGIT-SEQUENCE because it was >>>> NOT ON THE LIST of (allegedly "all") THE OLD digit-sequences! >>> >>> >>> But you keep saying the anti-diagonal is NEW and ignoring me when >>> I say it's not a new digit sequence. >>> >>> Then you repeat Cantor's proof again and again that it's NEW. >>> >>> You use terms NEW and NOT ON THE LIST, but evade me when I challenge >>> whether it contains any new digit sequence. >> >> And you just ignore the point that it must be new because it >> demonstrably isn't in the list. >> >> Sylvia. > > All you demonstrated was In what sense could a number be said to be in a list if it doesn't match any element of the list? Sylvia.
From: |-|ercules on 20 Jun 2010 05:42 "Sylvia Else" <sylvia(a)not.here.invalid> wrote ... > On 20/06/2010 5:03 PM, |-|ercules wrote: >> "Sylvia Else" <sylvia(a)not.here.invalid> wrote ... >>> On 20/06/2010 12:42 PM, |-|ercules wrote: >>>> "George Greene" <greeneg(a)email.unc.edu> wrote >>>>>> Is it a *NEW DIGIT SEQUENCE* or not? >>>>> >>>>> YES, DUMBASS, IT IS A NEW DIGIT-SEQUENCE because it was >>>>> NOT ON THE LIST of (allegedly "all") THE OLD digit-sequences! >>>> >>>> >>>> But you keep saying the anti-diagonal is NEW and ignoring me when >>>> I say it's not a new digit sequence. >>>> >>>> Then you repeat Cantor's proof again and again that it's NEW. >>>> >>>> You use terms NEW and NOT ON THE LIST, but evade me when I challenge >>>> whether it contains any new digit sequence. >>> >>> And you just ignore the point that it must be new because it >>> demonstrably isn't in the list. >>> >>> Sylvia. >> >> All you demonstrated was > > In what sense could a number be said to be in a list if it doesn't match > any element of the list? What sense is a number that's only definition is to not be on a list? That may seem less concrete than your question, but it's worth thinking what "anti-diagonals" entail. You're not just constructing 0.444454445544444445444.. a 4 for every non 4 digit and a 5 for a 4. You're constructing ALL 9 OTHER DIGITS to the diagonal digits. And it's not just the diagonal, it's the diagonal of ALL PERMUTATIONS OF THE LIST. So, the first digit of the list can be... well anything, so the antidiagonal starts with anything.. then the second digit of the second real can be anything, so the antidiagonals next digit is anything.. No wonder you think there are infinitely more irrationals for every rational. So here is your formula for finding a new real. 0.xxxxxx 0.yyyyy 0.zzzzzz 0.aaaaa 0.bbbbb Pick ANY row and pick ANY digit other than the first digit. So instead of 'a' we'll choose 7. Pick ANY row other than aaaa and pick ANY digit other than the second digit. So instead of 'y' we'll choose 4. Is that a *new sequence* or is it anything at all? Considering all possible digit sequences occur INFINITELY WIDE I don't think you can do it! Herc
From: Sylvia Else on 20 Jun 2010 08:34 On 20/06/2010 7:42 PM, |-|ercules wrote: > "Sylvia Else" <sylvia(a)not.here.invalid> wrote ... >> On 20/06/2010 5:03 PM, |-|ercules wrote: >>> "Sylvia Else" <sylvia(a)not.here.invalid> wrote ... >>>> On 20/06/2010 12:42 PM, |-|ercules wrote: >>>>> "George Greene" <greeneg(a)email.unc.edu> wrote >>>>>>> Is it a *NEW DIGIT SEQUENCE* or not? >>>>>> >>>>>> YES, DUMBASS, IT IS A NEW DIGIT-SEQUENCE because it was >>>>>> NOT ON THE LIST of (allegedly "all") THE OLD digit-sequences! >>>>> >>>>> >>>>> But you keep saying the anti-diagonal is NEW and ignoring me when >>>>> I say it's not a new digit sequence. >>>>> >>>>> Then you repeat Cantor's proof again and again that it's NEW. >>>>> >>>>> You use terms NEW and NOT ON THE LIST, but evade me when I challenge >>>>> whether it contains any new digit sequence. >>>> >>>> And you just ignore the point that it must be new because it >>>> demonstrably isn't in the list. >>>> >>>> Sylvia. >>> >>> All you demonstrated was >> >> In what sense could a number be said to be in a list if it doesn't >> match any element of the list? > > > What sense is a number that's only definition is to not be on a list? > > That may seem less concrete than your question, but it's worth thinking > what "anti-diagonals" entail. > > You're not just constructing 0.444454445544444445444.. a 4 for every non > 4 digit and a 5 for a 4. > > You're constructing ALL 9 OTHER DIGITS to the diagonal digits. Why? We only need one number that's not in the list. Doing what you suggest just creates many more numbers that are not in the list. > > And it's not just the diagonal, it's the diagonal of ALL PERMUTATIONS OF > THE LIST. > > So, the first digit of the list can be... well anything, so the > antidiagonal starts with anything.. > then the second digit of the second real can be anything, so the > antidiagonals next digit is anything.. The problem with that is before you can permute a list, you have to prove that a list exists. If it doesn't exist, you can't permuted it. Cantor assumes that a list exists, and then proceeds to show that that leads to a contradiction. Which is fair enough. But you can't just assume the list exists, and then use arguments about permuting the list to prove that it exists, or to negate the proof that it doesn't exist. That's circular. <snipped rest based on false premise> Sylvia.
From: George Greene on 20 Jun 2010 10:32
On Jun 20, 2:59 am, "|-|ercules" <radgray...(a)yahoo.com> wrote: > I still maintain all possible variations of digit sequences are present > up to infinite width on the list. WHAT list? |