THE CANTOR ARGUMENT SO FAR
in [Logic]
|
From: |-|ercules on 19 Jun 2010 22:42 "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. But I still maintain all possible variations of digit sequences are present up to infinite width on the list. Attacking the wording of the above does not attack the simple concept therein. The fact 0.1 and 0.2 are finite doesn't either. Do I have a point or not? I'm sure you all follow my meaning, but go on full offensive anyway and don't acknowledge what I MEAN. Herc
From: Rupert on 20 Jun 2010 01:12 On Jun 20, 8:21 am, "|-|ercules" <radgray...(a)yahoo.com> wrote: > ------------------------SCI.MATH----------------------------- > > Take any list of reals > > 123 > 456 > 789 > > Diag = 159 > AntiDiag = 260 > > It's a NEW DIGIT SEQUENCE and it works on EVERY LIST. > > ---------------------------HERC------------------------------ > > defn(herc_cant_3) > The list of computable reals contains every digit (in order) of all possible infinite sequences. > > ..as a result of containing ALL (infinitely many) finite prefixes. > > THEREFORE YOU CANNOT CONSTRUCT A NEW DIGIT SEQUENCE > > --------------------------SCI.MATH-------------------------- > > BUT: > > 0.0 > 0.1 > 0.2 > ... > 0.01 > 0.02 > 0.03 > ... > 0.99 > 0.101 > 0.102 > ... > > ALSO contains every finite prefix > > AND 0.111... is not on that list. > > THEREFORE ANTI-DIAG STILL *IS* A NEW DIGIT SEQUENCE. > > -----------------------------HERC------------------------------ > > A correction to a correction does not prove the original assertion. > > You STILL have not come up with a NEW DIGIT SEQUENCE. > > You use the term NEW DIGIT SEQUENCE for the finite example 260 > then you BAIT AND SWITCH and call it NEW NUMBER because > An AD(n) =/= L(n,n). > > Is it a *NEW DIGIT SEQUENCE* or not? > > Herc Let L be a countably infinite list of countably infinite sequences of decimal digits. Cantor's diagonal construction shows how to construct a sequence of decimal digits which is not in L. It is not in L, because, given any sequence which is in L, we can find a position for which the sequence in L differs from the sequence constructed by Cantor's diagonal construction.
From: |-|ercules on 20 Jun 2010 02:02 "Rupert" <rupertmccallum(a)yahoo.com> wrote > On Jun 20, 8:21 am, "|-|ercules" <radgray...(a)yahoo.com> wrote: >> ------------------------SCI.MATH----------------------------- >> >> Take any list of reals >> >> 123 >> 456 >> 789 >> >> Diag = 159 >> AntiDiag = 260 >> >> It's a NEW DIGIT SEQUENCE and it works on EVERY LIST. >> >> ---------------------------HERC------------------------------ >> >> defn(herc_cant_3) >> The list of computable reals contains every digit (in order) of all possible infinite sequences. >> >> ..as a result of containing ALL (infinitely many) finite prefixes. >> >> THEREFORE YOU CANNOT CONSTRUCT A NEW DIGIT SEQUENCE >> >> --------------------------SCI.MATH-------------------------- >> >> BUT: >> >> 0.0 >> 0.1 >> 0.2 >> ... >> 0.01 >> 0.02 >> 0.03 >> ... >> 0.99 >> 0.101 >> 0.102 >> ... >> >> ALSO contains every finite prefix >> >> AND 0.111... is not on that list. >> >> THEREFORE ANTI-DIAG STILL *IS* A NEW DIGIT SEQUENCE. >> >> -----------------------------HERC------------------------------ >> >> A correction to a correction does not prove the original assertion. >> >> You STILL have not come up with a NEW DIGIT SEQUENCE. >> >> You use the term NEW DIGIT SEQUENCE for the finite example 260 >> then you BAIT AND SWITCH and call it NEW NUMBER because >> An AD(n) =/= L(n,n). >> >> Is it a *NEW DIGIT SEQUENCE* or not? >> >> Herc > > Let L be a countably infinite list of countably infinite sequences of > decimal digits. Cantor's diagonal construction shows how to construct > a sequence of decimal digits which is not in L. It is not in L, > because, given any sequence which is in L, we can find a position for > which the sequence in L differs from the sequence constructed by > Cantor's diagonal construction. Hypothesis: a real number contains a finite sequence that is not computable. Contradiction Therefore: all digits of every real are contained in the list of computable reals. _________________________________________________________________ This may not IMPLY that all infinite digit sequences are computable, but it trivially defeats this argument: 123 456 789 Diag = 159 AntiDiag = 260 A new digit sequence can be found on all real lists. Herc
From: Sylvia Else on 20 Jun 2010 02:50 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.
From: |-|ercules on 20 Jun 2010 02:59
"George Greene" <greeneg(a)email.unc.edu> wrote >> But I still maintain all possible variations of digit sequences are present >> up to infinite width on the list. > > You DO NOT maintain that. > A number is either on the list or it isn't. > All FINITE PREFIXES of a number being on the list IS NOT THE SAME > THING AS > THE NUMBER being on the list! I still maintain all possible variations of digit sequences are present up to infinite width on the list. Herc |