CANTOR DISPROOF <<<<<<<<<<<<<<<<
in [Logic]
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From: |-|ercules on 20 Jun 2010 03:14 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 -- If you ever rob someone, even to get your own stuff back, don't use the phrase "Nobody leave the room!" ~ OJ Simpson
From: Math-a-nator on 20 Jun 2010 11:33 POST IT *AGAIN*!!!! *POST IT* TO SCI.MATH!!!! POST IT *EVERY SINGLE* DAY!!!! POST IT *BEFORE* YOU POST IT!!!! POST IT *AFTER* YOU POST IT!!!! POST IT *AGAIN*!!!! "|-|ercules" <radgray123(a)yahoo.com> wrote in message news:885tecF9rsU1(a)mid.individual.net... > Hypothesis: Ah have nothin to day and ah am sayin it.
From: |-|ercules on 20 Jun 2010 12:45 "Math-a-nator" <MorePornLips(a)example.com> wrote... >> Hypothesis: Ah have nothin to day and ah am sayin it. > > 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: Colin on 20 Jun 2010 13:19 On Jun 20, 11:45 am, "|-|ercules" <radgray...(a)yahoo.com> wrote: > [snip] (Yawn.) So, you're spewing your usual jism that there's nothing more to the real numbers than the computable reals, i.e., that "real number" and "computable real" are synonyms? Well, Master Debater, riddle me this: everyone knows the real numbers are closed under the basic operation of taking the supremum of a bounded sequence. Can you prove this is true of the computable reals?
From: George Greene on 20 Jun 2010 13:38
On Jun 20, 3:14 am, "|-|ercules" <radgray...(a)yahoo.com> wrote: > Hypothesis: a real number contains a finite sequence that is not computable. This IS NOT the hypothesis. The hypothesis (yours) IS that EVERY real is computable. THAT PROVABLY LEADS to a contradiction (since computer programs HAVE to be finite and there are therefore only a countably infinite number of them, the same number AS THERE ARE DIGITS in a real, which means that the list of computable reals IS SQUARE). > Contradiction You can't just SAY "Contradiction"! You have TO PROVE THAT there is a contradiction. There isn't. All finite prefixes of a real being on a list IS NOT THE SAME AS the real ITSELF being on the list. Pi IS NOT ON the list of all its finite prefixes. The decimal expansion of 1/3 IS NOT ON the list of all its finite prefixes. You, unfortunately, ARE SO DAMN STUPID that you will insist on talking about strings bearing some relation to a list OTHER than BEING ON IT (or not). Being ON the list, being an actual ELEMENT OF the list, is THE ONLY thing that ACTUALLY MATTERS for purposes of these proofs. > Therefore: all digits of every real are contained in the list of computable reals. Well, yes, if the mere existence of a non-computable real implied a contradiction, THEN that WOULD imply that all reals were computable. BUT IT DOESN'T, SO THEY AREN'T. > _________________________________________________________________ > > This may not IMPLY that all infinite digit sequences are computable, YES, DUMBASS, IT WOULD imply that, IF you could derive that contradiction! > but it trivially defeats this argument: What is the ANTECEDENT of your pronoun "it" above?? YOU HAVE NOT SUPPLIED anything THAT COULD "trivially defeat this argument"! > > 123 > 456 > 789 > > Diag = 159 > AntiDiag = 260 > > A new digit sequence can be found on all real lists. You cannot EVEN STATE the argument, DUMBASS! The new sequence IS NOT ON the list it CAME from! The anti-diagonal is NOT on the list! The new digit sequence canNOT be found ON the list -- that is what MAKES it NEW! The new digit sequence is (instead) computed FROM the list! |