Can anyone spot the CONTRADICTION???
in [Math]
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From: |-|ercules on 15 Jun 2010 23:34 "Peter Webb" <webbfamily(a)DIESPAMDIEoptusnet.com.au> wrote > Cantor said and proved that > any purported list of all Reals cannot contain all Reals. His proof is > simple and clear, provides an explicit construction of at least one > missing Real. Like so... 123 456 789 Diag = 159 Anti-diag = 260 Where are you getting a (missing real) '260' when >the list of computable reals contain every digit of ALL possible infinite >sequences (3) ___________________________________________________________________ "Daryl McCullough" <stevendaryl3016(a)yahoo.com> wrote >>the list of computable reals contain every digit of ALL possible infinite >>sequences (3) >> >>OK does everyone get (1) (2) and (3). > > If you state it carefully, then yes, everyone gets it: ___________________________________________________________________ Herc
From: Math-a-nator on 16 Jun 2010 01:35 http://upload.wikimedia.org/wikipedia/commons/thumb/8/89/Trenecito.jpg/364px-Trenecito.jpg
From: George Greene on 16 Jun 2010 01:35 On Jun 15, 11:34 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > Where are you getting a (missing real) '260' when > > >the list of computable reals contain every digit of ALL possible infinite > >sequences IT DOESN'T, DUMBASS. The only reason you THINK it does is because YOU CAN'T SPEAK ENGLISH. There are ONLY TEN digits in this numeration system! "All you have to do to contain every digit" is contain all 10 of them, which you can do EITHER in the 1x10 list 0123456789, OR in the 10x1 list below! You do NOT NEED to use a list of infinitely wide "computable" reals (let alone the list of ALL of them, which is a list that itself IS NOT computable) in order to "contain every digit of ALL possible infinite sequences". The infinite list of all possible FINITE sequences (which IS computable) ALSO "contains", in YOUR sense of "contain" (a word which you personally are WAY TOO STUPID TO EVEN DEFINE) "every digit of all possible infinite sequences". In English, the phrase "every digit" IS SINGULAR. It generalizes over multiple cases, each of which means ONE digit. It means each and every digit TAKEN INDIVIDUALLY. For that reason, IN ADDITION to accomplishing your goal of "containing every digit of ALL possible infinite sequences" by using only the list of finite sequences, YOU COULD ALSO accomplish that goal using the following VERY finite 10x1 list: 0 1 2 3 4 5 6 7 8 9 .. THAT list contains every digit of all possible infinite sequences, since every digit IS ONE OF those 10 (in that number-base). If you are going to require one element of the list to contain multiple digits from the sequence in the correct order, then, OBVIOUSLY, NO computable real contains "every digit of" ANY (infinite) non-computable sequence ("infinite" was in parentheses because every non-computable sequence has to be infinite). If it contained ALL digits of some non- computable sequence (in the correct order and occurring the correct number of times, which, for at least two of the 10 digits, will be infinitely often), then IT WOULD BE EQUAL to the non-computable sequence, which would contradict the fact that it was computable. digit (in order) then it would be EQUAL to
From: |-|ercules on 16 Jun 2010 05:39 "George Greene" <greeneg(a)email.unc.edu> wrote > On Jun 15, 11:34 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: >> Where are you getting a (missing real) '260' when >> >> >the list of computable reals contain every digit of ALL possible infinite >> >sequences > > IT DOESN'T, DUMBASS. > The only reason you THINK it does is because YOU CAN'T SPEAK ENGLISH. > There are ONLY TEN digits in this numeration system! > "All you have to do to contain every digit" is contain all 10 of them, > which > you can do EITHER in the 1x10 list > 0123456789, > OR in the 10x1 list below! > > You do NOT NEED to use a list of infinitely wide "computable" reals > (let alone the list of ALL of them, which is a list that itself IS NOT > computable) > in order to "contain every digit of ALL possible infinite sequences". > > The infinite list of all possible FINITE sequences (which IS > computable) > ALSO "contains", in YOUR sense of "contain" (a word which you > personally > are WAY TOO STUPID TO EVEN DEFINE) "every digit of all possible > infinite sequences". > > In English, the phrase "every digit" IS SINGULAR. It generalizes over > multiple > cases, each of which means ONE digit. It means each and every digit > TAKEN INDIVIDUALLY. > For that reason, IN ADDITION to accomplishing your goal of > "containing every digit of ALL possible infinite sequences" > by using only the list of finite sequences, YOU COULD ALSO > accomplish that goal using the following VERY finite 10x1 list: > 0 > 1 > 2 > 3 > 4 > 5 > 6 > 7 > 8 > 9 > . > THAT list contains every digit of all possible infinite sequences, > since every digit IS ONE OF those 10 (in that number-base). > > If you are going to require one element of the list to contain > multiple digits > from the sequence in the correct order, then, OBVIOUSLY, NO computable > real contains "every digit of" ANY (infinite) non-computable sequence > ("infinite" was in parentheses because every non-computable sequence > has to be infinite). If it contained ALL digits of some non- > computable > sequence (in the correct order and occurring the correct number of > times, > which, for at least two of the 10 digits, will be infinitely often), > then IT WOULD BE > EQUAL to the non-computable sequence, which would contradict the fact > that > it was computable. > > digit (in order) then it would be EQUAL to ............? Why didn't you speak up in YESTERDAY'S topic? ***>the list of computable reals contain every digit of ALL possible infinite sequences (3) ***>OK does everyone get (1) (2) and (3). defn(herc_cant_3) The list of computable reals contains every digit (in order) of all possible infinite sequences. Derivation Given the increasing finite prefixes of pi 3 31 314 ... This list contains every digit (in order) of the infinite expansion of pi. Given the increasing finite prefixes of e 2 27 271 ... This list contains every digit (in order) of the infinite expansion of e. Given the increasing finite prefixes of ALL infinite expansions, that list contains every digit (in order) of every infinite expansion. So herc_cant_3 is true. The list of computable reals contains every digit (in order) of all possible infinite sequences. Herc
From: Tim Little on 16 Jun 2010 21:48
On 2010-06-16, |-|ercules <radgray123(a)yahoo.com> wrote: > defn(herc_cant_3) > The list of computable reals contains every digit (in order) of all > possible infinite sequences. So what? So does the finite list: 000... 111... 222... 333... 444... 555... 666... 777... 888... 999... For any digit in any position of any possible infinite sequence of decimal digits, there is an entry in the list that has that digit in the correct position. What do you think that proves? - Tim |