"Sylvia Else" <sylvia@not.here.invalid> wrote > On 19/06/2010 7:07 PM, |-|ercules wrote: >> "Sylvia Else" <sylvia@not.here.invalid> wrote ... >>> On 19/06/2010 4:11 PM, |-|ercules wrote: >>> >>>> To support your argument you should at least show that you've formed a >>>> new sequence of digits. >>> >>> I'll explain it simply then. The first digit of the created number >>> differs from the first digit of the first number in the list. The >>> second digit differs from the second digit of the second number in the >>> list. >>> >>> In general, digit n differs from digit n of the nth number in the list. >>> >>> So for all n, the created number differs from number n. Therefore the >>> created number is not in the list - it is a new sequence of digits. >> >> No I've told you all 20 times that does not create any new sequence at all. >> >> All you've done is >> CONSTRUCT a digit sequence like so >> An AD(n) =/= L(n,n) >> >> And then you say, it's different to each number like so >> >> PROOF >> An AD(n) =/= L(n,n) >> >> But you have not demonstrated a NEW SEQUENCE OF DIGITS. > > How can it not be a new sequence of digits if it's not in the list? > >> >> All you've done is this >> >> [ An AD(n) =/= L(n,n) -> An AD(n) =/= L(n,n) ] -> Superinfinity >> >> Your actual 'proof' is a specific example of the above 'proof'! >> >> [ An AD(n) = (L(n,n) + 1) mod 9 -> An AD(n) =/= L(n,n) ] -> Superinfinity >> >> Do you agree with the above version of Cantor's proof? > > That is not a statement of Cantor's proof. For a start, it leaves out > the assumption that the list of numbers is a list of all the reals. > >>>> >>>> If you actually read my derivation of herc_cant_3 instead of blindly >>>> dismissing it, >>>> you'll see it holds, just like all digits of PI appear in order below >>>> this line, if interpreted >>>> correctly. >>>> >>>> Herc >>>> >>>> ___________________ >>>> >>>> 3 >>>> 31 >>>> 314 >>>> 3141 >>>> ... >>>> >>>> >>> >>> herc-cant-3 is not a derivation. It's a wild leap of faith. Nothing is >>> proved therein. >>> >>> Sylvia. >> >> >> Then which step do you disagree with? >> >> >> 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. >> > > This one: > >> Given the increasing finite prefixes of ALL infinite expansions, >> that list contains every digit (in order) of every infinite expansion. > > You provide no justification for that statement. It doesn't follow from > what came previously. You just assert it. > > Sylvia.
If all digits of a single infinite expansion can be contained with increasing finite prefixes, and the computable set of reals has EVERY finite prefix, then all digits of EVERY infinite expansion are contained.
