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.
