"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.
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?
> >> >> 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.
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 -- "There are more things in Cantor's paradise, Horatio, than are dreamt of by your computers." ~ Barb Knox
