CANTOR DISPROOF <<<<<<<<<<<<<<<< [Math]

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From: Sylvia Else on 24 Jun 2010 22:14

On 25/06/2010 6:46 AM, Graham Cooper wrote:

> You want me to clarify what you wrote in my name?

What Mike and I are trying to do is to determine what the steps in your
proof actually mean. This turns out to be like getting blood out of a
stone. One could easily conclude that you don't actually want people to
understand your proof.
>
> Sheesh that's a new one.
>
> We can revert to 'possible sequences' rather than 'permutations'
> (from an infinite set of digits)

You can use any terminology you want. In that regard, all we ask is that
you define your terms, provide clarifications of them when
clarifications are requested, and then stick to the definitions as so
clarified.

Sylvia.

From: Alan Smaill on 25 Jun 2010 04:42

Graham Cooper <grahamcooper7(a)gmail.com> writes:

> On Jun 25, 2:46�pm, Sylvia Else <syl...(a)not.here.invalid> wrote:

[hey, you *can* snip when replying]

>> Herc, does your proof depend on the fact that the list is a list of
>> *all* computable reals, or not?
>>
>> If it does, then please prove that it is a list of them all.
>>
>> If not, please remove the word all from step 1 so that it doesn't
>> confuse things later on.
>>
>> Sylvia.
>
>
> It's a subset of all computer programs. Namely the ones
> that halt on every input. Namely the output of those programs
> as described in The TM list
>
> TM1
> TM2
> ...
>
>
> The tm list contains ALL computable numbers. As in a way
> to generate them.
>
> All computable numbers is a hypothetical list. A subset of
> outputs of all tms.
>
> It is your onus to have a list that is diagonalize-able
> so you are allowed to use a hypothetical list of purely
> numbers. As this Is a subset of the physically possible
> list of computer outputs (including blanks) the claim to
> list ALL the reals would still hold
>
> i provide a possible list of reals including blanks
> and you try to diagonalize the hypothetical subset of just numbers.

You can give that list just fine; it won't diagonalise.

* it would give back a "real" with blanks for some digits, and
* if a blank corresponds to a diagonal position, you might get something
you started with.

So what?
The argument doesn't apply in this case.
If you want to show there is something wrong, then
you have to start where the claim starts.

You can just omit the gaps -- but that's not computable.
You can forget about computability of the *list* and omit the
gaps -- but then you cannot show that the anti-diagonal
itself is computable.

>
> Herc

--
Alan Smaill

From: Graham Cooper on 25 Jun 2010 05:10

Can you trim the post. iPhone backspace works in 2 modes
letter at a time at 10hz or word at a time at 2hz. Very useful

Herc

From: Sylvia Else on 25 Jun 2010 06:23

On 25/06/2010 7:07 PM, Graham Cooper wrote:
> On Jun 25, 6:54 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:

>> OK.
>>
>> "1 start with an infinite list of all computable reals".
>>
>> That is any list of all the computable reals, howsoever constructed.
>>
>> "2 let w = the maximum width of complete permutation sets"
>>
>> Where a complete permutation set is all the possible combinations of
>> some finite number of digits. So this step doesn't involve doing
>> anything with the list described in step 1? It's a completely
>> independent step?
>>
>> Sylvia.
>
>
> Hmmm. Did you consider that the CPS found in the list of
> step 1 was what I meant. Step 1 - consider this list...
>

I'm reluctant to assume you mean anything unless it's stated. It seems
to cause difficulties. However, apparently CPS is an abbreviation for
"complete permutation set".

So the list of all computable reals contains as a subset complete
permutation sets whose width is unbounded. Slightly rewording 2, gives us:

"2 let w = the maximum width of those complete permutation sets"

and the next step is

"3 contradict 2"

How is it to be contradicted?

Sylvia.

From: Graham Cooper on 25 Jun 2010 13:40

On Jun 25, 8:23 pm, Sylvia Else <syl...(a)not.here.invalid> wrote:
> On 25/06/2010 7:07 PM, Graham Cooper wrote:
>
>
>
>
>
> > On Jun 25, 6:54 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
> >> OK.
>
> >> "1 start with an infinite list of all computable reals".
>
> >> That is any list of all the computable reals, howsoever constructed.
>
> >> "2 let w = the maximum width of complete permutation sets"
>
> >> Where a complete permutation set is all the possible combinations of
> >> some finite number of digits. So this step doesn't involve doing
> >> anything with the list described in step 1? It's a completely
> >> independent step?
>
> >> Sylvia.
>
> > Hmmm. Did you consider that the CPS found in the list of
> > step 1 was what I meant. Step 1 - consider this list...
>
> I'm reluctant to assume you mean anything unless it's stated. It seems
> to cause difficulties. However, apparently CPS is an abbreviation for
> "complete permutation set".
>
> So the list of all computable reals contains as a subset complete
> permutation sets whose width is unbounded. Slightly rewording 2, gives us:
>
> "2 let w = the maximum width of those complete permutation sets"
>
> and the next step is
>
> "3 contradict 2"
>
> How is it to be contradicted?
>
> Sylvia.

There is no (finite) maximum.

Yes i realize my answer resembles Rupert's

Herc