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

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From: herbzet on 21 Jun 2010 01:16

Daryl McCullough wrote:
>
> So what's really going on here, in the minds of several people, is that
> Herc is a complete ignoramus, and is mathematically incompetent, and the
> reason he can't accept Cantor's theorem is because he lacks the patience,
> intelligence, mathematical training, and reasoning ability necessary to
> follow a simple mathematical proof.
>
> In Herc's mind, something very different is happening. Cantor made a
> bogus proof, and for whatever reason, many mathematicians were bamboozled
> into believing that it was correct. Ever since then, logic students have
> been brainwashed into accepting this bogus proof, and are either unable
> or unwilling to see it as nonsense. They don't want to rock the boat,
> or they are too timid to question authority, or they are just sheep who
> believe anything they are told by the "experts" regardless of how
> nonsensical.
>
> (You can replace "Herc" by "WM" here, and you get essentially the same
> two alternate explanations of what is going on.)
>
> People arguing with Herc are in essence attempting to come up with
> a convincing case that Herc is a complete mathematical incompetent.
> (And here's the tough part) The argument that Herc is an incompetent
> has to be convincing to Herc, himself.

No it doesn't -- sheesh.

> This is an almost inconsistent
> requirement. If Herc is incompetent (which he certainly seems to be)
> then how can you possibly convince HIM of that fact? You can give
> him arguments, but by assumption, he is incompetent at recognizing
> valid arguments (if he could recognize valid arguments, he wouldn't
> be disputing Cantor's proof).
>
> My conjecture is that it is completely impossible to make a dent in
> the convictions of people like Herc and WM. It doesn't help to give
> a valid argument to people incapable of recognizing valid arguments.

Herc is a troll who is HAVING A BALL jerking all the "smart guys" around.

What a bunch of maroons.

--
hz

From: |-|ercules on 21 Jun 2010 01:40

"Sylvia Else" <sylvia(a)not.here.invalid> wrote ...
> On 21/06/2010 1:11 PM, |-|ercules wrote:
>> "Sylvia Else" <sylvia(a)not.here.invalid> wrote
>>> On 21/06/2010 2:45 AM, |-|ercules wrote:
>>>> "Math-a-nator" <MorePornLips(a)example.com> wrote...
>>>>>> Hypothesis: Ah have nothin to day and ah am sayin it.
>>>>>
>>>>>
>>>>
>>>>
>>>>
>>>>
>>>> it's worth thinking what "anti-diagonals" entail.
>>>>
>>>> You're not just constructing 0.444454445544444445444.. a 4 for every non
>>>> 4 digit and a 5 for a 4.
>>>>
>>>> You're constructing ALL 9 OTHER DIGITS to the diagonal digits.
>>>>
>>>> And it's not just the diagonal, it's the diagonal of ALL PERMUTATIONS OF
>>>> THE LIST.
>>>
>>> Why?
>>>
>>> Suppose you have your list, and you label each line.
>>>
>>>
>>> 1 0.xxxxxx
>>> 2 0.yyyyy
>>> 3 0.zzzzzz
>>> 4 0.aaaaa
>>> 5 0.bbbbb
>>>
>>> Now choose your anti-diagonal. For this purpose, X is anti-x, and so
>>> on. So the anti-diagonal is 0.XYZAB.
>>>
>>> X != x in line labelled 1, Y != y in line labelled 2, and so on.
>>> Clearly, it's not in the list.
>>>
>>> Now permute your list. Note that the lines retain their labels.
>>>
>>> 4 0.aaaaa
>>> 2 0.yyyyy
>>> 1 0.xxxxxx
>>> 3 0.zzzzzz
>>> 5 0.bbbbb
>>>
>>> It is still true that X != x in line labelled 1, Y != y in line
>>> labelled 2, and so on. Clearly, the 0.XYZAB is still not in the list.
>>> We can also immediately see that 0.AYXZB is not in the list either. So
>>> now we have two numbers that are not in the list.
>>>
>>> Sylvia.
>>
>>
>> There is no structure in the anti-diagonal. Well there is SOME if you
>> choose 0.222... and it can't cross 0.1111... on the list.
>>
>> You select ANY digit at all, then select ANY digit at all for digit 2,
>> keep on going and it criss crosses through the infinite list in
>> diametrically
>> opposed digital fashion.
>>
>> You've lost the plot. The anti-diagonal had SOME HOPE of establishing
>> a missing element because it had any_digit_that_was_different, but when
>> it can be selected at will from any of infinite digits, the ONLY criterion
>> is you eventually fill the list selections top down, anti-diag is
>> practically ANYTHING.
>>
>> It's really ridiculous to jump to the conclusion there's infinitely more
>> zig zag
>> missing reals when you can't specify a new sequence of digits.
>> Why cannot ANYONE see that the finite NEW SEQUENCE just isn't happening!
>>
>> 123
>> 456
>> 789
>>
>> Diag = 159
>> AntiDiag = 260
>
> 260 certainly isn't in the list. As it happens 159 isn't either, but
> it's easy enough to construct a list such that the diagonal is in the list.
>
> 159
> 456
> 789
>
> Diag = 159, in the list
> AntiDiag = 260, not in the list.
>
> Show me a list where I cannot construct an antidiagonal that is not in
> the list.
>
> Sylvia.

After 2 weeks someone took the bait.

My claim for the last 2 weeks is that new sequence just isn't happening!

Because of ole herc_cant_3.

Here are 2 derivations of herc_cant_3.

Derivation 1

Assume the hypothesis: there is a unique finite sequence of digits in some real
that is not computable.

Obvious contradiction.

Therefore: ALL digits of EVERY real appear in order in the computable set of reals.

Derivation 2

3
31
314
...

This list contains all digits in order of PI.

That list was all finite subsequences of PI.

The set of computable reals contains all finite subsequences of every real.

Set contains all finite subsequences of X -> set contains all digits of X in order.

Therefore

X = all reals

The set of computable reals contains all digits in order of all reals.

Do you follow either of those derivations of herc_cant_3?

Herc

From: Sylvia Else on 21 Jun 2010 01:42

On 21/06/2010 3:16 PM, herbzet wrote:

>
> Herc is a troll who is HAVING A BALL jerking all the "smart guys" around.

Or not. Herc is a paranoid schizophrenic, and subject to a variety of
delusions. What isn't clear is whether this Cantor stuff is a
conventional misunderstanding, or yet another delusion.

Sylvia.

From: |-|ercules on 21 Jun 2010 01:48

"Sylvia Else" <sylvia(a)not.here.invalid> wrote...
> On 21/06/2010 3:16 PM, herbzet wrote:
>
>>
>> Herc is a troll who is HAVING A BALL jerking all the "smart guys" around.
>
> Or not. Herc is a paranoid schizophrenic, and subject to a variety of
> delusions.

None of which you have proven.

I've been saying proof on sight for 8 years, onus is on you.

Herc

From: Sylvia Else on 21 Jun 2010 01:53

On 21/06/2010 3:40 PM, |-|ercules wrote:
> "Sylvia Else" <sylvia(a)not.here.invalid> wrote ...
>> On 21/06/2010 1:11 PM, |-|ercules wrote:
>>> "Sylvia Else" <sylvia(a)not.here.invalid> wrote
>>>> On 21/06/2010 2:45 AM, |-|ercules wrote:
>>>>> "Math-a-nator" <MorePornLips(a)example.com> wrote...
>>>>>>> Hypothesis: Ah have nothin to day and ah am sayin it.
>>>>>>
>>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> it's worth thinking what "anti-diagonals" entail.
>>>>>
>>>>> You're not just constructing 0.444454445544444445444.. a 4 for
>>>>> every non
>>>>> 4 digit and a 5 for a 4.
>>>>>
>>>>> You're constructing ALL 9 OTHER DIGITS to the diagonal digits.
>>>>>
>>>>> And it's not just the diagonal, it's the diagonal of ALL
>>>>> PERMUTATIONS OF
>>>>> THE LIST.
>>>>
>>>> Why?
>>>>
>>>> Suppose you have your list, and you label each line.
>>>>
>>>>
>>>> 1 0.xxxxxx
>>>> 2 0.yyyyy
>>>> 3 0.zzzzzz
>>>> 4 0.aaaaa
>>>> 5 0.bbbbb
>>>>
>>>> Now choose your anti-diagonal. For this purpose, X is anti-x, and so
>>>> on. So the anti-diagonal is 0.XYZAB.
>>>>
>>>> X != x in line labelled 1, Y != y in line labelled 2, and so on.
>>>> Clearly, it's not in the list.
>>>>
>>>> Now permute your list. Note that the lines retain their labels.
>>>>
>>>> 4 0.aaaaa
>>>> 2 0.yyyyy
>>>> 1 0.xxxxxx
>>>> 3 0.zzzzzz
>>>> 5 0.bbbbb
>>>>
>>>> It is still true that X != x in line labelled 1, Y != y in line
>>>> labelled 2, and so on. Clearly, the 0.XYZAB is still not in the list.
>>>> We can also immediately see that 0.AYXZB is not in the list either. So
>>>> now we have two numbers that are not in the list.
>>>>
>>>> Sylvia.
>>>
>>>
>>> There is no structure in the anti-diagonal. Well there is SOME if you
>>> choose 0.222... and it can't cross 0.1111... on the list.
>>>
>>> You select ANY digit at all, then select ANY digit at all for digit 2,
>>> keep on going and it criss crosses through the infinite list in
>>> diametrically
>>> opposed digital fashion.
>>>
>>> You've lost the plot. The anti-diagonal had SOME HOPE of establishing
>>> a missing element because it had any_digit_that_was_different, but when
>>> it can be selected at will from any of infinite digits, the ONLY
>>> criterion
>>> is you eventually fill the list selections top down, anti-diag is
>>> practically ANYTHING.
>>>
>>> It's really ridiculous to jump to the conclusion there's infinitely more
>>> zig zag
>>> missing reals when you can't specify a new sequence of digits.
>>> Why cannot ANYONE see that the finite NEW SEQUENCE just isn't happening!
>>>
>>> 123
>>> 456
>>> 789
>>>
>>> Diag = 159
>>> AntiDiag = 260
>>
>> 260 certainly isn't in the list. As it happens 159 isn't either, but
>> it's easy enough to construct a list such that the diagonal is in the
>> list.
>>
>> 159
>> 456
>> 789
>>
>> Diag = 159, in the list
>> AntiDiag = 260, not in the list.
>>
>> Show me a list where I cannot construct an antidiagonal that is not in
>> the list.
>>
>> Sylvia.
>
> After 2 weeks someone took the bait.

But you can't do what I asked, and it has nothing to do with what
follows anyway.

>
> My claim for the last 2 weeks is that new sequence just isn't happening!
>
> Because of ole herc_cant_3.
>
> Here are 2 derivations of herc_cant_3.
>
> Derivation 1
>
> Assume the hypothesis: there is a unique finite sequence of digits in
> some real
> that is not computable.
>
> Obvious contradiction.

Therefore there is no unique finite sequence of digits in some real that
is not computable.

>
> Therefore: ALL digits of EVERY real appear in order in the computable
> set of reals.

That doesn't follow. A contradiction implies the inverse of the
assumption, and nothing more.

>
> Derivation 2
>
> 3
> 31
> 314
> ..
>
> This list contains all digits in order of PI.
>
> That list was all finite subsequences of PI.

This next step is in reality a wild leap.

>
> The set of computable reals contains all finite subsequences of every real.

As is the next.

>
> Set contains all finite subsequences of X -> set contains all digits of
> X in order.
>
> Therefore
>
> X = all reals
>
> The set of computable reals contains all digits in order of all reals.
>
> Do you follow either of those derivations of herc_cant_3?

Nup.

Sylvia.