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

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From: Sylvia Else on 23 Jun 2010 02:30

On 23/06/2010 3:52 PM, herbzet wrote:
>
>
> Mike Terry wrote:
>> "Sylvia Else" wrote:
>>> herbzet wrote:
>>>> Sylvia Else wrote:
>>>>> 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 implies that he is not also a troll.
>>>>
>>>>> What isn't clear is whether this Cantor stuff is a
>>>>> conventional misunderstanding, or yet another delusion.
>>>>
>>>> It's the same old tired Cantor troll b.s.
>>>
>>> I didn't realise before how long this has been going on for.
>>>
>>> But I don't think he's a troll - he appears to have a genuine belief
>>> that the world's mathematicians have got this wrong. If it's a
>>> conventional misunderstanding, he might yet be persuaded that he is
>>> mistaken.
>>
>> Personally I can't see this ever happening. When I started off with Herc
>> (years ago), it seemed like he was just making a simple mistake, and so it
>> should be easy enough to show where this mistake was. (And indeed it is
>> easy in a mathematical sense...)
>>
>> As I went further, I realised Herc knows nothing of normal mathematical
>> definitions (like um.. like the ones used in Cantor's proofs which he is
>> discussing), and nothing of mathematical reasoning (proofs starting from
>> definitions etc.). Also he has his own unclear (contradictory maybe?)
>> definitions for words he uses. So obviously a bit more work than I first
>> thought! :)
>>
>> Still, I thought if I break everything down into smaller and smaller steps,
>> explain exactly all the definitions involved, get Herc to clarify his own
>> definitions to make them precise etc., then I could still get him to realise
>> he's mistaken.
>>
>> But there is a much more basic problem - Herc actually refuses to engage in
>> "normal mathematical dialog". What I mean is that if you and I discussed
>> something, and I didn't understand a step in your proof, I'd point out what
>> I didn't understand, and you'd go away and expand the proof until I was
>> happy. Similarly, if I used a vague term, you could ask me to clarify it,
>> and I would break it down into well understood basic notions, quantifiers,
>> etc., and we'd move on... Neither of us would be offended by the process or
>> think we were being insulted, it's just business as usual for communicating
>> mathematics.
>>
>> Actually, I've never really thought of this as a "mathematical" skill, as
>> I've always thought of mathematics as being the interesting stuff we do on
>> top of all that. It's a basic skill which I'm sure I had around the age of
>> 10 (once I'd read simple proofs like the infinitude of the primes etc.),
>> although clearly at that age I didn't understand many definitions.
>>
>> Anyway, it's to be expected that posters won't all have the same level of
>> knowledge of working definitions, which is why we have "normal mathematical
>> dialog" to get along! I believe it's impossible to "talk maths" with
>> someone who simply refuses to engage in this behaviour.
>>
>> This includes Herc - I don't believe he will ever respond to a request to
>> clarify something into simpler terms. (Maybe some people's brains just
>> don't work in that analytic way?, and so they don't understand the need for
>> it?) And if you suggest a precise definition for something vague Herc is
>> saying, he will neither confirm nor deny that that is what he meant. (He
>> may even scold you for introducing irrelevent factors into the argument, and
>> suggest you should just ask him to explain, but if you do that of course you
>> won't get much of a clarification!)
>>
>> So what will Herc actually do if you follow my earlier idea of explaining in
>> greater and greater detail, asking for clarifications, refusing to go along
>> with vague confusing terminology until it is clarified and so on? [I
>> thought that surely if I did this thoroughly enough, Herc would have NO
>> CHOICE but to agree where he was wrong, or at least he would have to reply
>> in such a way that it was obvious to himself and others that he was not able
>> to answer the questions and support his claims.]
>>
>> The answer is that Herc will just ignore all your efforts and respond with
>> something vague, unrelated to the detail of your postings. E.g. he will
>> ignore your questions and ask you to "go away and work out all the possible
>> antidiagonals", or something. Perhaps he will write a piece at the end of
>> your post telling you where YOU are going wrong, and repeat his demand that
>> you answer some ambiguous or irrelevent question. (And yes, with enough
>> persistence he will become abusive.) What he WILL NOT do is respond
>> meaningfully to any requests for mathematical clarification! Later on he'll
>> start another thread using the same unclear terminology, and nothing will
>> have moved on.
>>
>> I think Herc's problem with Cantor's are only sustainable while he is
>> allowed to confuse himself with his
>> ambiguous/contradictory/plain-old-incorrect terminology, but while he will
>> not engage in "meaningful mathematical dialogue" I don't see how anything
>> will change...
>
> Good stuff, Mike.
>
> But in your YEARS of dealing with Herc, has the idea not occurred
> to you that Herc is arguing in bad faith? That he is a TROLL who
> is HAVING A BALL jerking around a dumb sucker for YEARS AT A STRETCH?
>
> Has that idea not occurred to you, Mike?
>

I'm sure it's occured to him, just as it's occured to me.

But Herc is the person who got himself arrested, charged and locked up
(though not convicted) over an apparent threat to contaminate food in
relation to Australian Skeptics Association's refusal to test him for
his channeling ability.

http://www.theage.com.au/articles/2002/03/08/1015365742538.html

I suppose that might just mean that he's a paranoid schizophrenic who's
also a troll, but given that schizophrenic's are prone to delusions, it
seems entirely likely that he genuinely believes his position, and has
pressed it over years because he feels, albeit misguidedly, that it's a
point that needs to be got across. Of course, that would also mean that
our attempts to correct him are an exercise in futility. But much is
learned in the process of trying to explain something to someone else,
even if that other person never understands.

Sylvia.

From: Sylvia Else on 23 Jun 2010 02:33

On 23/06/2010 4:15 PM, herbzet wrote:
>
>
> Sylvia Else wrote:
>> herbzet wrote:
>>> Sylvia Else wrote:
>>>> Graham Cooper wrote:
>>>>> Sylvia Else wrote:
>>>>>> Sylvia Else wrote:
>>>>>>> Graham Cooper wrote:
>>>>>>
>>>>>>>> IN FACT
>>>>>>
>>>>>>>> 3 It takes 10^x reals to list every permutation of digits x digits
>>>>>>>> wide
>>>>>>>> So with infinite reals you can list Every permutation of digits
>>>>>>>> infinite digits wide.
>>>>>>
>>>>>>> That's just an assertion. Let's see your proof. You might think it's
>>>>>>> obvious, but in Maths, obvious doesn't count.
>>>>>>
>>>>>>> Sylvia.
>>>>>>
>>>>>> Are you going to ignore this Herc? Let's see the colour of your money.
>>>>>> If you can prove it, do so.
>>>>>
>>>>> You agreed the width of all permutations approached oo
>>>>> since the list of reals is considered infinitely long
>>>>> your claim is that the limit does not equal the infinite case
>>>>
>>>> The width is not in question. What you have failed to prove is that
>>>> every permutation can be *listed*. Since that's the core issue in your
>>>> entire attack on Cantor, you cannot be allowed to get away with merely
>>>> asserting it. Prove it!
>>>
>>> Idiot -- is it not clear by now that he's not going to do that?
>>>
>>> Do you imagine that you're going to "corner" Herc somehow into
>>> displaying some rigor? Do you enjoying chasing after that dollar
>>> bill on a string?
>>
>> I can do it until I get bored, can't I? Sometimes it's not the
>> destination that's important, but the journey.
>
> Well, there's plenty of abusive people around for you to waste
> your time on, if that's your thing.

His abusiveness is unfortunate, and I wish he'd control himself. On the
other hand, he provides useful practice at arguing with abusive people.
The particular lesson is to remember what it is one is trying to
achieve, and not to allow oneself to be provoked.

Sylvia.

From: Graham Cooper on 23 Jun 2010 02:37

On Jun 23, 4:04 pm, Sylvia Else <syl...(a)not.here.invalid> wrote:
> On 23/06/2010 3:03 PM, Graham Cooper wrote:
>
>
>
>
>
> > On Jun 23, 3:00 pm, Graham Cooper<grahamcoop...(a)gmail.com> wrote:
> >> On Jun 23, 2:57 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
>
> >>> On 23/06/2010 2:30 PM, Graham Cooper wrote:
>
> >>>> On Jun 23, 1:02 pm, Graham Cooper<grahamcoop...(a)gmail.com> wrote:
> >>>>> On Jun 23, 12:56 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
>
> >>>>>> On 23/06/2010 12:45 PM, Graham Cooper wrote:
>
> >>>>>>> On Jun 23, 12:25 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
> >>>>>>>> On 23/06/2010 10:09 AM, Sylvia Else wrote:
>
> >>>>>>>>> On 22/06/2010 4:49 PM, Graham Cooper wrote:
>
> >>>>>>>>>> IN FACT
>
> >>>>>>>>>> 3 It takes 10^x reals to list every permutation of digits x digits
> >>>>>>>>>> wide
> >>>>>>>>>> So with infinite reals you can list Every permutation of digits
> >>>>>>>>>> infinite digits wide.
>
> >>>>>>>>> That's just an assertion. Let's see your proof. You might think it's
> >>>>>>>>> obvious, but in Maths, obvious doesn't count.
>
> >>>>>>>>> Sylvia.
>
> >>>>>>>> Are you going to ignore this Herc? Let's see the colour of your money.
> >>>>>>>> If you can prove it, do so.
>
> >>>>>>>> Sylvia.
>
> >>>>>>> You agreed the width of all permutations approached oo
> >>>>>>> since the list of reals is considered infinitely long
> >>>>>>> your claim is that the limit does not equal the infinite case
>
> >>>>>> The width is not in question. What you have failed to prove is that
> >>>>>> every permutation can be *listed*. Since that's the core issue in your
> >>>>>> entire attack on Cantor, you cannot be allowed to get away with merely
> >>>>>> asserting it. Prove it!
>
> >>>>>> Sylvia.
>
> >>>>> Consider the list of computable reals.
>
> >>>>> Let w = the digit width of the largest set
> >>>>> of complete permutations
>
> >>>>> assume w is finite
> >>>>> there are 10 computable copies of the
> >>>>> complete permutations of width w
> >>>>> each ending in each of digits 0..9
> >>>>> which generates a set larger than width w
> >>>>> so finite w cannot be the maximum size
>
> >>>>> therefore w is infinite
>
> >>>>> Herc
>
> >>>> Where I say a sequence ends in a new
> >>>> digit I meant that new digit is at position w+1
> >>>> appended to the sequence
>
> >>>> Herc
>
> >>> And yet another proof that w is infinite when I'm clearly asking for a
> >>> proof that every permutation can be *listed*.
>
> >>> Let me ask this as a direct question - are you of the opinion that
> >>> infinite length implies listability?
>
> >>> Sylvia.
>
> >> Exactly what younare asking.
>
> >> Are you shifting the goals to whether an infinite list exists?
>
> >> Herc
>
> >> You're a nutter Sylvia. I gave a procedure for iterating
> >> infinitely wide permutations on a countable list.
>
> > iPhones are difficult to type
>
> >> You're a nutter Sylvia. I gave a procedure for iterating
> >> infinitely wide permutations on a countable list.
>
> > Exactly what you are asking .......
>
> It seemed a reasonable question. I ask for a proof of listability, and
> you provide a proof that the width is infinite.
>
> Leaving that aside, perhaps you're under the impression that this
> process, copied from another posting of yours
>
> ---
>
> Given a set of complete permutations w digits wide
>
> eg
>
> 00
> 01
> 10
> 11
>
> make 2 copies and append each of 0,1
>
> 00+0
> 01+0
> 10+0
> 11+0
>
> 00+1
> 01+1
> 10+1
> 11+1
> ----
>
> and extended indefinitely, ultimately lists all permutations.
>
> It's certainly an infinite list of permutations, but you haven't proved
> that it contains all of them. Since it's infinite in length, you can't
> go through them to check. Instead you need to identify an algorithm that
> will allow you to take any permutation and determine, in finite time,
> the finite number that defines its position in the list. With such an
> algorithm you could then say that since you can identify the position in
> the list of any permutation, the list must contain them all.
>
> With a list of rationals constructed using a diagonal method this is
> straight forward.
>
> http://en.wikipedia.org/wiki/File:Diagonal_argument.svg
>
> With a given rational expressed in decimal, you try multiplying it by
> sucessively higher prime numbers until the result is an integer. Since
> the original divisor must be finite, this will be achieved in finite
> time. This gives you the two numbers that form the ratio. The number of
> the position in the list is then just the number of steps through a
> diagonal chart required to reach that pair of numbers (the red ones are
> not counted, because the two numbers are not co-prime).
>
> http://en.wikipedia.org/wiki/File:Diagonal_argument.svg
>
> Since it's obvious that any pair of numbers can be reached after a
> finite number of steps, this proves that all the rationals are in the list.
>
> To prove that all permutations are in the list, you need to do something
> similar. So far you haven't.
>
> Sylvia.

The proof I just gave to count all permutations of oo width
is a different nature to counting all rationals.

Proving all permutations oo digits wide and proving it can be
done on a countable list is the one same proof.

Herc

From: herbzet on 23 Jun 2010 02:38

Sylvia Else wrote:
> herbzet wrote:
> > Sylvia Else wrote:
> >> herbzet wrote:
> >>> Sylvia Else wrote:
> >>>> Graham Cooper wrote:
> >>>>> Sylvia Else wrote:
> >>>>>> Sylvia Else wrote:
> >>>>>>> Graham Cooper wrote:
> >>>>>>
> >>>>>>>> IN FACT
> >>>>>>
> >>>>>>>> 3 It takes 10^x reals to list every permutation of digits x digits
> >>>>>>>> wide
> >>>>>>>> So with infinite reals you can list Every permutation of digits
> >>>>>>>> infinite digits wide.
> >>>>>>
> >>>>>>> That's just an assertion. Let's see your proof. You might think it's
> >>>>>>> obvious, but in Maths, obvious doesn't count.
> >>>>>>
> >>>>>>> Sylvia.
> >>>>>>
> >>>>>> Are you going to ignore this Herc? Let's see the colour of your money.
> >>>>>> If you can prove it, do so.
> >>>>>
> >>>>> You agreed the width of all permutations approached oo
> >>>>> since the list of reals is considered infinitely long
> >>>>> your claim is that the limit does not equal the infinite case
> >>>>
> >>>> The width is not in question. What you have failed to prove is that
> >>>> every permutation can be *listed*. Since that's the core issue in your
> >>>> entire attack on Cantor, you cannot be allowed to get away with merely
> >>>> asserting it. Prove it!
> >>>
> >>> Idiot -- is it not clear by now that he's not going to do that?
> >>>
> >>> Do you imagine that you're going to "corner" Herc somehow into
> >>> displaying some rigor? Do you enjoying chasing after that dollar
> >>> bill on a string?
> >>
> >> I can do it until I get bored, can't I? Sometimes it's not the
> >> destination that's important, but the journey.
> >
> > Well, there's plenty of abusive people around for you to waste
> > your time on, if that's your thing.
>
> His abusiveness is unfortunate, and I wish he'd control himself. On the
> other hand, he provides useful practice at arguing with abusive people.
> The particular lesson is to remember what it is one is trying to
> achieve, and not to allow oneself to be provoked.

Rationalize away.

I've no more time to waste on an apologist for Herc.

--
hz

From: Graham Cooper on 23 Jun 2010 02:43

On Jun 23, 3:52 pm, herbzet <herb...(a)gmail.com> wrote:
> Mike Terry wrote:
> > "Sylvia Else" wrote:
> > > herbzet wrote:
> > > > Sylvia Else wrote:
> > > >> 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 implies that he is not also a troll.
>
> > > >> What isn't clear is whether this Cantor stuff is a
> > > >> conventional misunderstanding, or yet another delusion.
>
> > > > It's the same old tired Cantor troll b.s.
>
> > > I didn't realise before how long this has been going on for.
>
> > > But I don't think he's a troll - he appears to have a genuine belief
> > > that the world's mathematicians have got this wrong. If it's a
> > > conventional misunderstanding, he might yet be persuaded that he is
> > > mistaken.
>
> > Personally I can't see this ever happening. When I started off with Herc
> > (years ago), it seemed like he was just making a simple mistake, and so it
> > should be easy enough to show where this mistake was. (And indeed it is
> > easy in a mathematical sense...)
>
> > As I went further, I realised Herc knows nothing of normal mathematical
> > definitions (like um.. like the ones used in Cantor's proofs which he is
> > discussing), and nothing of mathematical reasoning (proofs starting from
> > definitions etc.). Also he has his own unclear (contradictory maybe?)
> > definitions for words he uses. So obviously a bit more work than I first
> > thought! :)
>
> > Still, I thought if I break everything down into smaller and smaller steps,
> > explain exactly all the definitions involved, get Herc to clarify his own
> > definitions to make them precise etc., then I could still get him to realise
> > he's mistaken.
>
> > But there is a much more basic problem - Herc actually refuses to engage in
> > "normal mathematical dialog". What I mean is that if you and I discussed
> > something, and I didn't understand a step in your proof, I'd point out what
> > I didn't understand, and you'd go away and expand the proof until I was
> > happy. Similarly, if I used a vague term, you could ask me to clarify it,
> > and I would break it down into well understood basic notions, quantifiers,
> > etc., and we'd move on... Neither of us would be offended by the process or
> > think we were being insulted, it's just business as usual for communicating
> > mathematics.
>
> > Actually, I've never really thought of this as a "mathematical" skill, as
> > I've always thought of mathematics as being the interesting stuff we do on
> > top of all that. It's a basic skill which I'm sure I had around the age of
> > 10 (once I'd read simple proofs like the infinitude of the primes etc.),
> > although clearly at that age I didn't understand many definitions.
>
> > Anyway, it's to be expected that posters won't all have the same level of
> > knowledge of working definitions, which is why we have "normal mathematical
> > dialog" to get along! I believe it's impossible to "talk maths" with
> > someone who simply refuses to engage in this behaviour.
>
> > This includes Herc - I don't believe he will ever respond to a request to
> > clarify something into simpler terms. (Maybe some people's brains just
> > don't work in that analytic way?, and so they don't understand the need for
> > it?) And if you suggest a precise definition for something vague Herc is
> > saying, he will neither confirm nor deny that that is what he meant. (He
> > may even scold you for introducing irrelevent factors into the argument, and
> > suggest you should just ask him to explain, but if you do that of course you
> > won't get much of a clarification!)
>
> > So what will Herc actually do if you follow my earlier idea of explaining in
> > greater and greater detail, asking for clarifications, refusing to go along
> > with vague confusing terminology until it is clarified and so on? [I
> > thought that surely if I did this thoroughly enough, Herc would have NO
> > CHOICE but to agree where he was wrong, or at least he would have to reply
> > in such a way that it was obvious to himself and others that he was not able
> > to answer the questions and support his claims.]
>
> > The answer is that Herc will just ignore all your efforts and respond with
> > something vague, unrelated to the detail of your postings. E.g. he will
> > ignore your questions and ask you to "go away and work out all the possible
> > antidiagonals", or something. Perhaps he will write a piece at the end of
> > your post telling you where YOU are going wrong, and repeat his demand that
> > you answer some ambiguous or irrelevent question. (And yes, with enough
> > persistence he will become abusive.) What he WILL NOT do is respond
> > meaningfully to any requests for mathematical clarification! Later on he'll
> > start another thread using the same unclear terminology, and nothing will
> > have moved on.
>
> > I think Herc's problem with Cantor's are only sustainable while he is
> > allowed to confuse himself with his
> > ambiguous/contradictory/plain-old-incorrect terminology, but while he will
> > not engage in "meaningful mathematical dialogue" I don't see how anything
> > will change...
>
> Good stuff, Mike.
>
> But in your YEARS of dealing with Herc, has the idea not occurred
> to you that Herc is arguing in bad faith? That he is a TROLL who
> is HAVING A BALL jerking around a dumb sucker for YEARS AT A STRETCH?
>
> Has that idea not occurred to you, Mike?
>
> --
> hz

I'm not deliberately trolling. Transfer Prinicple said disputing
Cantors proof doesn't imply you don't understand it.

In fact most people disputing Cantor or Godel believed those
proofs a some point then changed their mind with more evidence.

When you cite Cantors proof all I see is
ad(n) =\= l(n,n) -> ad(n) =\= l(n,n)

my proof by induction in this thread is 100% more concrete
that the maximum digit width of complete permutations is oo

Herc