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Topic: Why can no one in sci.math understand my simple point?
Replies: 658   Last Post: Feb 17, 2013 10:15 AM

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Peter Webb

Posts: 945
Registered: 12/6/04
Re: Why can no one in sci.math understand my simple point?
Posted: Jun 19, 2010 11:10 PM
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"Mike Terry" <news.dead.person.stones@darjeeling.plus.com> wrote in message
news:NNqdnTtg2LuExoDRnZ2dnUVZ8lKdnZ2d@brightview.co.uk...
> "Peter Webb" <webbfamily@DIESPAMDIEoptusnet.com.au> wrote in message
> news:4c1c6be3$0$17177$afc38c87@news.optusnet.com.au...

>>
>> "Tim Little" <tim@little-possums.net> wrote in message
>> news:slrni1om15.jrj.tim@soprano.little-possums.net...

>> > On 2010-06-19, Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote:
>> >> So Cantor's proof when applied to computable Reals proves exactly
>> >> what in your opinion?

>> >
>> > That there is a real not on the list.
>> >
>> >

>> >> I might remind you that as the form of proof is identical to that
>> >> used by Cantor for all Reals, whatever you believe that Cantor's
>> >> proof applied to computable Reals proves, his proof applied to all
>> >> Reals must prove the same thing.

>> >
>> > It does prove exactly the same thing: in both cases, all such lists
>> > omit at least one real.
>> >
>> >

>> >> Its the same proof, after all, except limitting the set to just
>> >> computable Reals.

>> >
>> > No, there is a slight difference: the antidiagonal is a real number.
>> > It does not necessarily produce a computable real number.
>> >

>>
>> Of course it is computable. Cantor provides a simple construction for the
>> number.

>
> No, you're misunderstanding the meaning of computable.
>
> Hopefully you will be OK with the following definition:
>
> A real number r is computable if there is a TM (Turing machine)
> T which given n as input, will produce as output
> the n'th digit of r.
>
> So let us suppose there is a list L (not a "computable list", just a
> "list")
> of computable numbers in [0,1], covering all computerable numbers.
>
> [You have your own strange definition of "list", but I am using the term
> with it's standard mathematical meaning: L is just a function mapping N
> (natural numbers) to CR (computable reals). Perhaps we should also insist
> that lists are injections (no duplicates) - that's fine. YOU seem to want
> to define "list" to only include "computable" functions from N to CR, but
> that is NOT what everybody else (including Cantor) means by "list"!]
>
> L : N --> CR
>
> so we have the sequence (=list) of computable reals:
>
> ( L(0),
> L(1),
> L(2),
> ....)
>
> Each computable real has it's digital representation, so this list can be
> written: (using d(m,n) for n'th digit of L(m)
>
> L(0) digits : d(0,0), d(0,1), d(0,2), ...
> L(1) digits : d(1,0), d(1,1), d(1,2), ...
> L(2) digits : d(2,0), d(2,1), d(2,2), ...
> ...
>
> Now, given m and n, is there necessarily a TM that can take m and n as
> inputs, and ouput d(m,n)?
>
> Well, each L(m) individually is computable: there is a corresponding TM,
> TM_m such that given n as input it will compute d(m,n). We could say:
>
> TM_m (n) = d(m,n)
>
> But all the TMs can be different and completely unrelated to each other.
>
> Can we say there will always be a *single* TM TM_ALL_m, which "subsumes"
> all
> the TM_n, i.e. if given m and n as input, will compute d(m,n)? I.e.
>
> for all m,n: TM_ALL_m (m,n) = d(m,n) ?????
>
> Unfortunately for your argument, the answer is NO.
>
> But that is exactly what you would need to argue that the anti-diagonal is
> computable: You need a TM that could calculate d(m,m), but this needs the
> TM TM_ALL_m, and we do not have that!
>
> I know what you want to say at this point! :) You want to say that I have
> "explicitly given you" d(m,n), and I can only do this if d(m,n) is
> computable. (Right?) And you want to tell me that Cantor's diagonal
> proof
> is the same?
>
> Well, this is a misreading of Cantor's proof! Look closely:
>
> Paraphrasing of Cantor's proof:
>
> Given a function L: N --> [0,1], there
> exists r in [0,1], such that
> for all n, r != L(n) [i.e. r is not in the list]
>
> Proof:
> 1) Suppose L: N-->R
> 2) Define LD: (NxN)-->{0,1,2,3,4,5,6,7,8,9}
> such that LD(m,n) = n'th digit of L(m)
> 3) Define RD: N-->R
> such that RD(m) = [...antidiagonal digit m...]
> 4) Then RD determines a real r in [0,1]
> 5) Show for all n, r != L(n) from defn. of r above.
>
> Where in this proof does Cantor require LD(m,n) to be computable? (Answer
> =
> nowhere.)
>
> I think maybe you are thinking it must be computable, due to your
> misleading
> use of the phrase "explicitly given", but actually all Cantor does is
> argue
> that IF a (any) function L (not necessarily computable) EXISTS mapping N
> to
> [0,1], the mere existence of L implies the existence of a corresponding
> real
> r not in the list L. There is nothing requiring real computer programs to
> actually compute anything here! It's just a mathematical proof of
> existence
> of something.
>


What you are writing above is *not* Cantor's diagonal proof as it appears on
a million websites.

The whole point of my post was to use Cantor's proof exactly, which alows me
to demonstrate that Cantor's proof does *not* in of itself prove the
uncounatbility of the Reals.

Perhaps if you were to tell me where you think the error in my very simple
proof is, then we would be making progress.

More generally: you can't write down a list bof all computable Reals, such
that the nth digit of the nth term is known. Ant more than you can write dow
a list of all Reals, such that the nth digit of the nth term is known. That
is what Cantor proves; that is what I prove about computable numbers.

But thisw does not mean that the Reals are uncountable, as the computable
numbers are countable.

(And if you actually want to know why this is so, it is because the set of
computable numbers is not recursively enumerable. And nor for that matter is
the set of all Reals. This is what Cantor's proof actually shows, and it is
*not* the same as being uncountable).




> Hmmm, I can see this is where you will be objecting, but I can't see how
> to
> be more clear.
>
> OK - it's like the following (admittedly pretty dumb but correct) proof
> that
> I've just made up that there is no upper bound n_max in N which bounds all
> functions from N to N:
>
> Dumb but correct Proof:
> 1) Suppose there is such an n_max.
> i.e. for all f,n: f(n) < n_max
> 2) Then there is a *least* n with the same property
> as n_max: call this n_max_min.
> 3) There must be some F and m with
> F(m) = n_max_min - 1
> [...details omitted, but otherwise n_max_min - 1
> would contradict the mininum property for n_max_min]
> 4) But consider G(n) = F(n)+1
> 5) G is a function mapping N:-->N and
> G(m) = F(m)+1 = n_max_min
> 6) This contradicts (2)
> 7) Hence assumption (1) is false
>
> There is no assumption in my proof that any of the functions be
> "computable". Hopefully you would accept my proof, because it is similar
> to
> 1000 other proofs along the same lines.
>
> BUT... your Cantor objection is equivalent to saying that my proof only
> works for "computable" functions. Why? Because I have to "explicitly
> give
> you" the function F in (3), so that step (4) makes sense! How can I "add
> 1"
> to a function that is not computable? Well, obviously I *can*. Step (4)
> is
> not to be thought of as a step for someone to write in a computer
> program -
> it's a mathematical definition of G(m) in terms of other things known to
> exist at that point in the proof. Sure, if F were computable, then G
> would
> be, but nothing in the proof requires F to be!
>
> So too, it is with Cantor's proof. The "lists" involved are assumed to be
> nothing more than maps from N to the target set (e.g. [0,1]) with no
> assumption of computability.
>
> Hope this helps,
> Mike.
>
>
>
>




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6/15/10
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6/25/10
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6/25/10
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6/26/10
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6/26/10
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6/27/10
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6/27/10
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6/27/10
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6/27/10
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Newberry
6/27/10
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6/26/10
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6/27/10
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6/26/10
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6/26/10
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6/27/10
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6/26/10
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6/26/10
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6/26/10
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6/26/10
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6/27/10
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6/27/10
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6/27/10
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6/28/10
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6/28/10
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6/28/10
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6/28/10
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6/28/10
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6/28/10
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6/28/10
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6/28/10
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6/28/10
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6/28/10
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6/28/10
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6/30/10
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6/28/10
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6/28/10
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6/26/10
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6/27/10
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6/27/10
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6/27/10
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6/27/10
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fishfry
6/15/10
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6/15/10
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6/15/10
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6/16/10
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6/15/10
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6/16/10
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6/16/10
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6/16/10
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6/16/10
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6/16/10
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6/15/10
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6/15/10
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6/15/10
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6/15/10
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6/15/10
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6/15/10
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6/15/10
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6/15/10
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6/15/10
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6/15/10
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6/15/10
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6/15/10
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6/15/10
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6/16/10
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6/15/10
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6/15/10
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6/15/10
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6/15/10
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|-|ercules
6/16/10
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6/16/10
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6/15/10
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6/15/10
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6/15/10
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6/15/10
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6/15/10
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6/15/10
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6/16/10
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6/16/10
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6/16/10
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6/15/10
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6/15/10
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6/16/10
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6/16/10
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6/15/10
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6/15/10
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6/15/10
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|-|ercules
6/16/10
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6/16/10
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6/15/10
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6/15/10
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6/15/10
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6/15/10
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6/15/10
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6/16/10
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6/16/10
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6/16/10
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6/16/10
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6/15/10
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6/15/10
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6/15/10
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george
6/15/10
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6/15/10
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6/16/10
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6/16/10
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6/16/10
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6/16/10
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6/17/10
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6/17/10
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6/17/10
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6/17/10
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6/18/10
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6/18/10
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6/18/10
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6/18/10
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6/18/10
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6/18/10
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6/18/10
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6/19/10
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6/18/10
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6/18/10
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6/18/10
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ross.finlayson@gmail.com
6/17/10
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6/18/10
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ross.finlayson@gmail.com
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6/17/10
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6/17/10
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6/17/10
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6/17/10
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6/17/10
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6/18/10
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6/18/10
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6/18/10
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6/18/10
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6/18/10
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6/18/10
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6/18/10
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6/18/10
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6/18/10
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6/18/10
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6/18/10
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6/19/10
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6/19/10
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6/19/10
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6/19/10
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6/19/10
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6/20/10
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6/20/10
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6/20/10
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6/20/10
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6/20/10
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6/20/10
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6/21/10
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6/21/10
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6/23/10
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6/23/10
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6/21/10
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6/21/10
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6/20/10
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6/20/10
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6/20/10
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6/19/10
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6/19/10
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6/19/10
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6/20/10
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6/20/10
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6/20/10
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6/21/10
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6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/21/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/21/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/21/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/21/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/22/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/22/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/22/10
Read Re: Why can no one in sci.math understand my simple point?
David R Tribble
6/22/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Daryl McCullough
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
K_h
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
K_h
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Mike Terry
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Mike Terry
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/21/10
Read Re: Why can no one in sci.math understand my simple point?
Mike Terry
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Mike Terry
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/17/10
Read Musatov responds to WM on Cantor: intelligence, real
, judge for yourself: Cantor’s idea seems to me to assume
because two sets converge to infinity the nature of infinity
and the number of elements in each set must become equal.
Guest
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/17/10
Read Re: Musatov responds to WM on Cantor: intelligence,
real, judge for yourself: Cantor’s idea seems to me to ass
ume because two sets converge to infinity the nature of infi
nity and the number of elements in each set must become equa
l.
lwalke3@lausd.net
2/17/13
Read Re: Musatov responds to WM on Cantor: intelligence,
real, judge for yourself: Cantor’s idea seems to me to ass
ume because two sets converge to infinity the nature of infi
nity and the number of elements in each set must become equa
l.
2/17/13
Read Re: Musatov responds to WM on Cantor: intelligence,
real, judge for yourself: Cantor’s idea seems to me to ass
ume because two sets converge to infinity the nature of infi
nity and the number of elements in each set must become equa
l.
6/16/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
K_h
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
K_h
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
K_h
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
K_h
6/21/10
Read Re: Why can no one in sci.math understand my simple point?
Owen Jacobson
6/21/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/21/10
Read Re: Why can no one in sci.math understand my simple point?
Owen Jacobson
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
K_h
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Daryl McCullough
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Daryl McCullough
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Daryl McCullough
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Daryl McCullough
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/21/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/21/10
Read Re: Why can no one in sci.math understand my simple point?
Mike Terry
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Tim Little
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Peter Webb
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/16/10
Read Re: Why can no one in sci.math understand my simple point?
Jack Markan
6/16/10
Read Re: Why can no one in sci.math understand my simple point?
Jack Markan
6/16/10
Read Re: Why can no one in sci.math understand my simple point?
Aatu Koskensilta
6/16/10
Read Re: Why can no one in sci.math understand my simple point?
Aatu Koskensilta
6/16/10
Read Re: Why can no one in sci.math understand my simple point?
Jack Markan
6/16/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/16/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/16/10
Read Re: Why can no one in sci.math understand my simple point?
Jack Markan
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
Jack Markan
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/16/10
Read Re: Why can no one in sci.math understand my simple point?
Jack Markan
6/16/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/16/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/16/10
Read Re: Why can no one in sci.math understand my simple point?
Jack Markan
6/16/10
Read Re: Why can no one in sci.math understand my simple point?
Jack Markan
6/16/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/16/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
Jack Markan
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
Jack Markan
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
Jack Markan
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
lwalke3@lausd.net
2/17/13
Read Re: Why can no one in sci.math understand my simple point?
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
Aatu Koskensilta
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
lwalke3@lausd.net
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
Sylvia Else
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
Sylvia Else
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
lwalke3@lausd.net
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
|-|ercules
6/17/10
Read Re: Why can no one in sci.math understand my simple point?
Sylvia Else
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
|-|ercules
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Sylvia Else
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
|-|ercules
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Sylvia Else
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
|-|ercules
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Sylvia Else
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Sylvia Else
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
|-|ercules
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Sylvia Else
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
|-|ercules
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Sylvia Else
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
|-|ercules
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Sylvia Else
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
|-|ercules
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Sylvia Else
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
|-|ercules
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Sylvia Else
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
|-|ercules
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
|-|ercules
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Sylvia Else
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
|-|ercules
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Sylvia Else
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
|-|ercules
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Sylvia Else
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
|-|ercules
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Sylvia Else
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
|-|ercules
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
Sylvia Else
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
|-|ercules
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
lwalke3@lausd.net
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
|-|ercules
6/20/10
Read Re: Why can no one in sci.math understand my simple point?
|-|ercules
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
mueckenh@rz.fh-augsburg.de
6/19/10
Read Re: Why can no one in sci.math understand my simple point?
Virgil
6/18/10
Read Re: Why can no one in sci.math understand my simple point?
ostap_bender_1900@hotmail.com
6/21/10
Read Re: Why can no one in sci.math understand my simple point?
Sylvia Else
6/22/10
Read Re: Why can no one in sci.math understand my simple point?
Sylvia Else
6/27/10
Read Re: Why can no one in sci.math understand my simple point?
Frederick Williams

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