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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 20, 2010 8:16 PM
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"Mike Terry" <news.dead.person.stones@darjeeling.plus.com> wrote in message
news:B8WdnX3itoZ7zYPRnZ2dnUVZ7qednZ2d@brightview.co.uk...
> "Peter Webb" <webbfamily@DIESPAMDIEoptusnet.com.au> wrote in message
> news:4c1e2b53$0$316$afc38c87@news.optusnet.com.au...

>>
>> "Tim Little" <tim@little-possums.net> wrote in message
>> news:slrni1r0ra.jrj.tim@soprano.little-possums.net...

>> > On 2010-06-20, Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote:
>> >> Explain to me how my requirements for the input list of all
>> >> computable Reals is different to Cantor's requirements for the input
>> >> list of all Reals, other than the requirement that every item on the
>> >> list is computable?

>> >
>> > It is not. Your error comes later.
>> >
>> > Cantor's proof includes a construction taking a list L and defining an
>> > antidiagonal real antidiag(L) from it. Your error is supposing that
>> > this construction is a finite algorithm fitting the definition of
>> > "computable real". It is not. By stretching the definition of
>> > "algorithm" somewhat, it can be supposed to be an algorithm accepting
>> > finite input n and infinite input L, and producing the n'th
>> > antidiagonal digit. This is a stretch since algorithms are normally
>> > not supposed to have infinite inputs.

>>
>> The calculation of the nth digit only requires the first n digits to n
>> decimal places, and hence it is clearly a finite algorithm.
>>
>> Its simply ludicrous to suggest that the antidiagonal is not computable
>> given that a very simple algorithm will explicitly churn it out.

>
> Not so - the "very simple algorithm" you are suggesting requires "the
> input
> list" in its raw (infinite) form as input.


No. Computing the the anti-diagonall to n places only requires the first n
items on the list to n digits of accuracy.

And it clearly is computable. I can compute it. I take the nth digit of the
nth term, and ... blah blah.

How is this number any less computable than the square root of 2?

In both cases there is a finite algorithm to calculate the number to n
decimal places for all n.




> As such, this is not an
> algorithm that can be implemented on a Turing machine. I.e. the algorithm
> is not the sort of algorithm that counts as "computable". Maybe you will
> dispute this, but it's been explained to you several times (including one
> of
> my posts), and you can always go away and look up the definition of
> computable function / Turing Machine etc., but it seems you've not done
> this.


I don't have to look it up. I know it.

Obviously the anti-diagonal the computable. I can compute it to any required
degree of accuracy using a very simple algorithm which explicitly computes
it; you can't get much more computable than that.


>
>>
>> >
>> > However, there is no way that you can then prove the existence of a
>> > finite algorithm accepting only the *finite* input n and producing the
>> > n'th antidiagonal digit.
>> >

>>
>> Of course I can prove the existence of a finite algorithm. I can produce

> it.
>>
>> To produce the nth decimal of the anti-diagonal, look at the first n
>> items
>> on the purported list of all computable Reals.

>
> There! Was I right, or was I right? :-)


How is looking at the first n digits of the first n terms and using Cantor's
digit substitution to calculate the decimal place not computable?


>
> There is an infinite amount of data on this "purported list", and you are
> not allowed to base a computable function on an infinite amount of input
> data. To do so shows you simply do not understand what computable means.
>


I don't use the whole list. To calculate the nth digit of the anti-diagonal
I only need the first n terms to n decimal places accuracy. That is a finite
amount of data.

And, as a practical matter, if you want to give me a purported list of all
computable Reals, I can actually calculate it to any required degree of
accuracy in a finite number of steps.


> Now IF you could codify all this data somehow into a finite program, so
> you
> had a computable function D(m,n) which produced the n'th digit of the m'th
> number in the list, you would be OK. But you DON'T have such a computable
> function D.
>


Well, Cantor asks for a list of Reals. And D(m,n) is computable in my case
by definition; which means we can always evaluate this function (as a
computable Real must be able to be specified to any arbitrary degree of
accuracy).



> What you DO have, is for each m, a computable function D_m (n) which
> produces the n'th digit of the m'th number in the list. But how can you
> use
> these individual D_m in the definition of the antidiagonal? (You
> can't...)


I do. If D(n,n)=1 then antidiagonal(n) = 2, else antidiagonal(n) = 1.


>
> Do you not see this distinction?
>
> Knowing the existence of all the individual D_m is equivalent to knowing
> that the list (sequence of numbers) consists of computable reals.
>
> Knowing the existence of D (which is a single computable function) is
> equivalent to having a *computable* list of computable reals.
>


Cantor's proof asks to see the list and then produces a number not on it.

Same as my proof.

Yes, that requires that te list be specified ... but Cantor's proof and mine
are no different in that respect.



> Cantor's proofs do not require computable lists, they work with just any
> old
> lists...
>


Indeed. And my proof requires computable Reals in a list. That is the
difference.


>> Then substitute "1" for "2"
>> blah blah. How is that not a finite algorithm?

>
> As explained it is not a finite algorithm because it uses as input an
> infinite source of data.
>


No, to specify the anti-diagonal to n places requires only a finite amount
of data for all n, specifically the first n decimal places of the first n
terms.


> By your reckoning every single real number is computable, because we can
> have a TM that just accepts as input an infinite tape with the entire
> digit
> sequence encoded on it, and outputs that digit sequence.


No. I can explicitly calculate the nth decimal places with only n terms to n
places of accuracy. No infinite input is required.

In any event, it is a farcical argument. Of course I can calculate the
antidiagonal to any number of places of accuracy using only finite
processes; Cantor's proof is constructive.

>
> Surely you must be aware that this is NOT what computability means?
>


Being able to specify the nth digit of a number in a finite number of steps
for all n is a sufficient condition for compuatbility, and that is exactly
what Cantor's diagonal proof provides - a means of calculating the nth digit
of the anti-diagonal in a finite number of steps, using a finite input (the
first n digits of the first n terms).


> Regards,
> Mike.
>
>
>




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6/15/10
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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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fishfry
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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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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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6/16/10
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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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6/16/10
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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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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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