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Topic: 11 year olds homework
Replies: 46   Last Post: Nov 26, 2004 6:42 PM

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Angus Rodgers

Posts: 387
Registered: 12/6/04
Re: 11 year olds homework
Posted: Nov 20, 2004 8:34 PM
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[I'm sorry that I keep following up my own post, but after
having spent too long on this problem, I seem to have been
rather too eager to get it all finished with, and I spotted
another error just now - when I was in bed trying to forget
all about maths, and concentrate on a good ghost story!]

On Sat, 20 Nov 2004 23:12:28 +0000, I wrote:

>Suppose p \in S_oo. Then for all sufficiently large n,
>the vector A^n(p) is in the positive octant, P, and has
>u-coordinate < 1 (because A multiplies u-coordinates by
>the positive factor m - 1 < 1).
>
>[Damn! ...

... and blast! Because quite apart from the gap in the
proof, there is a trivial error here:

Because the (u, v, w) system is not normalised, the u-
coordinate of q is not q.u (as I hastily assumed), but
(q.u)/|u|^2, so the condition for n to be "large enough"
should have been that the u-coordinate of q be < 1/|u|^2
(which of course is still O.K., because the choice of
the value 1 was arbitrary in the first place), so that
we still have q.u < 1.

(|u|^2 = m^2(2m + 1), not that it matters.)

--
Angus Rodgers
(angus_prune@ eats spam; reply to angusrod@)
Contains mild peril



Date Subject Author
11/13/04
Read 11 year olds homework
Chris
11/13/04
Read Re: 11 year olds homework
Virgil
11/13/04
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Ryan Reich
11/13/04
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Virgil
11/14/04
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Randy Yates
11/14/04
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G. A. Edgar
11/17/04
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David Ames
11/17/04
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Stephen Herschkorn
11/17/04
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Road Runner News
11/18/04
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Jeremy Boden
11/18/04
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Rick Decker
11/18/04
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Gerry Myerson
11/20/04
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The Ghost In The Machine
11/18/04
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Jeremy Boden
11/18/04
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Dave Seaman
11/18/04
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Richard Henry
11/19/04
Read Re: 11 year olds homework
jmfbahciv@aol.com
11/19/04
Read Re: 11 year olds homework
Phil Carmody
11/19/04
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Paul Leyland
11/19/04
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Keith Ramsay
11/19/04
Read Re: 11 year olds homework
Christian Bau
11/19/04
Read Re: 11 year olds homework
Jeremy Boden
11/19/04
Read Re: 11 year olds homework
Phil Carmody
11/18/04
Read Re: 11 year olds homework
Tom Kirke
11/19/04
Read Re: 11 year olds homework
jmfbahciv@aol.com
11/19/04
Read Re: 11 year olds homework
jmfbahciv@aol.com
11/22/04
Read Re: 11 year olds homework
John Schoenfeld
11/14/04
Read Re: 11 year olds homework
Robert Israel
11/14/04
Read Re: 11 year olds homework
Robert Israel
11/14/04
Read Re: 11 year olds homework
Virgil
11/16/04
Read Re: 11 year olds homework
Angus Rodgers
11/20/04
Read Re: 11 year olds homework
Rouben Rostamian
11/20/04
Read Re: 11 year olds homework
Angus Rodgers
11/20/04
Read Re: 11 year olds homework
Angus Rodgers
11/20/04
Read Re: 11 year olds homework
Angus Rodgers
11/21/04
Read Re: 11 year olds homework
Angus Rodgers
11/21/04
Read Re: 11 year olds homework
Angus Rodgers
11/22/04
Read Re: 11 year olds homework
Angus Rodgers
11/26/04
Read Re: 11 year olds homework
Keith Ramsay
11/26/04
Read Re: 11 year olds homework
Angus Rodgers
11/13/04
Read Re: 11 year olds homework
Richard Henry
11/13/04
Read Re: 11 year olds homework
The Ghost In The Machine
11/13/04
Read Re: 11 year olds homework
Angus Rodgers
11/14/04
Read Re: 11 year olds homework
Phil Carmody
11/14/04
Read Re: 11 year olds homework
Angus Rodgers
11/14/04
Read Re: 11 year olds homework
Ignacio Larrosa Cañestro
11/21/04
Read Re: 11 year olds homework
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