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

 Messages: [ Previous | Next ]
 Angus Rodgers Posts: 387 Registered: 12/6/04
Re: 11 year olds homework
Posted: Nov 20, 2004 8:34 PM

[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:

&gt;Suppose p \in S_oo. Then for all sufficiently large n,
&gt;the vector A^n(p) is in the positive octant, P, and has
&gt;u-coordinate &lt; 1 (because A multiplies u-coordinates by
&gt;the positive factor m - 1 &lt; 1).
&gt;
&gt;[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 &lt; 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 &lt; 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 Chris
11/13/04 Virgil
11/13/04 Ryan Reich
11/13/04 Virgil
11/14/04 Randy Yates
11/14/04 G. A. Edgar
11/17/04 David Ames
11/17/04 Stephen Herschkorn
11/18/04 Jeremy Boden
11/18/04 Rick Decker
11/18/04 Gerry Myerson
11/20/04 The Ghost In The Machine
11/18/04 Jeremy Boden
11/18/04 Dave Seaman
11/18/04 Richard Henry
11/19/04 jmfbahciv@aol.com
11/19/04 Phil Carmody
11/19/04 Paul Leyland
11/19/04 Keith Ramsay
11/19/04 Christian Bau
11/19/04 Jeremy Boden
11/19/04 Phil Carmody
11/18/04 Tom Kirke
11/19/04 jmfbahciv@aol.com
11/19/04 jmfbahciv@aol.com
11/22/04 John Schoenfeld
11/14/04 Robert Israel
11/14/04 Robert Israel
11/14/04 Virgil
11/16/04 Angus Rodgers
11/20/04 Rouben Rostamian
11/20/04 Angus Rodgers
11/20/04 Angus Rodgers
11/20/04 Angus Rodgers
11/21/04 Angus Rodgers
11/21/04 Angus Rodgers
11/22/04 Angus Rodgers
11/26/04 Keith Ramsay
11/26/04 Angus Rodgers
11/13/04 Richard Henry
11/13/04 The Ghost In The Machine
11/13/04 Angus Rodgers
11/14/04 Phil Carmody
11/14/04 Angus Rodgers
11/14/04 Ignacio Larrosa CaÃ±estro
11/21/04 tinyurl.com/uh3t