mm-1109
===
Subject: Re: problem with mobius transformations
donÕt forget reßections thru diameters
> im trying to determine the set of mobius transformations T
such that
> T(D)=D, where D is the unit disk centered at 0 (without its
boundary).
> At first I thought it would only be the mobius
transformations that
> are rotations (i.e. T(z)=e^(it)z for some t in R) but my
professor
> tells me that there is a larger class of functions.
===
Subject: Re: problem with mobius transformations
> donÕt forget reßections thru diameters
> im trying to determine the set of mobius transformations T
such that
> T(D)=D, where D is the unit disk centered at 0 (without its
boundary).
> At first I thought it would only be the mobius
transformations that
> are rotations (i.e. T(z)=e^(it)z for some t in R) but my
professor
> tells me that there is a larger class of functions.
are reßections the only other transformations that map D onto
D?
===
Subject: Re: problem with mobius transformations
donÕt forget compositions
> donÕt forget reßections thru diameters
> im trying to determine the set of mobius transformations T
such that
> T(D)=D, where D is the unit disk centered at 0 (without its
boundary).
> At first I thought it would only be the mobius
transformations that
> are rotations (i.e. T(z)=e^(it)z for some t in R) but my
professor
> tells me that there is a larger class of functions.
> are reßections the only other transformations that map D
onto D?
7
===
Subject: Re: Old Arguments, Dik Winter and Rick Decker
> Just now I went to the website:
http://www.crank.net/harris.html
and noticed that ßame website put up by Erik Max Francis who
> apparently is the sole instigator and maintainer has links
to two
> webpages maintained by Dik Winter and Rick Decker where
they put up
> OLD arguments of mine that IÕve admitted were ßawed.
>
DeckerÕs site shows his version of what was then called Area
One.
Decker put together arguments from many sources, including
your
Several points need to be made about this:
1. The Area One result itself was *correct*. You were the
first to state it. Decker gives you ample credit for it.
2. But you never gave a correct proof of the Area One result!
That
was done by the late John Rickard. You had an incorrect
argument and you never understood why it was wrong. The
central proof in DeckerÕs website is RickardÕs 
proof, not
yours.
3. Decker later added commentary on Area Two. The Area Two
argument never made sense to me or, I think, to Decker. To
my knowledge, you never admitted - till just recently - that
the Area Two argument was incorrect. You just abandoned it
and walked away, as you have often done with other arguments.
If you can cite a post of yours from around the time Decker
posted his Area Two summary, acknowledging that your Area
Two argument was incorrect, I will gladly acknowledge making
a mistake here.
4. Dik WinterÕs post shows that one of your arguments is
incorrect
by emulating every step of it for an equation closely
resembling
FermatÕs equation, but for which the Fermat result is false.
Dik
many, many times asked you to comment on his posted argument
and
say what was wrong with it. I donÕt recall that you ever 
gave
a satisfactory reply. Again for the most part you simply
ignored
DikÕs requests. And to my knowledge, again till just 
recently,
I donÕt think you acknowledged that Dik was right and that
your
argument at that time was wrong. I believe that again you just
abandoned it and walked away. If you can refute me on this,
please quote a post from that time. Dik may also want to
comment.
You have similarly walked away without resolution from many
past
arguments. One of the most recent involved your claims
regarding
factorizations of the product of two large primes. A
counterexample
was found to your first claims almost immediately. You 
modified
the
claim slightly. Again a counterexample was found. You modified
the
claim again. And *again* a counterexample was found. Finally
you
simply abandoned the idea. You never acknowledged that your
basic
idea was wrong. Similarly in a recent argument with Virgil
centered on
coprimeness. Virgil presented an absolutely unambiguous,
step-by-step
proof. You denied that it was correct. You said that Virgil
was
assuming what he claimed to prove, i.e., that he was using a
circular
argument. That was incorrect. Virgil was right and you were
wrong.
Others,
including Arturo, joined in. Finally you just walked away,
never
actually admitting a mistake.
The most recent argument about (1 + sqrt(-167))/2: here you
did admit a mistake. The mistake was in your argument that
there
is a core error in current mathematics. You admitted an error
regarding RamsayÕs example, but you have *not* admitted the
obvious
fact that that example, as well as Rick DeckerÕs and others,
completely undermines your core error claims. You continue to
maintain, really with no argument at all, that there is a core
error in algebraic number theory.
Given your pattern of behavior, there is good reason to
maintain
old websites pointing out your mistakes. Of course vast
numbers of
them are out there in the sci.math archives. Perhaps someone
should
maintain a website of urlÕs to posts where you have admitted
mistakes,
or, more importantly, to posts by you with obviously
erroneous claims
that you later just abandoned with no comment. Or posts where
you
indulge in screaming obscenities. An index of such would be
useful
for future reference.
> The insinuation from that page given that it calls me a
crank is that
> IÕm holding on to these ideas that have been proven to be
wrong.
I am not.
>
I believe you did for a very long time.
> and Rick Decker present on their pages are correct. I admit
freely
> that both arguments shown are ßawed.
>
When and where did you first acknowledge this?
> Now then, why are these people maintaining web pages of old
arguments
> of mine long dropped down the toilet by me?
>
Because no one ever actually heard them plopping into the
water?
> Possibly they wish to maintain that because I have failed
arguments
> IÕm crazy.
>
Doubtful. You may be, but erroneous arguments donÕt prove 
it.
Otherwise we would all be crazy.
> Or possibly theyÕre trying to make sure no one forgets 
that
I had
> these attempts that didnÕt work.
>
DeckerÕs website actually gives you a fair amount of credit.
Most of the argument presented there is correct. At one time
you
thanked Decker profusely for translating your work into
correct
mathematical style!
> I say theyÕre assholes who will maintain their sites
indefinitely out
> of personal animosity towards me.
Well the feeling is mutual, I hate them too.
Rick DeckerÕs page is especially egregious in that he
maintains it on
> the Hamilton College website. Now IÕve contacted Hamilton
College to
> complain about his webpage, but they trust him.
>
They should. There is nothing wrong in what he said. Why did
you
contact them? IsnÕt there a question of free speech and/or
academic
freedom here? Are you trying to subvert that?
> Again, the pages noted contained OLD ßawed arguments of
mine that
> have long been dropped. Rick Decker and Dik Winter are just
a
> particular type of animal, willing to push things long past
the point
> where you should just let go.
>
Some things are valuable for purely historical reasons.
Actually,
I think Dik probably left his website out there because he
forgot
about it. ItÕs also possible he thought, since you may have
never
renounced that argument, that you might try to go back to it.
After you started complaining about it, he was not going
to take it down simply because he probably doesnÕt like 
being
pushed
around. If you hadnÕt got upset about it, it might have died
a natural
death.
> Rick Decker has included his college in this as well, and
IÕve
> notified them, but for the moment Hamilton College is
supporting their
> professor.
>
Good for them!
Nora B.
James Harris
===
Subject: Re: Old Arguments, Dik Winter and Rick Decker
well thought out rebutal.
Nora B.
Gawd Nora, if youÕre not single do you have sister? or a
daughter? or a
good female friend whoÕs just like you?
day!
Ivan.
===
Subject: Re: Old Arguments, Dik Winter and Rick Decker
> Just now I went to the website:
>
> http://www.crank.net/harris.html
>
> and noticed that ßame website put up by Erik Max Francis who
> apparently is the sole instigator and maintainer has links
to two
> webpages maintained by Dik Winter and Rick Decker where
they put up
> OLD arguments of mine that IÕve admitted were ßawed.
>
> The insinuation from that page given that it calls me a
crank is that
> IÕm holding on to these ideas that have been proven to be
wrong.
I do not think so. It calls you a crank because you do not
see the
proofs that show that you are wrong. You indulge into calling
those
who show you are wrong liars and whatever. You *never* go
into the
showings.
> I am not.
You are. Remember the time it took you to acknowledge Keith
RamsayÕs
counter-example? You thought you were right, so you called
Keith
Ramsay a liar, as you did everyone who pointed you to that
counter-
example. An early verification would have spared you a lot of
embarassment.
> and Rick Decker present on their pages are correct. I admit
freely
> that both arguments shown are ßawed.
Note that my pages do *not* state that you still hold to that
viewpoint.
They merely show the way you are reasoning.
> Now then, why are these people maintaining web pages of old
arguments
> of mine long dropped down the toilet by me?
I have posted that already earlier, but for some reason what
I write
does not enter your brain anywhere.
> Possibly they wish to maintain that because I have failed
arguments
> IÕm crazy.
Wrong. Everybody has failed arguments on occasion, but your
fierce
defence of them in view of opposition and sometimes actual
proofs of
the opposite make you a crank.
> Or possibly theyÕre trying to make sure no one forgets 
that
I had
> these attempts that didnÕt work.
Do you have an attempt now that *does* work?
> I say theyÕre assholes who will maintain their sites
indefinitely out
> of personal animosity towards me.
No, my animosity is not to you, it is to your attitude. I put
them on
because your infinite repetition of denying what was proven.
> Well the feeling is mutual, I hate them too.
In that case it is not mutual.
> Rick DeckerÕs page is especially egregious in that he
maintains it on
> the Hamilton College website. Now IÕve contacted Hamilton
College to
> complain about his webpage, but they trust him.
As Jesse pointed out, mine would be more egregious. (Sorry
Jesse, when
you came along as a subordinate of some US Army officer, I
just ducked.)
> Again, the pages noted contained OLD ßawed arguments of
mine that
> have long been dropped. Rick Decker and Dik Winter are just
a
> particular type of animal, willing to push things long past
the point
> where you should just let go.
I would think you are long past that point already a long
time ago.
> Rick Decker has included his college in this as well, and
IÕve
> notified them, but for the moment Hamilton College is
supporting their
> professor.
Pray report to my institute, and I will see what will happen.
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam,
nederland,
+31205924131
home: bovenover 215, 1025 jn amsterdam, nederland;
http://www.cwi.nl/~dik/
===
Subject: Re: Old Arguments, Dik Winter and Rick Decker
...
> As has been mentioned many times, failed arguments are not
> necessarily bad. In fact, Lagrange did a similar thing when
> he published a long paper on an approach to solve the
> quintic equation by radicals. I believe that this paper
> was crucial in helping Galois to develop his theory.
And I maintain that a paper publishing failed attempts would
have its
uses, if the failed attempts are accmpanied with the reason
why the
attempt failed.
Especially in the history of FLT failed attempts have lead to
quite a few
interesting leads in mathematics, because it was seen that
the reasoning
was not sound, and it was acknowledged. Ideals solved the
problem of
non-unique factorisation, a first general block to a simple
solution.
The next was the finding of special primes, which lead to the
class
field numbers. I would have hoped that most would-be solvers
of FLT
would have perused the history of failed attempts...
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam,
nederland,
+31205924131
home: bovenover 215, 1025 jn amsterdam, nederland;
http://www.cwi.nl/~dik/
===
Subject: Re: Old Arguments, Dik Winter and Rick Decker
> Now then, why are these people maintaining web pages of old
arguments
> of mine long dropped down the toilet by me?
> Possibly they wish to maintain that because I have failed
arguments
> IÕm crazy.
Nope. ItÕs because you defended those argument vigorously,
passionately
and hysterically to the point of verbally assaulting and
threatening those
who found the ßaws originally. ThatÕs the proof that you 
are
crazy.
> James Often in error, but never in doubt. Harris
--
There are two things you must never attempt to prove: the
unprovable --
and the obvious.
--
Democracy: The triumph of popularity over principle.
--
http://www.crbond.com
===
Subject: Re: a simple algebra question about inverses
> how does f(x)= (1-x)/x
become f^-1(x)= 1/(x+1)
the farthest i can get is x= 1-y/y and i get stuck there.
Likewise how does x= (y+4)/(y-3) simplify to y=(3x+4)/(x-1)
iÕm sorry if this is an inappropriate place to post this
question, but
>
Given y = f(x) = (a*x+b)/(c*x+d), with a*c <> b*d,
one can solve for x as a function of y as follows:
y = (a*x+b)/(c*x+d)
y*(c*x+d) = (a*x + b)
c*x*y + d*y = a*x + b
c*x*y - a*x = -d*y + b
x*(c*y - a) = -d*y + b
x = (-d*y + b)/(c*y - a)
===
Subject: Re: a simple algebra question about inverses
>how does f(x)= (1-x)/x
>become f^-1(x)= 1/(x+1)
>the farthest i can get is x= 1-y/y and i get stuck there.
xy = 1 - y
xy + y = 1
(x+1)y = 1
y = 1/(x+1)
>Likewise how does x= (y+4)/(y-3) simplify to y=(3x+4)/(x-1)
Now see if you can do that one.
--
Stan Brown, Oak Road Systems, Cortland County, New York, USA
http://OakRoadSystems.com
An expense does not have to be required to be considered
necessary. -- IRS Form 1040 line 23 instructions
===
Subject: Re: Public Notice: Copyright Violations
message
The law allows fair use.
You are not the law.
Dramatic, but idiotic.
Common practice on Usenet is that entire postings will be
quoted as a
> convenience to both the copier and the next reader.
HeÕs not talking about Usenet; heÕs talking 
about web pages
people set
up.
> As near as I can tell. heÕs complaining about people
quotinf his postings
to
> usenet. I donÕt think he has anything else. Complaining
about copying
> usenet postings is like complaining about copying toilet
paper patterns.
But see the reference to Penrose suing the Kimberly Clark
Corporation at
http://mathworld.wolfram.com/Tiling.html
--
Clive Tooth
http://www.clivetooth.dk
===
Subject: Re: Public Notice: Copyright Violations
> IÕve noticed people with webpages extensively quoting from
posts IÕve
> made and am now giving public notice that there is no right
to copy
> extensively, that is, to go beyond fair use, from my
writings without
> my express written permission.
Well, practice what you preach, Harris. You have clearly
lifted
things from my website and those of others, and I quote:
IÕve
with
a
the
is
no
to
Maybe you can get away with that under some bull fair use
clause,
but plagiarizing with webpages and express written permission
is
obvious out-and-out theft.
This is my notice to cease and desist.
Other complainants can write to me about the potential for
class
action, whatever that is. My attorneys Dewey, Cheatham and
Howe
are on retainer.
Servo
===
Subject: Re: Public Notice: Copyright Violations
If James doesnÕt want his words repeated, stop printing to
all the newsgroups and no one will use your crap.
Don
===
Subject: Re: Public Notice: Copyright Violations
> IÕve noticed people with webpages extensively quoting from
posts IÕve
> made and am now giving public notice that there is no right
to copy
> extensively, that is, to go beyond fair use, from my
writings without
> my express written permission.
People putting up webpages exceeding fair usage are in
violation of
> international copyright law and may face prosecution to the
full
> extent of those laws.
Let us know how that prosecution goes, will you? By posting
to Usenet
youÕre already giving thousands of NNTP servers permission
(in fact, a
request!) to make copies of your posts and distribute those
copies to
other servers and to any Usenet client who requests them.
Personally, I
think youÕd be insane to try to prosecute someone whose
computer just
makes copies of your posts for a little longer than usual or
serves them
up via a slightly different TCP-based protocol, but IÕve got
no legal
training and so IÕd love to see to what a court thinks about
it.
On the other hand, any legal action you undertake will just
earn you much
more negative publicity and cost you as much money as it
costs your
target, so maybe youÕll be less eager than I am to see a
legal precedent
set. Perhaps instead of trying to retroactively erase your
own history,
you might reconsider that history yourself, and see whether
it can teach
you any lessons about the lack of humility and the
persecution complex
displayed in your current writings.
Oh, and please try to crosspost less next time.
---
Roy Stogner
===
Subject: Re: Public Notice: Copyright Violations
> Common practice on Usenet is that entire postings will be
quoted as a
> convenience to both the copier and the next reader.
>
> HeÕs not talking about Usenet; heÕs talking 
about web pages
people set
up.
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam,
nederland,
+31205924131
home: bovenover 215, 1025 jn amsterdam, nederland;
http://www.cwi.nl/~dik/
===
Subject: Re: Public Notice: Copyright Violations
You are right, unfortunatly the media we are using (internet
digital etc)
is
still primative, and Copyright protection?? years from that
one. The best
is
as you ask/request just act IAW....... (quote from posting by
James
Harris <jstevh@msn.com>
/////////////////////////
////////////
//////////////////////////////
> IÕve noticed people with webpages extensively quoting from
posts IÕve
> made and am now giving public notice that there is no right
to copy
> extensively, that is, to go beyond fair use, from my
writings without
> my express written permission.
> People putting up webpages exceeding fair usage are in
violation of
> international copyright law and may face prosecution to the
full
> extent of those laws.
> And remember those laws are *international* as I suspect
some of you
> in countries other than the United States may feel safe.
> However, I am reminding you that you are to obey the law
wherever you
> may be, or you may find out just how great the reach of
those laws
> are.
> Why not just act in accordance with them without stressing
me to have
> to go after specific people?
> James Harris
===
Subject: Re: Public Notice: Copyright Violations
> IÕve noticed people with webpages extensively quoting from
posts IÕve
> made and am now giving public notice that there is no right
to copy
> extensively, that is, to go beyond fair use, from my
writings without
> my express written permission.
The fact that you have no idea what constitutes fair use says
a lot
> here.
> Even *internationally*.
Well, it is so unfair if you point out his errors to him...
===
Subject: Re: Fixed Point Iteration - Matter of convergence.
> I need to find the real root of the cubic equation
x^3+9x-3=0. I managed
to
> used the fixed point iteration method of rewriting the
equation as x=g(x)
> where g(x)=(3-x^3)/9.
> Using x0=1.0, i managed to perform four iterations using
Xn+1=g(Xn) to
find
> the estimates as follows.
> 1 0.2222222
> 2 0.3321140
> 3 0.3292631
> 4 0.3293670
> But given another scheme of
> Xn+1=3-Xn^3-8Xn
> Which is also correct but somewhat will not converge to the
required root
no
> matter what starting value that I chose.
For a fixpoint iteration formula to be convergent the absolute
value of the
derivative near the root need to be less than or equal to
one. You start
value
needs to be in the range near the root where this is true.
g(x) = 3 - x^3 -8x
gÕ(x) = - 3x^2 - 8
max gÕ(x) = -8
This formula is divergent for all real x
In the case of your first formula
g(x) = (3 - x^3)/9
gÕ(x) = 3/9 * x^2
x < sqrt(9/3) <=> gÕ(x) < 1
Since 1 < sqrt(9/3) the formula is convergent for x0 = 1
//Mattias F. Aldaron
--
Sigblock empty. By choice.
===
Subject: Re: Fixed Point Iteration - Matter of convergence.
> For a fixpoint iteration formula to be convergent the
absolute value of
the
> derivative near the root need to be less than or equal to
one. You start
value
> needs to be in the range near the root where this is true.
Naturally it should be less than one instead of less than or
equal to
one
Apologies // Mattias
--
Sigblock empty. By choice.
===
Subject: Re: JSH: My fear, consider this
> ItÕs so sad that IÕve tried to come up with 
simple examples
for so
> long, and posters like Nora Baron, Dik Winter and Arturo
Magidin
> have *successfully* come back with their own posts and kept
winning at
> convincing you all that I was wrong!
They frequently convince you that you were wrong too.
ItÕs been so frustrating that IÕm 
terrified that they will
just get
> away with it again, so hereÕs another angle as I
desperately try yet
> again to get someone to care about whatÕs mathematically
correct
> knowing the kind of people who are out there to come right
back and
> push incorrect math.
Previously I noted that I could use
P(x) = (x+8a)(x+b), and ab = 1, so P(x) = x^2 + (8a + b)x + 8.
Note: ab=1 implies a and b are units in whatever ring youÕre
in.
And I considered 8a + b = 17, as then you have
8/b + b = 17, so b^2 - 17b + 8 = 0.
Which implies that b = (17 + sqrt(257))/2 or b = (17 -
sqrt(257))/2.
This implies a = 2/(17+sqrt(257)) so a is a root of: 8a^2
-17a + 1 = 0
So, a is not an algebraic integer.
Just worth mentioning.
Now imagine *any* non-unit factor f in the ring of algebraic
integers,
> like 1+i that might be a factor of b, and let b = fz, and
substitute
> and you get
f^2 z^2 - 17fz + 8 = 0, so
f z^2 - 17z + 8/f = 0
and notice you STILL have that f on the front.
You mean in the left term?
I donÕt want to hear that it isnÕt applicable 
because f isnÕt
an
> integer, as if you will have to get a polynomial reducible
over Q if
> you pick the right f, as thatÕs just bogus.
The problem is that 17. For it to work, you need to have
something
> even!
What problem? YouÕve done a manipulation. Since b is a 
factor
of 8, so
is f. WhatÕs the problem? You say you want something to 
work:
what?
IÕm so damned tired. I canÕt be sure if anyone 
will listen to
me.
> Arturo Magidin or Dik Winter or Nora Baron or Rick Decker
will come
> back like they have before, now wonÕt they?
You havenÕt stated a problem, just done a substitution and
some
manipulations.
[rant deleted]
--
Will Twentyman
email: wtwentyman at copper dot net
===
Subject: Re: Core error proof, simpler, shorter
> It turns out you can prove that thereÕs an error in core
with rather
> basic math, using a quadratic:
Let
P(x) = (x+8a)(x+b), and ab = 1, so P(x) = x^2 + (8a + b)x + 8.
Then
a = 1/b and b = 1/a
and to highlight the simple case let (8a + b) = 9, and
substituting
> with
a = 1/b gives,
8(1/b) + b = 9, so 8 + b^2 = 9b, so
b^2 - 9b + 8 = (b-8)(b-1) = 0.
But why two solutions? Obviously, you can just have a=1/8,
and get
(x + 8(1/8))(x + 8) = (x + 8)(x + 1)
so itÕs trivially easy whatÕs going on with 
those two
solutions.
But letÕs make it interesting by considering 8a + b = 17, as
then you
> have
8/b + b = 17, so b^2 - 17b + 8 = 0,
but here itÕs really interesting as checking with the
quadratic
> formula, I have
b = (17 +/- sqrt(257))/2
and mathematicians teach that *now* something significant has
happened
> as that is irrational, and now consider what happens if we
now solve
> for ÔaÕ.
Using now b=1/a,
8a + 1/a = 17, so 8a^2 - 17a + 1 = 0.
BUT 8a^2 - 17a + 1 is a primitive non-monic polynomial
irreducible
> over Q!
That means that Ôa*cannot* be an algebraic 
integer, as
algebraic
> integers cannot be roots of primitive non-monic polynomials
> irreducible over Q!
But notice that ÔbIS an algebraic integer as 
itÕs the root
of a
> monic polynomial with integer coefficient.
Solving 8a^2 - 17a + 1 = 0 with the quadratic formula gives
a = (17 +/- sqrt(257))/16
but itÕs clear that *only* one of those roots can be like 
1/8
before,
> while the other is like 8 from before, but *neither* is an
algebraic
> integer!
YouÕre mixing your roots. Both are like 1/8, while both 
bÕs
are like 8
from before.
So whatÕs the core error?
The assumptions of some mathematicians would mean that
P(x) = (x+8a)(x+b),
is impossible in an ring where Ôaand 
Ôbhave properties
like
> integers, because itÕs impossible in the ring of algebraic
integers,
> if ab = 1 and (8a + b) is an integer, when the result is a
polynomial
> irreducible over Q that has Ôaas a root!
I have no idea what you are trying to say in this sentence.
Perhaps if
you stated the properties and what is claimed to be
impossible it would
help.
See the odd illogic that has been behind posters arguing with
me?
No. I donÕt see that youÕve made a clear 
statement of the
core error.
Clearly there isnÕt anything special about that case besides
our
> inability to *look* at the roots because of the
irreducibility, unlike
> with integers!
You clearly identified the roots. What do you mean by look at
the
roots if not that?
ItÕs an integer prejudice, which is kind of funny now, but
also silly.
It turns out that there *has* to be a ring beyond algebraic
integers,
> which I call the object ring, where thereÕs no problem.
There are plenty of rings that are extensions of the
algebraic integers.
WhatÕs your point? Note: the above statement you made makes
it clear
you have not studied rings.
Now you can fight the core error for all youÕre 
worth, and
youÕll just
> be silly.
What core error? You havenÕt stated one clearly enough to 
try
to fight it.
--
Will Twentyman
email: wtwentyman at copper dot net
===
Subject: determinant problem
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id i1OEFBx11199;
Hi everybody!!!
I have some interesting problem for solving:
A, B are real square matrices such that A2001 = 0 and AB = A
+ B.
Show that det B = 0.
attention.
Bye!!!
===
Subject: Re: determinant problem
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
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by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
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Hi jane,
did you perhaps mean A^(2001) = 0 ? If so, consider taking the
equation AB = B + A, and multiplying by A, on both sides,
a *few* times (this
sounds like a homework question so I want to avoid giving you
a
complete solution), then using the determinant.
>Hi everybody!!!
> I have some interesting problem for solving:
> A, B are real square matrices such that A2001 = 0 and AB =
A + B.
>Show that det B = 0.
>attention.
>Bye!!!
===
Subject: Riddle
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id i1OEF7d11032;
The person who makes it doesnÕt sell it. The person who 
sells
it
doesnÕt use it. The person who uses it doesnÕt 
know it. What
is it?
===
Subject: Re: help figuring a math problem
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id i1OEF6R11005;
>how do i figure this out :a tool room has 36 pairs of gloves
in stock
>at the end of each week, and it obtains 44 pairs from the
factory
>each week. it distributes 32 pairs a week. in how many weeks
will
>the tool room have 156 pairs of gloves in stock? answer is
in 10
>weeks but how do i get the answer
HereÕs how I would do the problem. The tool room gets 44 
pairs
every week and gives out only 32 pairs: it gains 44-32= 12
pairs of
gloves every week.
The tool room starts with 36 pairs and we want to get up to
156
pairs. That means we have to gain 156- 36= 120 pairs of
gloves. Gain
12 pairs every week, it will take 120/12= 10 weeks to do that.
===
Subject: differentiation problem
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id i1OEFCL11209;
Hi everybody!!!
I tried to solve this problem:
f(x) is a differentiable function on [a, b] such that f(x)2 +
f Ô(x)2
> 0 for all x in [a, b]. Show that the function has only
finitely many
distinct roots
If you have some ideas about it, write please- iÕll be
grateful for
Bye!!!
===
Subject: Re: differentiation problem
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
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by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
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by legacy.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
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>Hi everybody!!!
>I tried to solve this problem:
> f(x) is a differentiable function on [a, b] such that f(x)2
+ f
>Õ(x)2
>> 0 for all x in [a, b]. Show that the function has only
finitely
>many
>distinct roots
>If you have some ideas about it, write please- iÕll be
grateful for
>Bye!!!
Hi Jane,
assume f has infinitely many distinct roots in [a,b]. 
LetÕs
choose an infinite countable number of them and arrange them
in a
sequence z_n.
Because [a,b] is compact, there exists a subsequence z_n_k of
z_n
which converges to a z* in [a,b].
We may assume z_n_k <> z* for all k (z* can only appear once
in
z_n_k since z_i <> z_j for i <> j).
Since f is continuous in [a,b], f(z*) = f(lim (k->oo) z_n_k) =
lim (k->oo) f(z_n_k) = 0.
Now, f is differentiable at z*, and because
(f(z_n_k)-f(z*))/(z_n_k - z*) = (0-0)/(z_n_k - z*) = 0 for
all k,
it follows that fÕ(z*) = 0.
So f(z*)^2 + fÕ(z*)^2 = 0, contradicting f(x)^2 + 
fÕ(x)^2 > 0
for all x in [a,b].
Best wishes
Torsten.
===
Subject: game theory?
IÕve been wondering recently, in video games, if it is best
to attack
people
with high health and high attack first, or if it is better to
attack the
people with low health and low attack first. I realize that
this answer
wouldnÕt be the same for every situation, but there would be
some point at
which who is better to attack switches. ItÕs also occurred 
to
me, that you
arenÕt guaranteed to do x damage to everyone all the time,
but that x is
the
mean damage done in an attack (which applies to both the
player and
attacker). This all sounds a lot like something that would be
described by
game theory. Is there any part of game theory, or of any
other theory,
that
has analyzed this at all?
Jeremy
===
Subject: Re: game theory?
>IÕve been wondering recently, in video games, if it is best
to attack
people
>with high health and high attack first, or if it is better to
attack the
>people with low health and low attack first. I realize that
this answer
>wouldnÕt be the same for every situation, but there would 
be
some point at
>which who is better to attack switches. ItÕs also occurred
to me, that
you
>arenÕt guaranteed to do x damage to everyone all the time,
but that x is
the
>mean damage done in an attack (which applies to both the
player and
>attacker). This all sounds a lot like something that would
be described
by
>game theory. Is there any part of game theory, or of any
other theory,
that
>has analyzed this at all?
No, but in most games damaged enemies do not get weaker
(there is no
incapacitation, except maybe the time to drink a healing
potion).
Therefore, all else being equal, the standard strategy is to
concentrate
on enemies you can kill quickly.
However, many quirks exist, depending on the particular game:
- Where enemies can summon others, they should often be
killed first.
- Where harmless enemies can block the attacks of dangerous
ones, leave
them alive to get in the way.
- Where dead enemies leave ÔpresentsÕ, kill all 
you can, grab
the
goodies and run away.
- Tactically, you often want to find a corner where the number
of
attackers are limited.
..and so forth.
Gerry Quinn
--
http://bindweed.com
Screensavers, Games, Kaleidoscopes
Download free trial versions
===
Subject: Finding a meaningful Center of a data set
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
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Hi there, IÕm working on starting a site that organizes game
tournaments between teams of players. Each match affects
individual
ladder points based on the formula:
Player Win = 100 * (current ladder rank of opponant / current
ladder
rank)
Player Loss = 50 * (current ladder rank of opponant / current
ladder
rank)
So you gain 100 times the proportion of your skill (measured
in your
ladder points) versus your opponantÕs skill... OR you lose 
50
times
the the same proportion. ItÕs better to win than it is bad 
to
lose.
ie.
You have a rank of 100, and you play someone with a rank of
120. You
win. You get 100 * 120/100 points, or 120, and the loser
loses 50 *
120/100 or 60 points. If you had lost, he wouldÕve gained 84
points,
while you would lose 42 points.
ThatÕs the easy part. The tough part is when you try to
derive a
score for a team based on the member ranks.
A simple average wonÕt work, because it discourages new
recruiting --
who wants a 0 thrown into your team average? Also, if you
have one
player who is awesome, and the rest are duds, how can we
measure the
true overall team skill?
Median isnÕt sensitive enough. IÕve tried all 
kinds of
approaches
with other measures...
How I do a weighted average on a set of member scores, so
that the
values closest to center count for more than the values
further away
from center?
So if you have a clan with 10 guys above 1000, they can
recruit a new
player and that new playerÕs 0 will only count for a little
bit in the
average? Alternatively, if you had a clan of guys ranked 20
with one
1000, his score only counts for a little bit. At the same
time, the
clan score must reßect changes in the memberÕs score 
(not
stifße the
score from going up).
===
Subject: Re: JSH: Behave Rick Decker
Hey Harris, it doesnÕt look as if you were getting anywhere
in math,
besides giving the crowds big laughs. Why donÕt you give a
shot at
data compression? That is an area whith big bucks to be made.
I mean,
forget about that math for profit crap youÕre 
running, such a
pitiful
enterprise, and have a look at the data compression companies
which
keep popping up every six months or so! Seems there are
enough suckers
willing to sink their money into harebrained schemes if you
present
them with a half decent convincing sounding argument.
Over there at comp.compression, the chair of the chief
crackpot is
empty since Jules Gilbert seems to have evaporated, so you
can make
yourself comfty in it. And guess what? you can tell all your
friends
here that youÕre moving and they can come along, 
isnÕt that
great?
Harris, you really break oneÕs heart, you are such a sad
figure. Have
you seen a doctor? IsnÕt there anything they can do for you?
> You donÕt have to remove the webpage if you wish to be
obsessive about
> the issue, but at least update it to note that IÕve 
dropped
that math
> argument.
It seems to me thatÕs only fair.
ItÕs just plain pissedness to push failures in 
someoneÕs face
from the
> vantage point of your college, which is what youÕre doing.
For those who wonder what IÕm talking about, 
hereÕs a link to
the
> webpage:
http://www.cs.hamilton.edu/~rdecker/FLT/
Now so far Hamilton College is defending DeckerÕs right to
put up the
> webpage, and IÕm not saying he doesnÕt have 
that right!
But he needs to at least reßect basic facts, like that 
IÕve
admitted
> the argument is ßawed.
If he does not, IÕll push the case that heÕs 
deliberately
misleading
> readers, with malice aforethought, and depending on the
Hamilton
> College name and his position there so heÕs *making* the
school
> responsible.
> James Harris
===
Subject: Re: JSH: Behave Rick Decker
> You donÕt have to remove the webpage if you wish to be
obsessive about
> the issue, but at least update it to note that IÕve 
dropped
that math
> argument.
It seems to me thatÕs only fair.
ItÕs just plain pissedness to push failures in 
someoneÕs face
from the
> vantage point of your college, which is what youÕre doing.
For those who wonder what IÕm talking about, 
hereÕs a link to
the
> webpage:
http://www.cs.hamilton.edu/~rdecker/FLT/
I just checked it and apparently Decker added a note at the
end:
In the two years since this page was produced, James has
admitted to
problems with his approach and attempted to recast his
arguments using
the ring of algebraic integers for R.
However, while itÕs true that I *attempted* I failed, and
admitted
same, and have dropped that approach!!!
ThatÕs how I found out the problem with the freaking ring of
algebraic
integers!!!
Now like Decker doesnÕt know about that, eh? As if I 
havenÕt
been
hollering about it for months?
Decker here, instead of trying half-measures, should instead
just bite
the bullet and give complete information.
ThatÕs the role you place upon yourself when you decide to
play a
negative card. If he wants to criticize me, fine, but at a
*minimum*
he has an ethical obligation to not mislead others by not
giving
relevant information.
James Harris
===
Subject: Re: JSH: Behave Rick Decker
> You donÕt have to remove the webpage if you wish to be
obsessive about
> the issue, but at least update it to note that IÕve 
dropped
that math
> argument.
It seems to me thatÕs only fair.
Your view of fairness has always be warped out of true.
ItÕs just plain pissedness to push failures in 
someoneÕs face
from the
> vantage point of your college, which is what youÕre doing.
Are you suggesting that he should get a non-college webpage
URL just to
piss on you?
For those who wonder what IÕm talking about, 
hereÕs a link to
the
> webpage:
http://www.cs.hamilton.edu/~rdecker/FLT/
I just checked it and apparently Decker added a note at the
end:
In the two years since this page was produced, James has
admitted to
> problems with his approach and attempted to recast his
arguments using
> the ring of algebraic integers for R.
However, while itÕs true that I *attempted* I failed, and
admitted
> same, and have dropped that approach!!!
ThatÕs how I found out the problem with the freaking ring of
algebraic
> integers!!!
The only problems with the Algebaic Integers is that they are
beyond
JSHÕs understanding.
> Now like Decker doesnÕt know about that, eh? As if I
havenÕt been
> hollering about it for months?
Decker here, instead of trying half-measures, should instead
just bite
> the bullet and give complete information.
As I recollect, there are hundreds of questions that have
been put to
JSH which he never answered. Sauce for the goose!
ThatÕs the role you place upon yourself when you decide to
play a
> negative card. If he wants to criticize me, fine, but at a
*minimum*
> he has an ethical obligation to not mislead others by not
giving
> relevant information.
He has no more such an obligation than you have. And you have
certainly
not met any such obligation, so why shopuld you require him
to do what
you wonÕt do?
===
Subject: Re: JSH: Behave Rick Decker
> You donÕt have to remove the webpage if you wish to be
obsessive about
> the issue, but at least update it to note that IÕve 
dropped
that math
> argument.
It seems to me thatÕs only fair.
ItÕs just plain pissedness to push failures in 
someoneÕs face
from the
> vantage point of your college, which is what youÕre doing.
For those who wonder what IÕm talking about, 
hereÕs a link to
the
> webpage:
http://www.cs.hamilton.edu/~rdecker/FLT/
> I just checked it and apparently Decker added a note at the
end:
> In the two years since this page was produced, James has
admitted to
> problems with his approach and attempted to recast his
arguments using
> the ring of algebraic integers for R.
> However, while itÕs true that I *attempted* I failed, and
admitted
> same, and have dropped that approach!!!
> ThatÕs how I found out the problem with the freaking ring
of algebraic
> integers!!!
James, there is no problem with the ring of algebraic
integers. All of
your
attempts to show a problem have been mathmatically refuted. I
thought you
had dropped this. If you have another example, please give it
a shot.
I think your last post was ItÕs so sad that 
IÕve tried to
come up with
simple examples for so long, and posters like Nora Baron, Dik
Winter
and
Arturo Magidin have *successfully* come back with their own
posts and kept
winning at convincing you all that I was wrong!
Yes, they have *successfully* come back with their own posts.
I wish you
could understand that they are not Ôagainst
you, they are
trying to help
you with the math. ThatÕs what they do on this forum.
> Now like Decker doesnÕt know about that, eh? As if I
havenÕt been
> hollering about it for months?
> Decker here, instead of trying half-measures, should
instead just bite
> the bullet and give complete information.
You would not like the Ôcomplete informationhe 
would have
to add.
DeckerÕs added note is precisely true. Did you want him to
add , but his
every attempt to do so to this date has been shown to be
incorrect.?
KeithK
> ThatÕs the role you place upon yourself when you decide to
play a
> negative card. If he wants to criticize me, fine, but at a
*minimum*
> he has an ethical obligation to not mislead others by not
giving
> relevant information.
> James Harris
===
Subject: Re: JSH: Behave Rick Decker
> You donÕt have to remove the webpage if you wish to be
obsessive about
> the issue, but at least update it to note that IÕve 
dropped
that math
> argument.
It seems to me thatÕs only fair.
ItÕs just plain pissedness to push failures in 
someoneÕs face
from the
> vantage point of your college, which is what youÕre doing.
For those who wonder what IÕm talking about, 
hereÕs a link to
the
> webpage:
http://www.cs.hamilton.edu/~rdecker/FLT/
I just checked it and apparently Decker added a note at the
end:
In the two years since this page was produced, James has
admitted to
> problems with his approach and attempted to recast his
arguments using
> the ring of algebraic integers for R.
However, while itÕs true that I *attempted* I failed, and
admitted
> same, and have dropped that approach!!!
ThatÕs how I found out the problem with the freaking ring of
algebraic
> integers!!!
Now like Decker doesnÕt know about that, eh? As if I 
havenÕt
been
> hollering about it for months?
Decker here, instead of trying half-measures, should instead
just bite
> the bullet and give complete information.
ThatÕs the role you place upon yourself when you decide to
play a
> negative card. If he wants to criticize me, fine, but at a
*minimum*
> he has an ethical obligation to not mislead others by not
giving
> relevant information.
> James Harris
Call the army! Call the army!
===
Subject: Re: JSH: Behave Rick Decker
>> You donÕt have to remove the webpage if you wish to be
obsessive about
>> the issue, but at least update it to note that IÕve
dropped that math
>> argument.
>>
>> It seems to me thatÕs only fair.
>>
>> ItÕs just plain pissedness to push failures in 
someoneÕs
face from the
>> vantage point of your college, which is what youÕre 
doing.
>>
>> For those who wonder what IÕm talking about, 
hereÕs a link
to the
>> webpage:
>>
>> http://www.cs.hamilton.edu/~rdecker/FLT/
>I just checked it and apparently Decker added a note at the
end:
>In the two years since this page was produced, James has
admitted to
>problems with his approach and attempted to recast his
arguments using
>the ring of algebraic integers for R.
>However, while itÕs true that I *attempted* I failed, and
admitted
>same, and have dropped that approach!!!
>ThatÕs how I found out the problem with the freaking ring 
of
algebraic
>integers!!!
Guffaw. The problem you were going on about for months
you finally dropped. The current problem is no problem at
all - thereÕs simply no explanation in all that ab = 1 stuff
of
whatÕs going wrong.
>Now like Decker doesnÕt know about that, eh? As if I 
havenÕt
been
>hollering about it for months?
YouÕd prefer he mention _all_ the idiocies 
youÕve ever posted
here,
instead of just the ones that are relevant to his text?
>Decker here, instead of trying half-measures, should instead
just bite
>the bullet and give complete information.
>ThatÕs the role you place upon yourself when you decide to
play a
>negative card. If he wants to criticize me, fine, but at a
*minimum*
>he has an ethical obligation to not mislead others by not
giving
>relevant information.
>James Harris
************************
David C. Ullrich
===
Subject: Re: JSH: Behave Rick Decker
> You donÕt have to remove the webpage if you wish to be
obsessive about
> the issue, but at least update it to note that IÕve 
dropped
that math
> argument.
It seems to me thatÕs only fair.
ItÕs just plain pissedness to push failures in 
someoneÕs face
from the
> vantage point of your college, which is what youÕre doing.
For those who wonder what IÕm talking about, 
hereÕs a link to
the
> webpage:
http://www.cs.hamilton.edu/~rdecker/FLT/
> I just checked it and apparently Decker added a note at the
end:
> In the two years since this page was produced, James has
admitted to
> problems with his approach and attempted to recast his
arguments using
> the ring of algebraic integers for R.
> However, while itÕs true that I *attempted* I failed, and
admitted
> same, and have dropped that approach!!!
> ThatÕs how I found out the problem with the freaking ring
of algebraic
> integers!!!
> Now like Decker doesnÕt know about that, eh? As if I
havenÕt been
> hollering about it for months?
> Decker here, instead of trying half-measures, should
instead just bite
> the bullet and give complete information.
> ThatÕs the role you place upon yourself when you decide to
play a
> negative card. If he wants to criticize me, fine, but at a
*minimum*
> he has an ethical obligation to not mislead others by not
giving
> relevant information.
To rephrase this slightly...
Aww Mommy, I made a teensy mistake and that NASTY ickle boy
over there
keeps telling people about it. He is being HOWWIBLE to me.
Make him stop,
Mommy! Now!!
===
Subject: Re: JSH: Behave Rick Decker
> However, while itÕs true that I *attempted* I failed, and
admitted
> same, and have dropped that approach!!!
> ThatÕs how I found out the problem with the freaking ring
of algebraic
> integers!!!
No, you didnÕt. You have simply made other errors, which you
are now
defending as vigorously as you did the
previous ones.
> James Often in error, but never in doubt. Harris
--
There are two things you must never attempt to prove: the
unprovable -- and
the obvious.
--
Democracy: The triumph of popularity over principle.
--
http://www.crbond.com
===
Subject: Re: JSH: Behave Rick Decker
> You donÕt have to remove the webpage if you wish to be
obsessive about
> the issue, but at least update it to note that IÕve 
dropped
that math
> argument.
It seems to me thatÕs only fair.
ItÕs just plain pissedness to push failures in 
someoneÕs face
from the
> vantage point of your college, which is what youÕre doing.
Would you expunge the story of the tower of Babel from the
Bible because
it was a failure?
===
Subject: Re: JSH: Behave Rick Decker
> You donÕt have to remove the webpage if you wish to be
obsessive about
> the issue, but at least update it to note that IÕve 
dropped
that math
> argument.
I did so. What I am wondering now about, is how you came to
ask me about
The dates could quite plainly be seen on those pages, so why
the question?
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam,
nederland,
+31205924131
home: bovenover 215, 1025 jn amsterdam, nederland;
http://www.cwi.nl/~dik/
===
Subject: Re: JSH: Behave Rick Decker
> Now so far Hamilton College is defending DeckerÕs right to
put up the
> webpage, and IÕm not saying he doesnÕt have 
that right!
> But he needs to at least reßect basic facts, like that 
IÕve
admitted
> the argument is ßawed.
> If he does not, IÕll push the case that heÕs 
deliberately
misleading
> readers, with malice aforethought, and depending on the
Hamilton
> College name and his position there so heÕs *making* the
school
ThatÕs hilarious! This is the same threat you made to those
who identified
your argument is ßawed in the first place. First you 
threaten
anyone who
claims you are wrong, then when you finally admit you are
wrong, you
threaten everyone who posts your argument.
> James Often in error, but never in doubt. Harris
--
What a maroon! -- Bugs Bunny..
--
Democracy: The triumph of popularity over principle.
--
http://www.crbond.com
===
Subject: math problem
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
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by legacy.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.10 $, legacy) id i1OLfNT18046
well if it gets 44 pairs a week and distributes 32 that
leaves 12 pair
a week now 12*10=120 pairs of gloves in ten weeks and you
already have
36 now you add 120 plus 36 giving you the 156 pairs that is
is asking
for. 12(P) * 10(w) + 36 = 156 total pair.
p=pairs a week
w=weeks