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jstevh@msn.com science forum Guru
Joined: 21 Jan 2006
Posts: 951

Posted: Fri Jul 14, 2006 4:35 am Post subject:
JSH: The gap covers social reality



Can a short, simple and beautiful factoring approach be presented in
our modern world with all of its connectivity and NOT be picked up by
the mathematical community for a significant period of time, like
several days, if that community is as brilliant as many people think it
is?
I strongly suggest to you, no.
The thing is that I have several major mathematical finds and have
fought a long and hard battle against the real mathematical community,
which in my experience doesn't give a damn about mathematical proof and
easily lies about things mathematical.
But how do you prove that?
If I just put forward a full implementation of a factoring solution and
make certain there is evidence that even nonmathematicians would
accept immediately OF COURSE the mathematical community would jump on
boardjust as fast.
But my point is that the current mathematical community is no better
than the lay community when it comes to mathematics, and in fact is
worse, as it actively fights correct and important mathematical
results.
I'd have no chance if the factoring problem weren't connected to
trillions of dollars.
No chance. You people would just ignore this research like all the
rest, and some of you would call me names, call me a crackpot, and a
crank.
The time lag that is currently taking placethe gapis
incontrovertible proof that your community is not what it pretends to
be, that you are pretenders, lying about your actual mathematical
abilities and inclinations, and willing to sit quietly, on world
shaking mathematical finds.
James Harris 

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mensanator@aol.compost science forum Guru
Joined: 24 Mar 2005
Posts: 826

Posted: Fri Jul 14, 2006 4:40 am Post subject:
Re: JSH: The gap covers social reality



jst...@msn.com wrote:
Quote:  Can a short, simple and beautiful factoring approach be presented in
our modern world with all of its connectivity and NOT be picked up by
the mathematical community for a significant period of time, like
several days, if that community is as brilliant as many people think it
is?
I strongly suggest to you, no.
The thing is that I have several major mathematical finds and have
fought a long and hard battle against the real mathematical community,
which in my experience doesn't give a damn about mathematical proof and
easily lies about things mathematical.
But how do you prove that?

Write a Java program to prove it.
Quote: 
If I just put forward a full implementation of a factoring solution and
make certain there is evidence that even nonmathematicians would
accept immediately OF COURSE the mathematical community would jump on
boardjust as fast.
But my point is that the current mathematical community is no better
than the lay community when it comes to mathematics, and in fact is
worse, as it actively fights correct and important mathematical
results.
I'd have no chance if the factoring problem weren't connected to
trillions of dollars.
No chance. You people would just ignore this research like all the
rest, and some of you would call me names, call me a crackpot, and a
crank.
The time lag that is currently taking placethe gapis
incontrovertible proof that your community is not what it pretends to
be, that you are pretenders, lying about your actual mathematical
abilities and inclinations, and willing to sit quietly, on world
shaking mathematical finds.
James Harris 


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Abstract Dissonance science forum Guru Wannabe
Joined: 29 Dec 2005
Posts: 201

Posted: Fri Jul 14, 2006 5:50 am Post subject:
Re: The gap covers social reality



<jstevh@msn.com> wrote in message
news:1152851733.472319.237190@i42g2000cwa.googlegroups.com...
Quote:  Can a short, simple and beautiful factoring approach be presented in
our modern world with all of its connectivity and NOT be picked up by
the mathematical community for a significant period of time, like
several days, if that community is as brilliant as many people think it
is?
I strongly suggest to you, no.
The thing is that I have several major mathematical finds and have
fought a long and hard battle against the real mathematical community,
which in my experience doesn't give a damn about mathematical proof and
easily lies about things mathematical.
But how do you prove that?
If I just put forward a full implementation of a factoring solution and
make certain there is evidence that even nonmathematicians would
accept immediately OF COURSE the mathematical community would jump on
boardjust as fast.
But my point is that the current mathematical community is no better
than the lay community when it comes to mathematics, and in fact is
worse, as it actively fights correct and important mathematical
results.
I'd have no chance if the factoring problem weren't connected to
trillions of dollars.
No chance. You people would just ignore this research like all the
rest, and some of you would call me names, call me a crackpot, and a
crank.
The time lag that is currently taking placethe gapis
incontrovertible proof that your community is not what it pretends to
be, that you are pretenders, lying about your actual mathematical
abilities and inclinations, and willing to sit quietly, on world
shaking mathematical finds.

Yep! Got milk? 

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jstevh@msn.com science forum Guru
Joined: 21 Jan 2006
Posts: 951

Posted: Sat Jul 15, 2006 12:18 am Post subject:
Re: JSH: The gap covers social reality



mensanator@aol.com wrote:
Quote:  jst...@msn.com wrote:
Can a short, simple and beautiful factoring approach be presented in
our modern world with all of its connectivity and NOT be picked up by
the mathematical community for a significant period of time, like
several days, if that community is as brilliant as many people think it
is?
I strongly suggest to you, no.
The thing is that I have several major mathematical finds and have
fought a long and hard battle against the real mathematical community,
which in my experience doesn't give a damn about mathematical proof and
easily lies about things mathematical.
But how do you prove that?
Write a Java program to prove it.

My point here with the factoring problem is that mathematicians may
talk big about "pure math" and caring about mathematics because it's
supposedly interestingwhen it suits thembut they can just as easily
ignore very important mathematical ideas, when it doesn't.
My real point is that the "pure math" thing is bullshit.
Mathematicians just use it to get away with anything they want, and you
can't prove it except by presenting important and interesting
mathematicsletting them ignore it as I know they canand then,
later, prove that it is valuable.
So the gap is about later.
I need the gap because I know that the field is fully corrupted, so
entire math departments need to be shut down, even at major
universities.
That is, all of the "mathematicians" in these departments need to be
let go as they are not doing useful work.
But how do you build enough steam to get that kind of power?
Like I'm doing now, putting up a factoring idea, and letting the
supposedly brilliant mathematical world, do nothing, while it is slowly
worked out, on Usenet.
James Harris 

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David Moran science forum Guru Wannabe
Joined: 13 May 2005
Posts: 252

Posted: Sat Jul 15, 2006 1:03 am Post subject:
Re: JSH: The gap covers social reality



<jstevh@msn.com> wrote in message
news:1152922718.049275.231040@75g2000cwc.googlegroups.com...
Quote:  mensanator@aol.com wrote:
jst...@msn.com wrote:
Can a short, simple and beautiful factoring approach be presented in
our modern world with all of its connectivity and NOT be picked up by
the mathematical community for a significant period of time, like
several days, if that community is as brilliant as many people think it
is?
I strongly suggest to you, no.
The thing is that I have several major mathematical finds and have
fought a long and hard battle against the real mathematical community,
which in my experience doesn't give a damn about mathematical proof and
easily lies about things mathematical.
But how do you prove that?
Write a Java program to prove it.
My point here with the factoring problem is that mathematicians may
talk big about "pure math" and caring about mathematics because it's
supposedly interestingwhen it suits thembut they can just as easily
ignore very important mathematical ideas, when it doesn't.
My real point is that the "pure math" thing is bullshit.

No it's not. As a REAL mathematician, I look at pure math as something that
helps to understand applied mathematics. I am often referring to theorems
from my pure math classes to solve a problem in applied mathematics.
Quote: 
Mathematicians just use it to get away with anything they want, and you
can't prove it except by presenting important and interesting
mathematicsletting them ignore it as I know they canand then,
later, prove that it is valuable.
So the gap is about later.
I need the gap because I know that the field is fully corrupted, so
entire math departments need to be shut down, even at major
universities.
That is, all of the "mathematicians" in these departments need to be
let go as they are not doing useful work.

And you are?
Quote: 
But how do you build enough steam to get that kind of power?
Like I'm doing now, putting up a factoring idea, and letting the
supposedly brilliant mathematical world, do nothing, while it is slowly
worked out, on Usenet.
James Harris

Dave 

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jstevh@msn.com science forum Guru
Joined: 21 Jan 2006
Posts: 951

Posted: Sat Jul 15, 2006 1:55 am Post subject:
Re: JSH: The gap covers social reality



David Moran wrote:
Quote:  jstevh@msn.com> wrote in message
news:1152922718.049275.231040@75g2000cwc.googlegroups.com...
mensanator@aol.com wrote:
jst...@msn.com wrote:
Can a short, simple and beautiful factoring approach be presented in
our modern world with all of its connectivity and NOT be picked up by
the mathematical community for a significant period of time, like
several days, if that community is as brilliant as many people think it
is?
I strongly suggest to you, no.
The thing is that I have several major mathematical finds and have
fought a long and hard battle against the real mathematical community,
which in my experience doesn't give a damn about mathematical proof and
easily lies about things mathematical.
But how do you prove that?
Write a Java program to prove it.
My point here with the factoring problem is that mathematicians may
talk big about "pure math" and caring about mathematics because it's
supposedly interestingwhen it suits thembut they can just as easily
ignore very important mathematical ideas, when it doesn't.
My real point is that the "pure math" thing is bullshit.
No it's not. As a REAL mathematician, I look at pure math as something that
helps to understand applied mathematics. I am often referring to theorems
from my pure math classes to solve a problem in applied mathematics.
Mathematicians just use it to get away with anything they want, and you
can't prove it except by presenting important and interesting
mathematicsletting them ignore it as I know they canand then,
later, prove that it is valuable.
So the gap is about later.
I need the gap because I know that the field is fully corrupted, so
entire math departments need to be shut down, even at major
universities.
That is, all of the "mathematicians" in these departments need to be
let go as they are not doing useful work.
And you are?

My research speaks for itself.
I have given a definition of mathematical proof:
http://mymath.blogspot.com/2005/07/definitionofmathematicalproof.html
Figured out the key properties that define rings that are like the ring
of integers:
http://mymath.blogspot.com/2005/03/objectring.html
Found my own prime counting function, which unlike any other known
relies on summing a partial difference equation, which is also why it
finds primes on its own, unlike any other known:
http://mymath.blogspot.com/2005/06/countingprimes.html
Fighting mathematicians who have done their best to ignore my research
I wrote the first prime counting function article for the Wikipedia,
where my latest version is now found in the history of the current
page:
http://en.wikipedia.org/w/index.php?title=Prime_counting_function&oldid=9142249
There readers can see my prime counting function in its fully
mathematicized "pure" form, and see how it is a summation, so they can
make the leap to understanding how it relates to a partial differential
equation and an integration.
I had a paper published in a formally peer reviewed mathematical
journaland then the editors withdrew it after sci.math pressure
against it:
http://www.emis.de/journals/SWJPAM/vol203.html
Link is to a site mirror as the electronic journal DIED a few months
later.
That paper covered some pioneering research advancing modular algebra
or the algebra of congruences, extending on the work started by Gauss:
http://mymath.blogspot.com/2005/07/tautologicalspacesfactoring.html
Which is a line of attack I used to find a short proof of Fermat's Last
Theorem:
http://mymath.blogspot.com/2006/03/proofoffermatslasttheorem.html
But I've even considered problems in logic and set theory, handling
supposed contradictions:
http://mymath.blogspot.com/2005/06/threevaluedlogic.html
and
http://mymath.blogspot.com/2005/05/logicalformednessaxioms.html
and
http://mymath.blogspot.com/2005/06/3logicmorebasics.html
Even some of my minor research is significant, as I talked about a
simple way to find primes using quadratic residues:
http://mymath.blogspot.com/2006/04/methodforquicklyfindingprimes.html
The only explanation given the breadth of my research, and dramatic
events like a math journal imploding after publishing then retracting a
paper of mine is that it is so huge that mathematicians who are living
in a political society todaywhere their word is more important than
their researchare fighting a war to deny acceptance of any of it.
If any piece of my research is acknowledged as important from my
definition of mathematical proof to my ideas about finding primes then
they have to fear that the world will realize what they are doing, so
the math wars as I call them are political ones.
It is a fight of group power against mathematical truth.
James Harris 

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David Moran science forum Guru Wannabe
Joined: 13 May 2005
Posts: 252

Posted: Sat Jul 15, 2006 2:32 am Post subject:
Re: JSH: The gap covers social reality



<jstevh@msn.com> wrote in message
news:1152928545.537802.142400@h48g2000cwc.googlegroups.com...
Quote:  David Moran wrote:
jstevh@msn.com> wrote in message
news:1152922718.049275.231040@75g2000cwc.googlegroups.com...
mensanator@aol.com wrote:
jst...@msn.com wrote:
Can a short, simple and beautiful factoring approach be presented in
our modern world with all of its connectivity and NOT be picked up
by
the mathematical community for a significant period of time, like
several days, if that community is as brilliant as many people think
it
is?
I strongly suggest to you, no.
The thing is that I have several major mathematical finds and have
fought a long and hard battle against the real mathematical
community,
which in my experience doesn't give a damn about mathematical proof
and
easily lies about things mathematical.
But how do you prove that?
Write a Java program to prove it.
My point here with the factoring problem is that mathematicians may
talk big about "pure math" and caring about mathematics because it's
supposedly interestingwhen it suits thembut they can just as easily
ignore very important mathematical ideas, when it doesn't.
My real point is that the "pure math" thing is bullshit.
No it's not. As a REAL mathematician, I look at pure math as something
that
helps to understand applied mathematics. I am often referring to theorems
from my pure math classes to solve a problem in applied mathematics.
Mathematicians just use it to get away with anything they want, and you
can't prove it except by presenting important and interesting
mathematicsletting them ignore it as I know they canand then,
later, prove that it is valuable.
So the gap is about later.
I need the gap because I know that the field is fully corrupted, so
entire math departments need to be shut down, even at major
universities.
That is, all of the "mathematicians" in these departments need to be
let go as they are not doing useful work.
And you are?
My research speaks for itself.
I have given a definition of mathematical proof:
http://mymath.blogspot.com/2005/07/definitionofmathematicalproof.html
Figured out the key properties that define rings that are like the ring
of integers:
http://mymath.blogspot.com/2005/03/objectring.html
Found my own prime counting function, which unlike any other known
relies on summing a partial difference equation, which is also why it
finds primes on its own, unlike any other known:
http://mymath.blogspot.com/2005/06/countingprimes.html
Fighting mathematicians who have done their best to ignore my research
I wrote the first prime counting function article for the Wikipedia,
where my latest version is now found in the history of the current
page:
http://en.wikipedia.org/w/index.php?title=Prime_counting_function&oldid=9142249
There readers can see my prime counting function in its fully
mathematicized "pure" form, and see how it is a summation, so they can
make the leap to understanding how it relates to a partial differential
equation and an integration.
I had a paper published in a formally peer reviewed mathematical
journaland then the editors withdrew it after sci.math pressure
against it:
http://www.emis.de/journals/SWJPAM/vol203.html
Link is to a site mirror as the electronic journal DIED a few months
later.
That paper covered some pioneering research advancing modular algebra
or the algebra of congruences, extending on the work started by Gauss:
http://mymath.blogspot.com/2005/07/tautologicalspacesfactoring.html
Which is a line of attack I used to find a short proof of Fermat's Last
Theorem:
http://mymath.blogspot.com/2006/03/proofoffermatslasttheorem.html
But I've even considered problems in logic and set theory, handling
supposed contradictions:
http://mymath.blogspot.com/2005/06/threevaluedlogic.html
and
http://mymath.blogspot.com/2005/05/logicalformednessaxioms.html
and
http://mymath.blogspot.com/2005/06/3logicmorebasics.html
Even some of my minor research is significant, as I talked about a
simple way to find primes using quadratic residues:
http://mymath.blogspot.com/2006/04/methodforquicklyfindingprimes.html
The only explanation given the breadth of my research, and dramatic
events like a math journal imploding after publishing then retracting a
paper of mine is that it is so huge that mathematicians who are living
in a political society todaywhere their word is more important than
their researchare fighting a war to deny acceptance of any of it.
If any piece of my research is acknowledged as important from my
definition of mathematical proof to my ideas about finding primes then
they have to fear that the world will realize what they are doing, so
the math wars as I call them are political ones.
It is a fight of group power against mathematical truth.
James Harris

I don't care what your definition of a mathematical proof is. The only
definition that matters is the one that is formally accepted. I've taken an
entire class on how to write a proper proof, and I don't think your
expositions qualify as proofs.
Dave 

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Proginoskes science forum Guru
Joined: 29 Apr 2005
Posts: 2593

Posted: Sat Jul 15, 2006 3:17 am Post subject:
Re: JSH: The gap covers social reality



jst...@msn.com wrote:
Too bad you don't know what constitutes a "logical step".
This object ring has two properties:
1. 1 and 1 are the only rationals that are units in the ring.
2. Given a member m of the ring there must exist a nonzero member n
such that mn is an integer, and if mn is not a factor of m, then n
cannot be a unit in the ring.
There is only one ring that satisfies both conditions: the ring Z of
integers.
What follows is an actual proof. JSH may want to take notes.
The first part of property 2. just states that the object ring R must
be a subring of Q (the set of rational numbers). The second part
states:
(2b) If mn is not a factor of m, then n cannot be a unit in R.
Since P implies Q is the same as Not Q implies not P, (2b) is
equivalent to:
(2b') If n is a unit in R, then mn is a factor of m.
and (2b') is seen to be true in any case. [Proof: If n is a unit in R,
there exists an a in R such that an = 1, by definition of a unit. Then
(mn)(a) = m(na) = m,
so mn is a factor of m.]
Thus, we have reduced the definition of the "object ring" to (A) 1 and
1 are the only rationals that are units in R, and (B) R is a subset of
Q.
Now Z (the set of integers) satisfies this definition, so suppose R is
not Z. Since any ring that contains 1 also contains Z, and R is not Z,
R contains an element a/b, where a,b are integers, b is nonzero, b is
not 1 or 1, and
gcd(a,b) = 1.
Since gcd(a,b) = 1, there exist integers r and s such that
a r + b s = 1, so
(a/b) r + s = (1/b).
Now, a/b is in R, r is in R, and s is in R, and the result of sums and
products of elements of R is in R, so the lefthand side is in R. Hence
1/b is also in R; however, (1/b)*b = 1, and b is in R, which makes
(1/b) a unit. Since b is not 1 or 1, (1/b) can't be 1 or 1. This
contradicts (A).
Hence the only candidate for the "object ring" is Z. End of proof.
Quote:  Found my own prime counting function,

FORMULA
Quote:  which unlike any other known
relies on summing a partial difference equation, which is also why it
finds primes on its own, unlike any other known:

None of the other prime functions I know of require human intervention.
Quote:  http://mymath.blogspot.com/2005/06/countingprimes.html
Fighting mathematicians who have done their best to ignore my research
I wrote the first prime counting function article for the Wikipedia,
where my latest version is now found in the history of the current
page:
http://en.wikipedia.org/w/index.php?title=Prime_counting_function&old...
There readers can see my prime counting function in its fully
mathematicized "pure" form, and see how it is a summation, so they can
make the leap to understanding how it relates to a partial differential
equation and an integration.
I had a paper published in a formally peer reviewed mathematical
journaland then the editors withdrew it after sci.math pressure
against it:
http://www.emis.de/journals/SWJPAM/vol203.html

They withdrew it after they realized it had a mistake. Another paper in
the same issue of that journal (by Plotnikov) also contained a mistake.
BTW, this link shows that the "proof" you wrote doesn't match your
definition of a proof.
This short proof relies on the existence of the "object ring", whose
existence is doubtable. Thus, if the "object ring" falls, so does the
FLT proof.
Just because your research is broad doesn't mean you're a crank. Check
out Archimedes Plutonium's page, http://www.iw.net/~a_plutonium
Quote:  and dramatic
events like a math journal imploding after publishing then retracting a
paper of mine is that it is so huge that mathematicians who are living
in a political society todaywhere their word is more important than
their researchare fighting a war to deny acceptance of any of it.
If any piece of my research is acknowledged as important from my
definition of mathematical proof to my ideas about finding primes then
they have to fear that the world will realize what they are doing, so
the math wars as I call them are political ones.

And if not, JSH will remain an anonymous crank. The odds are
10^(10^100) to 1 in favor of the crank outcome.
Quote:  It is a fight of group power against mathematical truth.

Yeah, right.
 Christopher Heckman 

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Arturo Magidin science forum Guru
Joined: 25 Mar 2005
Posts: 1838

Posted: Sat Jul 15, 2006 3:25 am Post subject:
Re: JSH: The gap covers social reality



In article <1152933427.128800.190580@b28g2000cwb.googlegroups.com>,
Proginoskes <CCHeckman@gmail.com> wrote:
[.snip.]
Quote:  http://mymath.blogspot.com/2005/03/objectring.html
This object ring has two properties:
1. 1 and 1 are the only rationals that are units in the ring.
2. Given a member m of the ring there must exist a nonzero member n
such that mn is an integer, and if mn is not a factor of m, then n
cannot be a unit in the ring.
There is only one ring that satisfies both conditions: the ring Z of
integers.

Hmm.... No. The claim is false. The ring of algebraic integers also
satisfies the properties.
A rational is an algebraic integer if and only if it is an integer, so
condition 1 is satisfied.
The second clause of 2 is vacuous, as has been mentioned many times:
if n is a unit, then mn is an associate of m and hence a factor of m;
thus the converse holds. You yourself prove this in your post.
The first clause of 2 holds in the ring of algebraic integers: if m is
any algebraic integer, and f(x) is its minimal polynomial over Q, then
we can let n be the product of all roots of f(x) other than m,
following the convention that the empty product equals 1.
Quote:  What follows is an actual proof. JSH may want to take notes.
The first part of property 2. just states that the object ring R must
be a subring of Q (the set of rational numbers).

And this claim is false. There is no warrant for this assertion.

======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
 Calvin ("Calvin and Hobbes")
======================================================================
Arturo Magidin
magidin@math.berkeley.edu 

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Proginoskes science forum Guru
Joined: 29 Apr 2005
Posts: 2593

Posted: Sat Jul 15, 2006 4:44 am Post subject:
Re: JSH: The gap covers social reality



Arturo Magidin wrote:
Quote:  In article <1152933427.128800.190580@b28g2000cwb.googlegroups.com>,
Proginoskes <CCHeckman@gmail.com> wrote:
[.snip.]
http://mymath.blogspot.com/2005/03/objectring.html
This object ring has two properties:
1. 1 and 1 are the only rationals that are units in the ring.
2. Given a member m of the ring there must exist a nonzero member n
such that mn is an integer, and if mn is not a factor of m, then n
cannot be a unit in the ring.
There is only one ring that satisfies both conditions: the ring Z of
integers.
Hmm.... No. The claim is false. The ring of algebraic integers also
satisfies the properties.

Really?
sqrt(2) (either one ) is an algebraic integer. What nonzero integer
multiple of sqrt(2) is an integer?
 Christopher Heckman
Quote:  A rational is an algebraic integer if and only if it is an integer, so
condition 1 is satisfied.
The second clause of 2 is vacuous, as has been mentioned many times:
if n is a unit, then mn is an associate of m and hence a factor of m;
thus the converse holds. You yourself prove this in your post.
The first clause of 2 holds in the ring of algebraic integers: if m is
any algebraic integer, and f(x) is its minimal polynomial over Q, then
we can let n be the product of all roots of f(x) other than m,
following the convention that the empty product equals 1. 


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Proginoskes science forum Guru
Joined: 29 Apr 2005
Posts: 2593

Posted: Sat Jul 15, 2006 4:48 am Post subject:
Re: JSH: The gap covers social reality



Proginoskes wrote:
Quote:  Arturo Magidin wrote:
In article <1152933427.128800.190580@b28g2000cwb.googlegroups.com>,
Proginoskes <CCHeckman@gmail.com> wrote:
[.snip.]
http://mymath.blogspot.com/2005/03/objectring.html
This object ring has two properties:
1. 1 and 1 are the only rationals that are units in the ring.
2. Given a member m of the ring there must exist a nonzero member n
such that mn is an integer, and if mn is not a factor of m, then n
cannot be a unit in the ring.
There is only one ring that satisfies both conditions: the ring Z of
integers.
Hmm.... No. The claim is false. The ring of algebraic integers also
satisfies the properties.
Really?
sqrt(2) (either one ) is an algebraic integer. What nonzero integer
multiple of sqrt(2) is an integer?

Wait a minute ... I was reading the second condition as
2. Given a member m of the ring there must exist a nonzero INTEGER n
such that mn is an integer, and if mn is not a factor of m, then n
cannot be a unit in the ring.
Are there any other examples?
 Christopher Heckman
Quote:  A rational is an algebraic integer if and only if it is an integer, so
condition 1 is satisfied.
The second clause of 2 is vacuous, as has been mentioned many times:
if n is a unit, then mn is an associate of m and hence a factor of m;
thus the converse holds. You yourself prove this in your post.
The first clause of 2 holds in the ring of algebraic integers: if m is
any algebraic integer, and f(x) is its minimal polynomial over Q, then
we can let n be the product of all roots of f(x) other than m,
following the convention that the empty product equals 1. 


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Arturo Magidin science forum Guru
Joined: 25 Mar 2005
Posts: 1838

Posted: Sat Jul 15, 2006 8:10 pm Post subject:
Re: JSH: The gap covers social reality



In article <1152938695.479093.241790@h48g2000cwc.googlegroups.com>,
Proginoskes <CCHeckman@gmail.com> wrote:
Quote: 
Arturo Magidin wrote:
In article <1152933427.128800.190580@b28g2000cwb.googlegroups.com>,
Proginoskes <CCHeckman@gmail.com> wrote:
[.snip.]
http://mymath.blogspot.com/2005/03/objectring.html
This object ring has two properties:
1. 1 and 1 are the only rationals that are units in the ring.
2. Given a member m of the ring there must exist a nonzero member n
such that mn is an integer, and if mn is not a factor of m, then n
cannot be a unit in the ring.
There is only one ring that satisfies both conditions: the ring Z of
integers.
Hmm.... No. The claim is false. The ring of algebraic integers also
satisfies the properties.
Really?
sqrt(2) (either one ) is an algebraic integer. What nonzero integer
multiple of sqrt(2) is an integer?

You misread the condition; it says "there must exist a nonzero MEMBER
n such that mn is an integer". It does not say that n must be an
integer. Multiply sqrt(2) by sqrt(2) (following the proof I gave) to
get a multiple (in the ring) of sqrt(2), by a nonzero element of the
ring, which is an integer.

======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
 Calvin ("Calvin and Hobbes")
======================================================================
Arturo Magidin
magidin@math.berkeley.edu 

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Arturo Magidin science forum Guru
Joined: 25 Mar 2005
Posts: 1838

Posted: Sat Jul 15, 2006 8:13 pm Post subject:
Re: JSH: The gap covers social reality



In article <1152938881.994914.94380@i42g2000cwa.googlegroups.com>,
Proginoskes <CCHeckman@gmail.com> wrote:
Quote: 
Proginoskes wrote:
Arturo Magidin wrote:
In article <1152933427.128800.190580@b28g2000cwb.googlegroups.com>,
Proginoskes <CCHeckman@gmail.com> wrote:
[.snip.]
http://mymath.blogspot.com/2005/03/objectring.html
This object ring has two properties:
1. 1 and 1 are the only rationals that are units in the ring.
2. Given a member m of the ring there must exist a nonzero member n
such that mn is an integer, and if mn is not a factor of m, then n
cannot be a unit in the ring.
There is only one ring that satisfies both conditions: the ring Z of
integers.
Hmm.... No. The claim is false. The ring of algebraic integers also
satisfies the properties.
Really?
sqrt(2) (either one ) is an algebraic integer. What nonzero integer
multiple of sqrt(2) is an integer?
Wait a minute ... I was reading the second condition as
2. Given a member m of the ring there must exist a nonzero INTEGER n
such that mn is an integer, and if mn is not a factor of m, then n
cannot be a unit in the ring.
Are there any other examples?

Any other examples of what? Under the condition you give, I don't
think so, but I haven't really thought about it. Under the condition
as given, the ring of integers of any number field will satisfy the
condition; I am fairly sure that there are rings that properly contain
the algebraic integers and satisfy the condition: adjoin an element u
which is an algebraic number, but such that no power is a rational
number; such exist. Then there exists an integer d such that du is an
algebraic integer, at which point the same trick I used before gives
you a multiple of du which is an integer. There are many such rings,
and there is no unique maximal subring of the algebraic numbers that
satisfy the condition (since if u works, so does any conjugate of u,
but you can't have all the conjugates of u in such a ring or a
symmetric function evaluated in them would yield a noninteger
rational).

======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
 Calvin ("Calvin and Hobbes")
======================================================================
Arturo Magidin
magidin@math.berkeley.edu 

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