Nineteen months.
fernando revilla
numbers and Goldbach conjecture"
( See http://mathforum.org/kb/message.jspa?messageID=5116035&tstart=0)
I express:
That in the 19 months in which the paper has been in
public knowledge, no technical and/or conceptual errors
have been found. Thanks to all persons who have shown
sincere and honest interest. I'll be very pleased of
interchanging mathematical questions about the mentioned paper.
Fernando.
P.S. I want "the truth" nor "my truth".
Nico Benschop
NB:
For a short and direct proof of FLT, using base p number
representation (odd prime p exponent in x^p + y^p =/= z^p) see:
http://pc2.iam.fmph.uniba.sk/amuc/_vol74n2.html (pgs 169 - 184)
Method by "residue-and-carry",
==>> also applied to prove Goldbach's conjecture <<==
http://de.arxiv.org/abs/math.GM/0103091 (16 pgs)
http://home.iae.nl/users/benschop/ng-abstr.htm (10 pgs)
Intro "Why difficult when easy?",
the residue-and-carry method :
at http://home.iae.nl/users/benschop/residu-carry.doc
Nico Benschop
"fernando revilla" <frej...@ficus.pntic.mec.es> schreef in bericht
news:14748970.1172315780...@nitrogen.mathforum.org...
> About the paper
> "Hyperbolic Classification of Natural numbers and Goldbach conjecture"
>
> ( See http://mathforum.org/kb/message.jspa?messageID=5116035&tstart=0 )
>
> I express:
> That in the 19 months in which the paper has been in
> public knowledge, no technical and/or conceptual errors
> have been found. Thanks to all persons who have shown
> sincere and honest interest. I'll be very pleased of interchanging
>
> P.S. I want "the truth" nor "my truth".
NB: You claim (sci.math 10sep2006) about Goldbach's conjecture :
c ) Taking into account that the new six pages added do not spend a lot of
time to review,
I'll consider on July 17, 2007 that the mathematical community has
accepted that the
==>> Goldbach Conjecture is unprovable
[*] if I do not receive a communication of any fundamental error. ( Two
years in Internet ).
----
How about =>> : (5) 7feb2007
NB: For a short and direct proof of FLT, using base p number
representation (odd prime p exponent in x^p + y^p =/= z^p) see:
http://pc2.iam.fmph.uniba.sk/amuc/_vol74n2.html (pgs 169 - 184)
Method by "residue-and-carry",
also applied to prove Goldbach's conjecture, see:
http://de.arxiv.org/abs/math.GM/0103091 (16 pgs)
=>> http://home.iae.nl/users/benschop/ng-abstr.htm (10 pgs) <<=
Intro "Why difficult when easy?" : the residue-and-carry method :
at http://home.iae.nl/users/benschop/residu-carry.doc
Re[*]: Absence of disproof is not equivalent to proof . . . ;-(
Hisanobu Shinya
>
> numbers and Goldbach conjecture"
>
> ( See
> http://mathforum.org/kb/message.jspa?messageID=5116035
> &tstart=0)
>
> I express:
>
> That in the 19 months in which the paper has been in
>
> public knowledge, no technical and/or conceptual
> errors
> have been found. Thanks to all persons who have shown
>
> sincere and honest interest. I'll be very pleased of
>
> interchanging mathematical questions about the
> mentioned paper.
Would you really like to do so? I will have to ask many questions on your paper; indeed, so many. If you think you could endure that, then I will read your paper.
>
>
> Fernando.
>
> P.S. I want "the truth" nor "my truth".
Hisanobu Shinya
Hisanobu Shinya
I have seen in the Net that a man named Robin Chapman has pointed out a mistake in your paper.
Tonico
wrote:
> About the paper "Hyperbolic Classification of Natural
> numbers and Goldbach conjecture"
>
>
> I express:
>
> That in the 19 months in which the paper has been in
> public knowledge, no technical and/or conceptual errors
> have been found. Thanks to all persons who have shown
> sincere and honest interest. I'll be very pleased of
> interchanging mathematical questions about the mentioned paper.
>
> Fernando.
>
> P.S. I want "the truth" nor "my truth".
Well: send it then to any peer-reviewed journal. They have there
people of several specialities that review papers, and then some of
them will sit quietly to read thoru7gh all your paper.
If some journal rejects your paper, don't get discouraged: there're
lots of journals out there.
Regards
Tonio
Pd. A piece of advice: do NOT use the phrase "...in the 19 months in
which the paper has been in public knowledge, no technical and/or
conceptual errors have been found"
besides the fact that SOME mistakes already were pointed out at some
stage to that paper...:>)
ma...@cam.ac.uk
mathematics joural of good repute. With a bit of googling you can find
many proofs of Fermat, Goldbach and four colour theorem etc that have
been lying on the internet for years. Just because no one has bothered
to point out mistakes does not mean they are correct.
mak
fernando revilla
> How about =>> : (5) 7feb2007
Two years published, I suppose. Then, according to the
standard behaviour of mathematical community your proof
should be accepted.(Notice the conditional).
> Re[*]: Absence of disproof is not equivalent to
> proof . . . ;-(
This assertion is a tautology, then I have nothing to
say. Another tautology is: Absence of acknowledgment is
not equivalent to disproof.
Best regards.
Fernando.
fernando revilla
> > interchanging mathematical questions about the
> > mentioned paper.
>
> Would you really like to do so? I will have to ask
> many questions on your paper; indeed, so many. If you
> think you could endure that, then I will read your
> paper.
> Hisanobu Shinya
Of course, I would be very pleased to do that. I will
answer to all your questions. If a fundamental flaw is
found, I will honestly recognize it.
Best regards.
Fernando.
Tonico
wrote:
> Nico Benschop wrote:
> > How about =>> : (5) 7feb2007
>
> Two years published, I suppose. Then, according to the
> standard behaviour of mathematical community your proof
> should be accepted.(Notice the conditional).
Nop. It is NOT the same "published" and "published in a peer-reviewed
journal". There are several super-nonsenses in the net that were
"published" some good years ago, and that does NOT give them any
acceptation.
Send the purposed proof to a serious journal. If it is accepted,
suposedly because it is true, it'll begin to make some rather high
noise, and after some year everybody will be talking about you. After
all, it is Goldbach's Conjecture that we're talking about here.
Simply posting "the proof" in the net doesn't make it such.
Regards
Tonio
fernando revilla
> Well: send it then to any peer-reviewed journal. They
> have there
> people of several specialities that review papers,
> and then some of
> them will sit quietly to read thoru7gh all your
> paper.
> If some journal rejects your paper, don't get
> discouraged: there're
> lots of journals out there.
> Regards
Perhaps in the future.
> Pd. A piece of advice: do NOT use the phrase "...in
> the 19 months in
> which the paper has been in public knowledge, no
> technical and/or
> conceptual errors have been found"
> as a reinforcing argument for your paper: I'm afraid
> it won't work,
> besides the fact that SOME mistakes already were
> pointed out at some
> stage to that paper...:>)
Would you mind telling me about those mistakes?. If
true, then this story is over.
Thanks.
Fernando.
fernando revilla
> The only way to gain general acceptance is to publish
> your work in a
> mathematics joural of good repute. With a bit of
> googling you can find
> many proofs of Fermat, Goldbach and four colour
> theorem etc that have
> been lying on the internet for years. Just because no
> one has bothered
> to point out mistakes does not mean they are correct.
> mak
Thank you for your sincere and honest advice. I know
that things work that way and perhaps in the future I
will try again. But now I have several reasons for being
in open revolt.(Nothing to do with persecutor obsessions
of course).
Best regards.
Fernando.
Nico Benschop
"Hisanobu Shinya" <eprint...@yahoo.com> schreef in bericht
news:9483597.11724846898...@nitrogen.mathforum.org...
>>
>> "fernando revilla" <frej...@ficus.pntic.mec.es> schreef in bericht
>> news:14748970.1172315780755.JavaMail.jakarta@nitrogen. mathforum.org...
>> > About the paper
>> > "Hyperbolic Classification of Natural numbers and Goldbach conjecture"
>> >
>> > ( See
>> >
>> > I express: That in the 19 months in which the paper has
>>> been in public knowledge, no technical and/or conceptual
>>> errors have been found. Thanks to all persons who have
>>> shown sincere and honest interest. I'll be very pleased
>>> of interchanging mathematical questions about the mentioned
>>> paper. - - Fernando.
>> >
>> > P.S. I want "the truth" nor "my truth".
>> ------------------------------------------------------
>>
>> You claim (sci.math 10sep'06) re Goldbach's conjecture:
>>
>> c ) Taking into account that the new six pages
>> I'll consider on July 17, 2007 that the the
>> mathematical community has accepted that :
>> ==>> the Goldbach Conjecture is unprovable
>> if I do not receive a communication of any
>> ----
>> NB: How about =>> : (5) 7feb2007
>> For a short and direct proof of FLT, using base p
>> number representation (odd prime p exponent
>> http://pc2.iam.fmph.uniba.sk/amuc/_vol74n2.html
>
> I have seen in the Net that a man named Robin Chapman
> has pointed out a mistake in your paper.
He did not reply to my 5 sci.math postings of the
link to that publication, each 7-th of the month since
September 2006.
So it must have been some years ago, before publication
in Acta Mathematica of Univ. Bratislava (Nov.2005).
He did have some critique, which was mainly about
notation, sharply distinguishing between residues and
integers, which due to explicit use of the carry indeed
is crucial in the extension from residues to integers.
>>
>> Method by "residue-and-carry", also applied to
>> prove Goldbach's conjecture, see:
>> http://de.arxiv.org/abs/math.GM/0103091
>> (16 pgs)
>> http://home.iae.nl/users/benschop/ng-abstr.htm
>> (10 pgs) <<=
>>
>> Intro "Why difficult when easy?" :
>> the residue-and-carry method : at
>> http://home.iae.nl/users/benschop/residu-carry.doc
>>
>> Re[*]:
>> Absence of disproof is not equivalent to proof ;-(
Hisanobu Shinya
Okay, then. Dear sirs, I will read your paper as well.
Since I post whenever I find one ambiguous part of your paper, you need to answer it; otherwise, at least, I have the right to claim that you have not proved Fermat's Last Theorem.
Rule: If you stop, then you lose.
I would like to suggest that we discuss in this thread.
>
> >>
> >> Method by "residue-and-carry", also applied to
> >> prove Goldbach's conjecture, see:
> >> http://de.arxiv.org/abs/math.GM/0103091
> >> (16 pgs)
> >> http://home.iae.nl/users/benschop/ng-abstr.htm
> >> (10 pgs) <<=
> >>
> >> Intro "Why difficult when easy?" :
> >> the residue-and-carry method : at
> >> http://home.iae.nl/users/benschop/residu-carry.doc
> >>
> >> Re[*]:
> >> Absence of disproof is not equivalent to proof
> ;-(
>
Hisanobu Shinya
Hisanobu Shinya
Okay. How about discussing in this thread? Or if you want, you could start a new thread for review.
>
> Best regards.
>
> Fernando.
Hisanobu Shinya
Tonico
wrote:
Well, I don't have a list of those, or any other, remarks by anyone
and/or anywhere, but I seem to remember that R. Chapman or A. Magidin
(I can't be 100% sure) did point out some mistake(s) the first time
you came up with the announcement of your GC's proof some few months
ago.
Am I wrong? Perhaps you already fixed those flaws, or perhaps you are
convinced those were NOT actual ones.
Anyway, the gist of my message is still valid, imo: whether there were
(are) flaws in your paper or not, it'll be generally accepted by the
mathematical community only if it appears in some peer-reviewed
journal.
You may want to wait for "later" as much as you want and for the
reasons you want, but continuing to state that "18 months, 19 months,
345 months, etc" already passed on doesn't REALLY make your work more
respectable from a mathematical point of view...though you may believe
it does, of course.
Regards
Tonio
> Thanks.
>
> Fernando.
fernando revilla
> Okay. How about discussing in this thread? Or if you
> want, you could start a new thread for review.
It is the same to me. Do just as you want, you are who
kindly have chosen to read my paper.
Regards.
Fernando.
fernando revilla
> Well, I don't have a list of those, or any other,
> remarks by anyone
> and/or anywhere, but I seem to remember that R.
> Chapman or A. Magidin
> (I can't be 100% sure) did point out some mistake(s)
> the first time
> you came up with the announcement of your GC's proof
> some few months
> ago.
> Am I wrong? Perhaps you already fixed those flaws, or
> perhaps you are
> convinced those were NOT actual ones.
Yes, you are wrong. Neither R.Chapman nor A.Magidin have
commented anything about my paper. The fundamental flaw
in the first version of my paper was found by myself.
> Anyway, the gist of my message is still valid, imo:
> whether there were
> (are) flaws in your paper or not, it'll be generally
> accepted by the
> mathematical community only if it appears in some
> peer-reviewed
> journal.
> You may want to wait for "later" as much as you want
> and for the
> reasons you want, but continuing to state that "18
> months, 19 months,
> 345 months, etc" already passed on doesn't REALLY
> make your work more
> respectable from a mathematical point of
> view...though you may believe
> it does, of course.
> Regards
> Tonio
This sequence of messages will end with the topic"Twenty
four months". So do not worry about it.
Regards.
Fernando.
Hisanobu Shinya
I have read six pages. It seems that a sequence of definitions in the first few pages are not necessary, but let me read the rest to decide on that as well.
------------------------------------
First question:
In Theorem 1.2.1, you mention f_{+} and f_{-}. How are they defined?
With an answer to the question above, I can continue the tough reading.
------------------------------------
I suggest you not to use the "same nomenclature" for x-hat and x.
Besides, if I were you, I would not put the drawings like one in your paper. The moment a referee sees it, s/he will be exhausted.
Hisanobu Shinya
Nico Benschop
Nico Benschop
should be:
"extension by one positive carry < p_{k+1} of weight m_k"
(where modulus m_k = \prod first k primes)
fernando revilla
> I have read six pages. It seems that a sequence of
> definitions in the first few pages are not necessary,
> but let me read the rest to decide on that as well.
Of course they are not necessary if the purpose of the
paper is only the GC. Even more, the only R_C function
used in chapters 2 and 3, are affine functions in every
closed interval [m,m+1].
The purpose of Chapter 1 was to prepare a general theory
independently of if "all" the tools were used or not in
the next chapters
> First question:
>
> In Theorem 1.2.1, you mention f_{+) and f_{-}. How
> are they defined?
>
> With an answer to the question above, I can continue
> the tough reading.
I do not mention f_{+) and f_{-}. I suppose you mean
f'_{+} and f'_{-}. They are the "usual" lateral derivatives.
>
> I suggest you not to use the "same nomenclature" for
> x-hat and x.
>
> Besides, if I were you, I would not put the drawings
> like one in your paper. The moment a referee sees it,
> s/he will be exhausted.
>
> Hisanobu Shinya
Nothing to say, that would correspond to psychological
and/or aesthetic appreciations.
Regards.
Fernando.
Hisanobu Shinya
>
> > I have read six pages. It seems that a sequence of
> > definitions in the first few pages are not
> necessary,
> > but let me read the rest to decide on that as
> well.
>
> Of course they are not necessary if the purpose of
> the
> paper is only the GC.
Please let it be so, then! I wish a piece of paper focused only for Goldbach Conjecture.
> Even more, the only R_C
> function
> used in chapters 2 and 3, are affine functions in
> every
> closed interval [m,m+1].
>
> The purpose of Chapter 1 was to prepare a general
> theory
> independently of if "all" the tools were used or not
> in
> the next chapters
>
> > First question:
> >
> > In Theorem 1.2.1, you mention f_{+) and f_{-}. How
> > are they defined?
> >
> > With an answer to the question above, I can
> continue
> > the tough reading.
>
> I do not mention f_{+) and f_{-}. I suppose you mean
>
> f'_{+} and f'_{-}. They are the "usual" lateral
What is the lateral derivative? Do you mean left/right-hand derivative?
> derivatives.
>
>
>
> >
> > I suggest you not to use the "same nomenclature"
> for
> > x-hat and x.
> >
> > Besides, if I were you, I would not put the
> drawings
> > like one in your paper. The moment a referee sees
> it,
> > s/he will be exhausted.
> >
> > Hisanobu Shinya
>
> Nothing to say, that would correspond to
> psychological
> and/or aesthetic appreciations.
No. You will never get attention of mathematicians with that motto.
>
> Regards.
>
> Fernando.
Hisanobu Shinya
> claim to have an elementary proof of FLT, but you
> give no link to it, unfortunately.
I have done something like that several times in the past. But I will never do that again. Only persons like me will be interested in papers opened in that form.
> There are many
> ways to Rome, as they say. Moreover: a short and
> direct proof is usefull, especially the method used,
> because it may help to prove other hard problems,
> such as Goldbach.
Two comments:
It seems that the guy named Robin Chapman has commented on a paper which is listed in the references of your 2005 paper.
To tell the truth, in addition, I tried to read your proof, but I saw the term semigroup, which I do not know well about. I only know undergraduate modern algebra. Is this knowledge enough to read your paper?
> Which I did: my 'residue-and-carry'
> method also applies to Goldbach, but with another
> modulus (than p^k for FLT), namely the product of the
> first k primes, followed by careful extension with
> one carry of weight p_{k+1} and induction on k.
> Saying that any FLT proof after Wiles' (of 1995) is
> useless shows a lack of understanding of how
> mathematics develops! Frankly, to use the
> Tanyama-Shimura proof (of 150+20 pgs) as a method to
> prove FLT is a bit 'over-the-top', don't you think?
> It is like going to the next room via the Northpole.
I am sorry. I do not understand even the statement of Taniyama-Shimura.
> - - - NB
Nico Benschop
>> NB: Very well, Hisanobu. I notice that you yourself
>> claim to have an elementary proof of FLT, but you
>> give no link to it, unfortunately.
>
> But I will never do that again. Only persons like me will
> be interested in papers opened in that form.
NB: What do you mean by "persons like me",
and "opened in that form"?
It is standard practice to store a new paper at a preprint server,
in order to have it date-stamped and open it for discussion.
( Of course, it must be of some 'mature quality' ;-)
Both my FLT and Goldbach paper are at arXiv.org/math,
of which the FLT paper is published now. Your eagerness to
review it, beyond the reviewing by the math department and
editors of the University of Bratislava, made me curious -
especially your tone of discussion (menat to scare me off ?-)
>> NB: There are many ways to Rome, as they say.
>> Moreover: a short and direct proof is usefull, especially
>> the method used, because it may help to prove other
>> hard problems, such as Goldbach.
>
> HS: Two comments:
> It seems that the guy named Robin Chapman has commented
> on a paper which is listed in the references of your 2005 paper.
NB: Sure, they have been taken care of.
> HS: To tell the truth, in addition, I tried to read your proof,
> but I saw the term semigroup, which I do not know well about.
> I only know undergraduate modern algebra. Is this knowledge
> enough to read your paper?
NB: I only use undergraduate discrete math, assuming this includes
the semigroup of multiplicative residue arithmetic. The reason
that this suffices, despite the stigma of FLT, is the fact that the
'carry', as complement to residue arithmetic, is usually ignored in
number theory - for specific reasons eluded to in the link I gave to
a short intro http://home.iae.nl/users/benschop/residu-carry.pdoc
>> Which I did: my 'residue-and-carry'
>> method also applies to Goldbach, but with another
>> modulus (than p^k for FLT), namely the product m_k
>> of the first k primes, followed by careful extension with
>> a carry < p_{k+1} of weight m_k and induction on k.
>>
>> Saying that any FLT proof after Wiles' (of 1995) is useless
>> shows a lack of understanding of how mathematics develops!
>> Frankly, to use the Tanyama-Shimura proof (of 150+20 pgs)
>> as method to prove FLT is a bit over-the-top, don't you think?
>> It is like going to the next room via the Northpole. - - NB
>
> I am sorry. I do not understand even the statement of Taniyama-Shimura.
You don't need to because, as I mention : it is a way too difficult road,
and unnecessary, for approaching FLT - residues and carries will suffice!
But if your prefer to withdraw, I can understand. - - - NB
Nico Benschop
http://home.iae.nl/users/benschop/residu-carry.doc
fernando revilla
> Please let it be so, then! I wish a piece of paper
> focused only for Goldbach Conjecture.
As you can understand I am not going to change the
contents of my paper. The purpose is very clear
a) There is a fundamental flaw in my paper?
b) If not, is the conclusion correct?
I am the author of the paper, so I decide what I have to
write and you decide if you want to read it or not.
> What is the lateral derivative? Do you mean
> left/right-hand derivative?
Surely in my answer I have used bad English. Of course I
meant left/right-hand derivative, all the same the
notations f'_{-}(a) and f'_{+}(a) are universally
accepted. It was a surprise to me your question.
> No. You will never get attention of mathematicians
> with that motto.
That sentence seems to be an advice of a teacher to his
student and makes me feel younger.
As Nico Benschop told you in a previous post:
"But if your prefer to withdraw, I can understand."
If you want to continue, please, only mathematical
questions.
Regards.
Fernando.
l_f...@yahoo.fr
understand the meaning of your proposition 3.2.2. For example I don't
understand what a "characterization of the Goldbach conjecture in an
infinite set of even numbers" is. Did you define "characterization of
the Goldbach conjecture", and if so, where ?
fernando revilla
Well 3.2.2 is just the last proposition of the paper, so
it is not easy to abbreviate it in a few words, but I'll
try.
In the infinite set
S={a: a even, a>=16,a-3 no prime, a/2 no prime}
the following is true:
"a belonging to S is the sum of two prime numbers k and
a-k iff the essential points P_k and P_(k-1) are equal"
The essential points are related with the acceleration
of the area of regions conveniently chosen. This
characterization is valid in several dynamical process
but not for all. In some of them the characterization is
lost, because all the essential points degenerate to
(1/2,-1/2) for that reason that characterization depends
on the time.
Take into account that several hours are needed for
understanding all the details.
There are a lot of previous propositions that should be
understood.
Regards.
Fernando.
Hisanobu Shinya
>
> > Please let it be so, then! I wish a piece of paper
> > focused only for Goldbach Conjecture.
>
> As you can understand I am not going to change the
> contents of my paper. The purpose is very clear
>
> a) There is a fundamental flaw in my paper?
> b) If not, is the conclusion correct?
>
> I am the author of the paper, so I decide what I have
> to
> write and you decide if you want to read it or not.
>
>
> > What is the lateral derivative? Do you mean
> > left/right-hand derivative?
>
> Surely in my answer I have used bad English. Of
> course I
> meant left/right-hand derivative, all the same the
> notations f'_{-}(a) and f'_{+}(a) are universally
> accepted. It was a surprise to me your question.
I would like to ask, "Why did that surprise you?" But I do not, since I should ask only mathematical questions( I am just commenting, not asking.)
Anyway, thanks for clarification.
>
> > No. You will never get attention of mathematicians
> > with that motto.
>
> That sentence seems to be an advice of a teacher to
> his
> student and makes me feel younger.
>
> As Nico Benschop told you in a previous post:
>
> "But if your prefer to withdraw, I can understand."
>
> If you want to continue, please, only mathematical
> questions.
Yes, sir.
>
> Regards.
>
> Fernando.
galathaea
wrote:
> About the paper "Hyperbolic Classification of Natural
> numbers and Goldbach conjecture"
>
>
> I express:
>
> That in the 19 months in which the paper has been in
> public knowledge, no technical and/or conceptual errors
> sincere and honest interest. I'll be very pleased of
>
>
> P.S. I want "the truth" nor "my truth".
time
you are inevitable
if i knew the secret purpose
would that make it any less inevitable?
^^..
maybe this month we can pursue
a few minor topics in chapter 2
it appears that this is where many have gathered
and lost their way
so maybe a signpost or two?
let me describe some of the spell
as it cast over me
in 2.1.1
you classify geometric arrangements of essential regions
maybe if you explained to everyone
why you do not include in a)
---------------------
|. |
|. |
| . |
| . |
| . |
| .. |
| ...... |
| ........|
---------------------
(excuse my poor picture)
where the hyperbola intersects both
upper left and lower right corners?
that would establish the first few pages of chapter 2
as a commonly understood ground
and i suspect if we establish a few pages a month
we may be able to beat your month 24
..~~
i'd actually really appreciate a little understanding
from the other side as well
i have been fixated on theorem 2.8.2 often
an even number
alpha
also an adapted R-affine with essential points
P = (x , y )
k0 k0 k0
this theorem asserts that
0 < x < x < ... < x
4 = 5 = = alpha/2 - 1
and also that
x = x iff k is prime
k0-1 k0 0
and also that
y < y < ... < y < 0
4 = 5 = = alpha/2 - 1
and that
y = y iff alpha - k is prime
k0-1 k0 0
may i ask how you approached this theorem?
by this i mean
did you think the relationships possible
and construct the upper/lower essential polynomials
as a tool in the proof?
or were you the playing with polynomials
and discovered these relations?
how did you build the ontology for this proof?
on this i am very interested in your process...
**********#-.-&&&~~~~~~~~
another month
i wish you a beautiful future
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar
Nico Benschop
"Hisanobu Shinya" <eprint...@yahoo.com> schreef in bericht
news:17979822.1172596033...@nitrogen.mathforum.org...
> To tell the truth, in addition, I tried to read your proof, but
> I only know undergraduate modern algebra.
> Is this knowledge enough to read your paper?
NB: Just in case your are interested about semigroups (which is
in essence the associative algebra of function composition) and
their practical applications, have a look at my (online) book:
. . . "Associative Digital Network Theory"
http://home.iae.nl/users/benschop/preface.htm
It has three parts:
- - state machines (associative algebra),
- - arithmetic (associative and commutative),
- - logic (associative and commutative and idempotent),
divided up in a total of 11 chapters and 3 appendices.
(the latter including the proofs of FLT and Goldbach
by the residue-and-carry method).
For intro to the relation of semigroups and FLT :
see http://home.iae.nl/users/benschop/sgrp-flt.htm
and http://home.iae.nl/users/benschop/carry.htm
>> Which I did: my 'residue-and-carry' method also applies to Goldbach,
>> but with another modulus (than p^k for FLT), namely the product of
>> the first k primes, followed by careful extension with one carry of
>> weight p_{k+1} and induction on k. Saying that any FLT proof after
>> Wiles' (of 1995) is useless shows a lack of understanding of how
>> mathematics develops! Frankly, to use the Tanyama-Shimura proof
>> (of 150+20 pgs) as a method to prove FLT is a bit 'over-the-top',
>> don't you think? It is like going to the next room via the Northpole. - -
>> NB.
Hisanobu Shinya
> >
> > If you want to continue, please, only mathematical
>
> > questions.
>
> Yes, sir.
>
> >
> > Regards.
> >
> > Fernando.
Dear Professor Revilla,
I would like to ask a few questions on Definition 1.3.4. It says:
an R function distinguishes primes iff the h_{k-hat} functions are differentiable only at the non-natural abscissa and ordinate points.
1. What are the "ordinate points"?
2. If h_{k-hat} is nondifferentiable only at naturals (i.e., including not only primes but composite integers as well), then could h_{k-hat} still have some properties which characterize (in some way) only primes? Or is there any argument concerning that later in the paper? (I have read through up to 1.3.)
HS
Hisanobu Shinya
Thanks for the information. By the way, will I need to buy some articles of yours to understand your 2005 paper? Hopefully, I want to read your paper by the middle of this March. If it is self-contained, I might be able to do that.
HS
fernando revilla
> I would like to ask a few questions on Definition
> 1.3.4. It says:
>
> an R function distinguishes primes iff the h_{k-hat}
> functions are differentiable only at the non-natural
> abscissa and ordinate points.
> 1. What are the "ordinate points"?
It means:
If (x^,y^) is a point that belongs to the graph of h_k^
then:
"h_k^ is differentiable at x^ iff (x^ non natural and y^
non natural)".
I.e. the h_k^ functions are only differentiable in the
points whose abscissa(x^) and ordinate(y^) are not
natural.
> 2. If h_{k-hat} is nondifferentiable only at naturals
> (i.e., including not only primes but composite
> integers as well), then could h_{k-hat} still have
> some properties which characterize (in some way) only
> primes? Or is there any argument concerning that
> later in the paper? (I have read through up to 1.3.)
If R distinguishes primes according to the definition
1.3.4 then, the primes are completely characterized.
Notice that if R distinguishes primes then, we have
created an special geometrical structure that allows to
distinguish a prime p^ from a natural no prime n^
because in the second case appears at least a vortex
point(see definition 1.4.1) in the hyperbola x^y^=n^.
Thank you very much.
Fernando.
fernando revilla
> in 2.1.1
> you classify geometric arrangements of essential
> al regions
>
> maybe if you explained to everyone
> why you do not include in a)
>
> ---------------------
> |. |
> |. |
> | . |
> | . |
> | . |
> | .. |
> | ...... |
> | ........|
> ---------------------
>
> (excuse my poor picture)
>
> where the hyperbola intersects both
> upper left and lower right corners?
I understand. That essential region does not exist. In
the page 16 we prove that if the hyperbola contains the
point P(n,n'+1) then, the abscissa x of point Q verifies
n<x<n+1.
I spent two years tryng to relate the GC in an adequate
way with the theory of Chaotic Dynamical Systems. I did
not get good results. There was a point in which I
thought that one and important question was to visualize
geometrically primes. So, using continuous deformations
of hyperbolas, I created the Hyperbolic classification
of natural numbers which allows to do that.
After that, I was six months thinking 8 hours a day and
with no idea coming to my mind. One day one "happy idea"
appeared: to analyze partially the areas and to find a
relation between these and the sum of two numbers. The
most important thing I discovered was that "almost" all
the essential regions, the second derivative of the area
is 0.
All the same, I have spent about seven thousand hours to
the GC and it is very difficult to understand where the
ideas come from. Perhaps a reward to tenacity?.
>
> another month
> i wish you a beautiful future
>
Regards and thank you very much.
Fernando.
l_f...@yahoo.fr
(I'm going to assume that everything you have written in your paper
from
the beginning to proposition 3.2.1 is true, I don't have time to check
everything).
On 28 fév, 00:29, fernando revilla <frej0...@ficus.pntic.mec.es>
wrote:
> In the infinite set
>
> S={a: a even, a>=16,a-3 no prime, a/2 no prime}
>
> the following is true:
>
> "a belonging to S is the sum of two prime numbers k and
> a-k iff the essential points P_k and P_(k-1) are equal"
>
Let's see if I understand properly : let a be a number in the set S.
For each
adapted R-affine function, there is a condition, let's call it C(R),
such
that a is the sum of two prime numbers if and only if condition C(R)
is
true (according to your proposition 2.8.3, we should state C(R) as
"there
exists a number k such that the essential points P_k and P_(k-1) are
equal").
What I don't understand is what kind of information you can get from
this. Given a number a in the set S, is it more tractable to try and
find a function R such that C(R) is true than try directly to write
the number a as a sum of two prime numbers ?
Also I don't understand the part about the fact that the
characterization should not be true in all the cases. You show that
when the function R approaches the identity function, all the
essential points have the same limit, but as the identity function is
not adapted, I don't understand how you can deduce anything from this.
fernando revilla
> Let's see if I understand properly : let a be a
> number in the set S.
> For each
> adapted R-affine function, there is a condition,
> let's call it C(R),
> such
> that a is the sum of two prime numbers if and only if
> condition C(R)
> is
> true (according to your proposition 2.8.3, we should
> state C(R) as
> "there
> exists a number k such that the essential points P_k
> and P_(k-1) are
> equal").
> What I don't understand is what kind of information
> you can get from
> this. Given a number a in the set S, is it more
> tractable to try and
> find a function R such that C(R) is true than try
> directly to write
> the number a as a sum of two prime numbers ?
I do not know if to find R such that C(R) is true is
more or less tractable. But notice that this is not the
point, the point is that the set {n^:n natural} shares
the same arithmetic than {n:n natural} and the mentioned
characterization of the GC is related to a dynamical
process.
> Also I don't understand the part about the fact that
> the
> characterization should not be true in all the cases.
> You show that
> when the function R approaches the identity function,
> all the
> essential points have the same limit, but as the
> identity function is
> not adapted, I don't understand how you can deduce
> anything from this.
First of all we should say semi adapted because for the
adapted the acceleration of the area function is not
well constructed. Well, it does not matter.
All right, the identity function is not semi adapted and
the characterization C(R) has been lost. But the
identity function provides the set {n: n natural} with
the associated temporal states n -> n ( in other words
the naturals placed in the real line in the usual way).
In the semi adapted R, we have the associated temporal
states n->n^. The identity function and the R semi
adapted have the same arithmetic I would insist, so in
the set S, C(R) depends on the time.
Regards.
Fernando.
Hisanobu Shinya
Questions:
In pp. 14, there are three drawings. Could you explain those to me? How should I interpret type 2 and 3? How are they different?
What is P-hat?
How should I interpret the drawing for type 1? I really have no idea.
Thanks.
HS
fernando revilla
> Questions:
>
> In pp. 14, there are three drawings. Could you
> explain those to me?
As R distinguishes primes, then the h_k^ functions are
continuous but no differentiable at n^( n>=1 natural) as
a consequence they have different tangents to the left
and to the right.
> How should I interpret type 2
> and 3? How are they different?
Conceptually are not different, the symmetry of the
problem permits to work in y>=x. In in chapter 2, type
2 and 3 will see that provide different accelerations.
> What is P-hat?
p-hat=p^=R(p)
> How should I interpret the drawing for type 1? I
> really have no idea.
The same explanation as in your first question. Notice
that we have decided to work in x>=1. The shape
corresponding to type 1 allows us to distinguish a
natural number from a non natural.
Regards.
Fernando.
NFB
> > "Hisanobu Shinya" <eprinthshi...@yahoo.com> schreef
> need to buy some articles of yours to understand
> your 2005 paper?
NB: No, all given refs are free;-)
It's just your effort to read and understand them.
If you've any questions, let me know.
> Hopefully, I want to read your paper by the middle of
> March. If it is self-contained, I might be able to do that.
> HS- Hide quoted text -
>
> - Show quoted text -
Hisanobu Shinya
I am sorry. I no longer have time to read your articles.
>
> > Hopefully, I want to read your paper by the middle
> of
> > March. If it is self-contained, I might be able to
> do that.
>
> > HS- Hide quoted text -
> >
> > - Show quoted text -
>
>
Hisanobu Shinya
Hisanobu Shinya
I am sorry. I no longer have time to read your paper.
Hisanobu Shinya