mm-2079 Mathematics is not new age cultism; if you want to introduce new ideas, then you need to characterize or define them precisely. See, that's your problem; maybe might be Philosophy, but it's certainly not Mathematics. Gibberish. You aren't. Maybe if you would define your new things then he would see. But what he saw might not be what you are expecting. Well, if it doesn't, then why do you imagine either t5hat it is an extension of N or that it has any interest or utility? Which is part of why you haven't been able to come up with anything coherent. How to manipulate numbers without understanding them. That's Theology, not Mathematics. What numbers? Do your unspecified numbers follow the field or ring axioms? If not, in what sense are they numbers? What is a size and -- Unsolicited bulk E-mail subject to legal action. I reserve the right to publicly post or ridicule any abusive E-mail. Reply to domain Patriot dot net user shmuel+news to contact me. Do not So after all your claims of polynomial time, you still do not even have an algorithm worked out? What an ass! Well, reality is I can't get a program to work, so I can't exactly hold on to that belief, now can I? So, yes, I'm back-tracking as I can't get an implementation to work, and now find myself theorizing more, and often understanding less. But that's how a real researcher operates. So, yes, I admit it, much less confident now, in research mode trying to figure it all out. James Harris What belief? It's either right or wrong. You accuse the others of holding onto their false beliefs instead of using science and now here you're saying I can't hold on to that belief. Theorizing is really the wrong word. Specially since the first step in the scientific process is the hypothesis. So you should be Hypothesizing. Nope it isn't. Maybe you should drop math work in favour of the scientific process lessons. I suggest your local high school, sign up for a grade 9 science class [well actually earlier than that...]. Somehow I doubt that. I'm going to predict within the next week you'll solve factoring again and call at least two different people jerks for censoring your work. Tom But back when we all told you the same thing, that we could not hold on to that belief, you told us we would go to fail for it. Thats the way you seem to operate... understanding less each day. But that will not stop your next outrageous claim, I am sure. No. That is how a crank operates. A real researcher works through the theory first, then gets it published. BTW, did you get your rejection from the Annals of Maths yet? Then why are you here? Not to get picky but the normal procedure for research is 1. Hypothesis. What if? 2. Theory. I think that. 3. Experiment. Do it. 4. Observations. See the results. 5. Conclusions. Was the theory correct. Then when you have a result [solution, new problem, etc] the paper usually takes the form 1. Problem statement. What we are talking about. 2. Theorems, Lemmas and Proofs. Build a train of thought 3. Observations [if any]. show that this works... 4. Conclusion. Problem {solved|open|mooted|changed}. Writing a paper and doing research are TWO different things. For instance when I did my FPHT research [to determine the branch] I did the research in those phases. 1. What is the branch of a n-dimension FPHT over a finite field? I wonder if it's countable and there is a relationship between the dimensions. 3. Let's count the branch for n=1,2,4,8 4. The branch for n=1,2,4,8 is 2, 3, 4, 6, ... 5. Conclusion the theory seems to be supported. At which point I started the paper. 1. What is the branch of a n-dimensional FPHT over a finite field? 2. Theorems, proof [... read the paper on eprint ;-)] 3. Observations. This proof agrees with the empiracal results. 4. Conclusion the branch is defined by 2 * Beta {n/4} for n ge 4 and is 2, 3 for n = 1, 2 respectively. While this particular paper wasn't super deep this example shows how a real research project is supposed to work. Harris's method amounts to experiment, conclude, repeat. So he aims mindlessly and shoots and then can't understand why he's always missing... Tom [N.B. The relevence of my FPHT paper is that FPHTs are quick complete transforms that are efficient in software and especially hardware. As a result of my paper they can be used in wide trail designs because the branch is boundable. They're also more efficient than MDSes in hardware as the FPHT is highly parallizable] For Group Permutation computations, except GAP, are Maple or Mathematica are able to handle these kinds of computations? or any other softwares else..? Hmmm... Yes, it is a puzzle. It should work. But it does not seem to work. I suspect that the answer lies somewhere in a fundamental flaw in the algebraic integers and Galois theory. What do you think of that idea? For the same reason that all your other efforts did not work... you are an idiot. [JSH] Good advice: try small numeric examples. Use a computer if you like, but _try_ them. I know your Java program used a small list of primes to build on, I suppose for speed, but that's premature optimization of the most harmful kind: *first* get it working right, from first principles, with no speed tricks. The older version of your method Rick Decker explained (I'm sorry, but I truly could not understand your presentation) hit problems already with M=3*3. If you think there's some special reason for why squares can't work, fine, it hit other problems before getting as far as M=17*19. Examples that small are easy to work out in full detail, and then you can check them, step by step, against what you _thought_ your equations were telling you. You _could_ find mistakes swiftly this way. But if the program defers to a different method for small integers, you won't bump into problems until the method actually comes into play, at larger integers. Then the numeric details get so messy that it can be hard to see what went wrong. If you had first checked to be sure that every odd integer less than 10,000 was correctly factored (which should take a trivial amount of computer time -- seconds at most), you would not have publicly insisted that any of your methods to date were correct. They all fail on examples that small -- and then they're not going to start working by magic on larger examples either. I don't know why you feel no shame about repeatedly making false claims, or about accusing those of pointing out the errors of lying (and worse), but if there's a part of you that would still appreciate earning some respect, find the discipline to do the basic sanity check above before proclaiming and ranting and threatening. If you can actually factor all 4-digit integers correctly with a method, you _may_ be on to something real then; but if you post a method that fails on examples that small, and insist that it's perfect, then of course you'll look like an idiot (and for darned good reason -- think about it). boundary=----=_NextPart_000_0008_7DE37031.DDC391A9 by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) with ESMTP id j1D9CLA11481 by c-67-174-39-191.client.comcast.net with esmtp --------------------------------------------------------------------- Take that! Fikani bwino Note that e = 4 is idempotent in Z12 but 8 is not. Now it should be easy to see how 4 Z12 = Z3 = Z18/ker(FI) --Bill Dubuque Let (x_n) be a given sequence in a metric space (X,d). Suppose that FOR EVERY subsequence (x_{n_k}) , (obviously, don't consider the trivial circumstance in which (x_{n_k}) is equal to (x_n) itself) (x_{n_k}) converges to a given fixed element ' l ' in X. Then (x_n) converges to ' l '. Is it true? Why? If x_n DOES NOT converge to l, then there is a delta-ball centered at l with infinitely many terms of the sequence outside that ball. Take your subsequence from among those outside terms. -- G. A. Edgar http://www.math.ohio-state.edu/~edgar/ Take any infinite subsequence that corresponds to a tail of the original. If you meant, by your restriction, no sequences of this sort, consider any two subsequences {x_(n_k)} and {x_(n_m)} that contain all the elements of the original (duplicates are allowed, but every element of the original MUST be in one or the other. By assumption, these each converge to l, and so for all i,j larger than some particular n_k and n_m respectively, the two subsequences lie within a distance e of l, any positive e. Thus for n larger than the maximum of this n_k, n_m, the main sequence is within a distance e of l, and so converges to it. Yes, it's true. Since every susequence converges to 'l', then the subsequence x_2,x_3,x_4,x_5,... converges to 'l', and this implies that (x_n)_n converges to 'l'. Jose Carlos Santos by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id j1DEA5B04954; For details, see my websites http://home.iprimus.com.au/pidro/ http://www.users.bigpond.com/pidro/home.htm Or the original papers on the subject: 1) Exact equations of Fermat's last theorem, Nonlinear Studies, Vol. 5, No. 2, 1998 3) The new nonstandard analysis, Nonlinear Analysis and Phenomena, Vol. II, No. 1, 2005 (this is a new journal and this issue is due for release this month). Regarding the adics they are presently ill-defined since the integers, as real numbers are ill-defined. Two of the axioms of the real number system, namely, the trichotomy and completeness axioms are false. Counterexamples to them were constructed by Brouwer (Benacerrap and Putnam, Philosphy of Math., Cambridge U Press, 1985) and Banach-Tarski (Kline, Mathematics: The loss of certainty, Oxford U Press, 1980) E. E. Escultura mathematicians Re: The counterexamples to FLT (some big snips to save space) I feel I did not address many big issues and want to address them before I leave this thread. And I have said some good points about EEE's thoughts and alot of bad points about EEE's thoughts and this is how it should be. The good points is that EEE recognizes that the Natural-Numbers of Andrew Wiles FLT are a fake set. And that the world of mathematics needs to move into the direction of recognition that the Finite Integers/Counting Numbers/Natural Numbers become Infinite Integers as long as there is an endless adding of 1. The entire subject of Number Theory in mathematics is a fake subject because it does not have a full grasp that these Integers are the Adics. And the reason Number-Theory has so many ancient unsolved problems and why FLT needs 100 pages of arcane arm twisting argument is because mathematicians fail to understand they are working with Infinite Integers and not Finite Integers. Physics had a similar history when Quantum Mechanics replaced Newtonian Mechanics yet the old physicists could not wrestle with the newfound knowledge and stubbornly stuck to the old system. So EEE deserves credit that FLT is false and that the numbers need repair. But the bad points about EEE, I have not enumerated sufficiently and I want to do that. Bad points: (1) EEE is stuck with the idea that mathematicians and mathematics spearheads and is more fundamental than physicists and physics. Here EEE is very wrong because math and mathematicians are a tiny subdepartment of physics and it is physics that makes clear all and any piece of mathematics. It is physics, starting with 1990 and onwards through physics experiments that are the ultimate Proof of any mathematical claim. Example: is FLT. It is not Andrew Wiles with some hornswaggle of an argument that is 100 or 200 pages long that is going to prove FLT. It is not EEE with some new set of axioms to define Reals or Integers that is going to solve FLT. It is Experimental Physicists who some day report that the Quantized Hall Effect of its strange and bizarre Rational Numbers are actually Adics and that a corner of physics requires out of necessity these Adics to explain that corner of physics. Once that news is blaired out and validated by other experimental physicists and by theoretical physicists. That day is the day in which Physics will have proved FLT. Proved that the Natural-Numbers that Pythagoreas, that Archimedes, that Kepler, that Gauss, that Riemann, that Poincare had all thought were Finite Integers, were Natural-Numbers, were Counting Numbers were all wrong. And that these numbers were really Infinite Integers and Adics. So EEE is foolish to think that mathematicians and mathematics is going to solve any big and noteworthy thing in mathematics or in physics. It is physics that is going to solve all things in mathematics and in physics. (2) Recently EEE has the claim of what he calls new Reals. Here again he has failed to see the problem in terms of physics. To be a good mathematician means you have to be a good physicist first. Back in the 1990s I wanted to know what the number set intrinsic to Loba geometry was. I hypothesized that the REals were the intrinsic set to Euclidean Geometry and that the Adics were the intrinsic set to Riem. geometry. In geometry we have three values of positive, zero and negative and thus we have three geometries of Riem, Eucl, and Loba. But in physics we have Duality not tri-ality. I was stuck and troubled with Doubly Infinites. The Reals were rightward infinite strings and the Adics were leftward infinite strings. So, according to Physics I should stop with just the Reals and Adics because those two give Duality. That Double Infinites are just nonsense. But what about the 3 geometries, and should Duality say that one of those geometries is also nonsense? Perhaps the REals are really Loba geometry and not Euclidean but I have not yet worked that out in my mind. And that would leave Euclidean Geometry as a fictional geometry just as Newtonian Mechanics is a fictional physics. Both the Adics and the REals have a zero point. And so Euclidean GEometry is a geometry based on a single point of zero and nothing more. Whereas Riem geometry are all the Adics and Loba geometry is all the Reals (if I work it out). In light of that, when we look at EEE, as someone who ignores physics and thinks that math and math axioms champions all of math and all of physics, we see EEE claiming that his new REals are some singular super set. EEE fails to realize that physics Duality require the world of mathematics has 2 sets of numbers, both independent of each other and both describing a realm very much different from one another. Again, it will be experimental-physicists who will prove my above notions and not some ivory towered mathematician who knows diddly about physics and experiments. (snip) (3) The above paragraph by EEE fails to consider Physics. Physics duality is one of the most vital truths of our age. Physics is not tri-ality nor singular-ality. So physics demands there to be 2 sets of numbers that make up all of Algebra for mathematics. Since the 1990s I have proposed that these two sets be: Reals ---- infinite strings rightward, with a finite portion leftwards Adics ---- infinite strings leftward, with a finite portion rightwards There is room only for 2 sets according to Physics so the above Reals and Adics cover all the bases. If EEE had learned or discovered more physics and had realized that Physics was the bases for mathematics, then he would have realized that his new Reals is a comedy trip. (snip) (4) One gets the picture that EEE like Brouwer or Banach or Tarski or Wiles can sit in ivory towers and make mathematical proofs and can make mathematical arguments that have the ring of truth. But the reality of it all is that the Experimental Physicists allied with theoretical physicists from now and into the far future will be the persons Proving mathematical statements. Will be the persons correcting the axioms of the 20th century and past centuries. It is the Experimental-Physicists that will announce some day that a corner of physics necessitates Adics and not Natural-Numbers. And then all of physics will be seen as containing Adics which were previously thought to be Natural-Numbers. And when that announcement comes FLT will be proven false. And all the old axioms dumped into the trashcan. Mathematics is true only as it is USeful and true according to physics. Physics is the prover of all mathematical statements of all mathematical ideas because mathematics is just a tiny department inside of Physics. (5) EEE never really understood the blemish of the Successor Axiom in that it forces the Natural-Numbers to become Adics. The Successor Axiom is the endless adding of 1. And the not-so-bright mathematicians of the 20th century never put their minds to the rigor of logic to realize if the Successor Axiom was included in the Peano axioms that those Counting Numbers cannot be controlled. Can not be halted and said that you must be a finite-integer and never cross over into becoming infinite-integer as a adic. EEE never spent time on talking long and hard on the contradiction and inconsistency that the Successor Axiom is in the Peano axioms and simultaneously is in the method of producing the Adics. So if you have a Successor in the Finite Integers and have a Successor in the Adics and yet like Wiles claim those two sets are distinct is a failure of a prudent mind. You cannot have an endless adding of one and call your set Finite Integers and have an endless adding of 1 and call that set the Adics and say they are distinct and different sets. So, in the 1990s and 2000-2005 EEE never talked in depth about the Successor Axiom and how it is contradictory to Adics and Natural-Numbers. Instead EEE has latched onto his new crank turnwheel of algorithm and procedure for producing digits. But, EEE, is not the Successor axiom of endless adding of 1 a algorithm and procedure for producing digits? Is not the next Adic achieved by the procedure of endless adding of 1? Seems that EEE has another lapse of logic here and is not focused. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies Is Hom_Z(Q/Z,Q/Z) countable or uncountable? Why? Would it make a difference if I asked about Hom_Z(Hom_Z(Q/Z,Q/Z),Q/Z) ? Tony Hi all, I am trying to prove the following which I would appreciate any input on : Denote |_| by the coproduct. I want to show that if M_i is a family of R-modules and N_i are submodules of M_i, then |_| (M_i / N_i) = ( |_| M_i ) / (|_| N_i ) I am trying to do this using definition of coproduct...but I'm not sure if I am getting it right. So in order to see if ( |_| M_i ) / (|_| N_i ) is the coproduct of (M_i / N_i), I need to show that ( |_| M_i ) / (|_| N_i ) satisfies the universal property of coproducts. So, I make the following diagram : | | | | / X The morphisms I specify F_i from M_i / N_i to ( |_| M_i ) / (|_| N_i ) which I need to specify as part of the definition of coproduct will be that m_i + N_i goes to (0,0,...,0,m_i,0,0,...) + |_| N_i where m_i is an element of M_i. Now if f_i are a family of maps from M_i / N_i to the R-module X, Now I define G from ( |_| M_i ) / (|_| N_i ) to X by sending (m1,m2,m3,...) + |_| N_ i to summation f_i (m_i + N_i). I'm going to need to state of course that all of these tuples that I am writing down have all but finitely many terms zero, as I tacitly identify the coproduct with the direct sum (am I allowed to do that? That is, am I allowed to state the words direct sum and use the fact that all but finitely many terms are zero when I am trying to prove something entirely in terms of category theory stuff like coproduct?) Then, I think these maps work...and if H is another morphism from ( |_| M_i ) / (|_| N_i ) to X making this diagram commute, I think I can show that H equals G (I did it last night and I'll have to recreate it again but I think it's ok)... Am I right with my maps and with everything? Tony I presume that R is a commutative ring with unity. Yes, it is allowed, since the co-product and the direct sum are both the representation of the functor prod_{i e I} Hom_R(M_i,.), hence they are naturally isomorphic. If you know the notion of exact sequences and functors, it is easier to show stuff like this by the gathering the so-called universal property in the equivalence of functors Best, J. They are not equal, just equivalent in the category. sure if I is the ) following Again here just equivalent (isomorphic). ) be that (m1,m2,m3,...) I hope you're not summing the morphisms here? am identify am I finitely terms of Yes you are since you're using the universal property of the coproduct; ie that any two objects in R-Mod satisfying the property will be equivalent -- isomorphic. |_| show that but I I didn't have time to check, hope someone else does. But why don't you components are) and look at the kernel? No, I'm summing f_i (m_i + N_i) . The target of f_i is X, an R-module, so this sum makes sense. Also, this sum makes sense since in the element (m1,m2,m3,...) + |_| N_i , only finitely many of the m_i are non-zero. To everyone who responded: you have answered my question to my satisfaction, in a variety of interesting and insightful ways. I could not have asked for a better response, and it exemplifies sci.math at its finest. (I'll thank all 5 responders - David Kastrup, Stuart Newberger, Johan Mebius, Peter Montgomery, G. A. Edgar - collectively here so as not to clutter up your busy day with numerous individual posts!) Dave (1) If I well understand a truncated distribution means that we bound the distribution such that the integral of the density from zero (or the lowest bound?) to the upper bound is one and, doing that we have to keep the same shape than the untruncated corresponding distribution. Am I right? I would like to know intuitively what is a scale parameter when we have a truncated distribution, what does this mean exactly? (2) Could you please check if this is the right expression of a truncated log-normal density function?: f(w) = (K/w) exp((ln(w)-ln(m*a0+(1-m)*a1)/2 s^2) (1) K is the scale parameter, the support is [a0, a1], 0