mm-1369 === Subject: Cooperative Human-Robot Learning System using a Virtual Reality Telerobotic Interface System using a Virtual Reality Telerobotic Interface. Conference on Advances in Internet Technologies and Applications, Purdue University, West Lafayette, Indiana, U.S.A. http://www.compactech.com/kartoun/ === Subject: Re: players's problem, who wins? >Hi all, >I have three players A, B, C, each with equal probabily to win, that's >to say, when A plays B, P(A wins)=P(B wins)=1/2. And similar to all >pairs, AB, AC, and BC... >Now A, B starts to play, C waits, the winner of A-B will play C, the >loser of A-B will wait... so on and so forth, the winner of the >pair-match will always continue to play the waiter, the loser of the >pair-match will wait for next round... >If A wins two consequtive runs, we call A wins the overall competition >and the game stops... >Now A, B start first to play, what is the probability of A wins the >overall competition? As I understand it, the game stops whenever one player wins the head to head matches twice in a row and that player is declared overall winner. If the is the case, then I make the odds on A:B:C winning overall to be 5:5:4, or in probability terms, 5/14, 5/14 and 4/14 SPOILER BELOW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . After the first play, let ABC represent the outcome of A having won the last play, playing B in the current round and C waiting. Given ABC, then BCA is next or A wins: If A wins the first round then subsequent plays result in: A wins overall or BCA next round B wins overall or CAB next round C wins overall or ABC next round A wins overall or BCA,next round and the 3 step cycle repeats. Thus A wins in this line with probability 1/2^2 + 1/2^5 + 1/2^8 +... = (1/4)/(1-1/8) (geometric series) If A loses the first round then subsequent plays result in: B wins overall or CAB next round C wins overall or ABC next round A wins overall or BCA next round B wins overall or CAB next round, and the 3 step set cycle repeats. Thus A wins in this line with probability 1/2^4 + 1/2^7 + 1/2^10 +... = (1/16)/(1-1/8) The total probability of A winning overall is 5/14 The total probability of B winning overall is 5/14 The total probability of C winning overall is 4/14 === Subject: Re: Dividing by Zero and Axiomatic Set Theory >One of the major questions in the philosophy of mathematics is >whether or not mathematical objects are real, that is, having an >independent pre-existence, or whether they are human creations. That has nothing to do with the question of Division by zero. That question relates to two other questions: 1. What do you mean by number? 2. What do you mean by quotient. If the answer to 1. is real number, whether defined axiomatically or constructed, and the answer to 2. is a/b is the unique number c such that b*c=a, then 0/0 is not defined. If the answers are different then it is incumbent on the poster to explain his private nomenclature. >Thus, Bertrand Russel's barber paradox is due to a slight error in >phrasing: There is no error in the phrasing; Russel posed the question for the purpose of illustrating the paradox, and the phrasing that he used was correct for that purpose. >Clearly, here, the set of all objects, and the smaller set of all >sets, are perfectly meaningful. That's not at all clear, and in, e.g., GBN, ZFC, it's false. Whether it is true is na.95ve set theory depends on your conceptual model. >Because a wild and wooly reality is not tamed with axioms and >postulates, nothing can be directly deduced about it But the resulting logical systems often turn out to be surprisingly useful; the Wigner problem. >They motivate our choice of which formal systems to talk about. Only to a limited extent; there is a huge body of Mathematics that was not inspired by external reality. >Physical reality led us to talk about the properties of numbers, and >about the properties of sets. But external reality did not lead us to talk about, e.g., holomorphic functions. -- Shmuel (Seymour J.) Metz, SysProg and JOAT 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 === Subject: Re: Topology question > Yes, I overlooked the limitation of the the functions f:S -> X to C(S,X). If that's how you read the question, you must have wondered what the topology on X has to do with anything. === Subject: hysterical gift idea Need a unique gift idea for that picky guy or gal who's impossible to shop for? Why not a Dead Leprechaun?!? Underground comedian and all-around malcontent T.G. Fleming has finally gathered together his greatest hits to form the hilarious collection Dead Leprechaun in a Tire-Swing. Filled with the fierce social commentary, biting sexual satire, strange stories, and bizarre ruminations that Fleming is known (and often reviled) for, Dead Leprechaun in a Tire-Swing will spice up any given bowel movement or trip to the beach! Click the link below to read excerpts and learn how to order your very own Dead Leprechaun! http://www.fallingskyhazard.com/catalog.htm === Subject: Re: Probability m out of n people meeting??? >Let's say that you have the above situation. and let's say that mWhat is the probability that m of those n people will meet, and the >remaining n-m people don't meet anyone? ... the probability that >two people meet and the 3rd person just gets lost is >1 - (5/32) - (4/32) = 23/32. Not so. You've overlooked one of the four distinct possible outcomes, namely, the case when A overlaps with B, and B overlaps with C, but C does not overlap with A. There's a web page on the site you referenced that discusses the various possible meeting combinations for different values of n. >I thought that at one time, I'd read a treatment of this problem which >compared it to the birthday problem in which you compute the probability >of at least two people in a room having the same birthday, but I can't >seem to find it... The web site you referenced does indeed contain a page on the generalized birthday problem, giving the explicit formula for the probability of any set of coincidences, but of course that's a much simpler problem because, in that case, overlap is a transitive relation. === Subject: Re: Probability m out of n people meeting??? >>Let's say that you have the above situation. and let's say that m>What is the probability that m of those n people will meet, and the >>remaining n-m people don't meet anyone? ... the probability that >>two people meet and the 3rd person just gets lost is >>1 - (5/32) - (4/32) = 23/32. > Not so. You've overlooked one of the four distinct possible outcomes, > namely, the case when A overlaps with B, and B overlaps with C, but > C does not overlap with A. There's a web page on the site you > referenced that discusses the various possible meeting combinations > for different values of n. You're right! I should've thought of that. This reminds me of the time that I tried to generalize the Gamblers Ruin problem for more than 2 people to calculate the probability that a particular player wins. When I posed that problem, the answer I got was that the problem wasn't fully defined. When a player exits the game after going broke, the rules and scoring must change in order to acommodate n-1 people. This gives me more to think about. Instead of just the probability of m out of n people, meeting, there is also the question of what is the probability that A meets B, B meets C, C meets D, etc. >>I thought that at one time, I'd read a treatment of this problem which >>compared it to the birthday problem in which you compute the probability >>of at least two people in a room having the same birthday, but I can't >>seem to find it... > The web site you referenced does indeed contain a page on the > generalized birthday problem, giving the explicit formula for the > probability of any set of coincidences, but of course that's a much > simpler problem because, in that case, overlap is a transitive > relation. Yeah, I found it. I'll have to read it through. A long time ago, Id gotten some e-mails from the author of this website, and I thought I'd seen him mention the birthday problem in the context of the meeting problem. The e-mails are in a place where I can't lay my hands on them right now. I couldn't find the exact phrase that I was looking for on the generalized birthday problem page, but I guess I'll have to read it through and see if I can get an answer. I know that there is at least an integral for doing this. The only reason that I'm hesitant to use that is because I'd like to write a program which can do any kind of meeting problem, and if I'm going to do integration, that can be time consuming, unless I have a very fast integration method. Anyone else? Anybody knowledgable in qeueing theory? -- ------------------------------- Patrick D. Rockwell === Subject: Re: New Famous Proof > Nonsense. I talk to myself all the time, and on occasion I > respond. >> >> >> For example: >> >> Me: Now where did I put my car keys? [1] >> Me: Did you look on the night table? [2] >> Me: No I didn't, I think I will. [3] >> Me: Hey, twarn't nothin'. [5] >> >> I ask you. Was that a conversation? >> > Any utterance could be classified as a conversation, but we take a > more methodical approach, > the definition is you learnt something from what was said. > A 'null conversation' is just a series of utterances where nothing > is learnt, we don't > include this type since the general obversation of conversations is > extra knowledge. > stated by you > so you didn't learn anything from this statement. > Similarly for [2] and [3]. > [4] You looked on the table. This new information came from your > senses, > eyes, hearing, tactile, not from any of the statements made in [1] > [2] or [3]. [5] This is correct, since a remedial plan of action > could find the keys the utterences were superfluous, nothin'. > Herc >> Have you folks spotted the connexion between what you are saying >> and the notorious private language argument of Wittgenstein? (For >> those interseted, it is all in the /Philosophical Investigations/.) >> I might summarize it thus: if it's a language, it _cannot_ be >> private; and if it's private, it _cannot_ be a language. > this is the fact I'm relying on for the proof to hold, to show how > 'redundant' proofs still stand up mathematically. in practice more > than one person converses, but that has no theoretical merit. Pardon me: yer what? Sorry, M'r Fawlty: I no understan', M'r Fawlty! >> (To avoid the anticipated nit-picking: >> /private/ here means logically private.) You'll also find it >> discussed *phenomenally* deeply in the works of Saul Kripke ... >> whose analysis is the post-Wittgenstein /locus classicus/. >> And remember too that Wittgenstein explicitly made it plain that >> what he was putting forward was not in any sense a theory: just a >> set of remarks to bear in mind when one's thinking seems to be going >> astray. Here is a possible example of the kind of thing that I have >> in mind: In Broken Images, by Robert Graves: >> He is quick, thinking in clear images; >> I am slow, thinking in broken images. >> He becomes dull, trusting to his clear images; >> I become sharp, mistrusting my broken images. >> Trusting his images, he assumes their relevance; >> Mistrusting my images, I question their relevance. >> Assuming their relevance, he assumes the fact, >> Questioning their relevance, I question the fact. >> When the fact fails him, he questions his senses; >> When the fact fails me, I approve my senses. >> He continues quick and dull in his clear images; >> I continue slow and sharp in my broken images. >> He in a new confusion of his understanding; >> I in a new understanding of my confusion. >> John >> johnDOTmorrisonATtescoDOTnet >> -- >> Anything which can be understood can also be misunderstood. > An observation in its atomic form can't be negated can it? > Herc It can: by contradicting the observer. However, I don't think that is quite what you mean ... John johnDOTmorrisonATtescoDOTnet -- There are two sorts of fool: the fool who thinks that what is old is good, and the fool who thinks that what is new is better. - [Ancient Chinese proverb] === Subject: Re: New Famous Proof >> Anything which can be understood can also be misunderstood. > An observation in its atomic form can't be negated can it? > Herc > It can: by contradicting the observer. However, I don't think that is > quite what you mean ... of course, that just leaves... a non-observation in its atomic form. This is my solution to absolute truth, what can a brain in a vat actually deduce? Ex there is something. Herc === Subject: Re: New Famous Proof >> Anything which can be understood can also be misunderstood. > An observation in its atomic form can't be negated can it? > Herc >> It can: by contradicting the observer. However, I don't think >> that is quite what you mean ... > of course, that just leaves... a non-observation in its atomic form. > This is my solution to absolute truth, what can a brain in a vat > actually deduce? > Ex > there is something. > Herc Sorry, mate: it's a silly time of the year to go into such matters at such depth. How about in January - when both of us have had /more/ time to think about all the implications? I'm not Welsh - but, if I were, I would add: nadolig llawen y blwyddyn newydd da! When *both* our brains are not in vats - then, let us continue! I await a sensible response in about two weeks - or, as we Brits would have it, a fortnight. I wish you and _all_ your friends all the best now, and into 2005 ... John johnDOTmorrisonATtescoDOTnet -- Now that you know that 'George Bush' is an anagram of 'shoe bugger', you can at last stop wondering what the 'W' stands for. - Mark F. Hunter === Subject: Re: New Famous Proof >> Anything which can be understood can also be misunderstood. > > An observation in its atomic form can't be negated can it? > > Herc >> >> It can: by contradicting the observer. However, I don't think >> that is quite what you mean ... > of course, that just leaves... a non-observation in its atomic form. > This is my solution to absolute truth, what can a brain in a vat > actually deduce? > Ex > there is something. > Herc > Sorry, mate: it's a silly time of the year to go into such matters at > such depth. How about in January - when both of us have had /more/ time to > think about all the implications? > I'm not Welsh - but, if I were, I would add: nadolig llawen y blwyddyn > newydd da! When *both* our brains are not in vats - then, let us continue! > I await a sensible response in about two weeks - or, as we Brits would have > it, a fortnight. I wish you and _all_ your friends all the best now, and > into 2005 ... no problem! actually that's where my philosophy begins and ends. Exists X is true! i should look at some of the formal provers, introducing Ex is one of the primitive steps so I could see what the others are. no comments on theory please during the 'fall off a seey prac! Herc === Subject: sum (k * C(n, k)) ? For n sum (k * C(n, k)) k=0 I found a post here which says it's equal to 2^n * n/2 n * 2^(n-1) to show some kind of linkage between the original formula and 1) the number of all subsets of an n-element set (2^n) and 2) the sum of the first n positive integers ((n * (n + 1)) / 2). But, for the life of me, I can't figure out how he came up with that. Can anyone enlighten me in fairly simple, non-step-skipping, terms? Also, does that original equation *mean* anything in combinatorial terms? All I can make out is that it adds up the elements of the nth row of Pascal's Triangle after multiplying each term by its index into the row. But, what that *means*, I have no idea. === Subject: Re: sum (k * C(n, k)) ? >For >sum (k * C(n, k)) >k=0 >I found a post here which says it's equal to >2^n * n/2 Replace each of the two terms k * C(n, k) and (n-k) * C(n, k) by their average (n/2) * C(n, k). Then the sum is (n/2) * Sum C(n,k), giving the result above. Mike Guy === Subject: Re: sum (k * C(n, k)) ? > For > sum (k * C(n, k)) > k=0 > I found a post here which says it's equal to > 2^n * n/2 > n * 2^(n-1) > to show some kind of linkage between the original formula and 1) the > number of all subsets of an n-element set (2^n) and 2) the sum of the > first n positive integers ((n * (n + 1)) / 2). But, for the life of > me, I can't figure out how he came up with that. Can anyone enlighten > me in fairly simple, non-step-skipping, terms? > Also, does that original equation *mean* anything in combinatorial > terms? All I can make out is that it adds up the elements of the nth > row of Pascal's Triangle after multiplying each term by its index into > the row. But, what that *means*, I have no idea. The given sum counts the number of subsets with a distinguished element (swades, for short) of an n-element set. Swades may be counted in two ways: a) generate the ordinary subsets, then choose the distinguished element; this gives sum(k*C(n,k)). b) Pick first the distinguished element (in n ways), then add elements to form a swade. The elements added may be those in any of the 2^(n-1) subsets of the original set without the picked element, hence we get n*2^(-1) swades. J H Nieto === Subject: Re: sum (k * C(n, k)) ? >> For >> n >> sum (k * C(n, k)) >> k=0 >> I found a post here which says it's equal to >> 2^n * n/2 >> n * 2^(n-1) >> to show some kind of linkage between the original formula and 1) the >> number of all subsets of an n-element set (2^n) and 2) the sum of the >> first n positive integers ((n * (n + 1)) / 2). But, for the life of >> me, I can't figure out how he came up with that. Can anyone enlighten >> me in fairly simple, non-step-skipping, terms? >> Also, does that original equation *mean* anything in combinatorial >> terms? All I can make out is that it adds up the elements of the nth >> row of Pascal's Triangle after multiplying each term by its index into >> the row. But, what that *means*, I have no idea. > The given sum counts the number of subsets with a distinguished element > (swades, for short) of an n-element set. > Swades may be counted in two ways: > a) generate the ordinary subsets, then choose the distinguished element; > this gives sum(k*C(n,k)). > b) Pick first the distinguished element (in n ways), then add elements to > form a swade. The elements added may be those in any of the 2^(n-1) > subsets of the original set without the picked element, hence we get > n*2^(-1) it should be n*2^(n-1), of course > swades. > J H Nieto === Subject: Re: sum (k * C(n, k)) ? The binomial theorem states: n sum C(n,k) * x^k = (1+x)^n k=0 Differentiating both sides with respect to x yields: n sum k * C(n,k) * x^(k-1) = n * (1+x)^(n-1) k=0 Substituting x = 1 gives you the formula. As far as a combinatorial interpretation, k * C(n,k) is the number of ways to pick a k-element subsets from an n-element set, where one of the k elements of the chosen set is distinguished. The only real-life application I can think of for this is the Powerball lottery, where a player picks 6 numbers and designates one the powerball. Jeremy === Subject: Re: sum (k * C(n, k)) ? with this without using calculus? I'm reading through a Discrete Mathematics (DM) book and that's where I ran into the problem. As far as I can see, DM is supposed to be doable without calculus (the study of discrete sets as opposed to continuous functions -- plus, the author avoids anything to do with it). Also, the author doesn't even introduce the Binomial Theorem until the next chapter. interpretation. That's very useful. === Subject: Re: sum (k * C(n, k)) ? >with this without using calculus? I'm reading through a Discrete >Mathematics (DM) book and that's where I ran into the problem. As far >as I can see, DM is supposed to be doable without calculus (the study >of discrete sets as opposed to continuous functions -- plus, the author >avoids anything to do with it). Also, the author doesn't even >introduce the Binomial Theorem until the next chapter. >interpretation. That's very useful. Here is a direct argument: sum[k=0..n] k n! / ((k!)(n - k)!) = sum[k=1..n] k n! / ((k!)(n - k)!) = sum[k=1..n] n! / ((k-1)!(n - k)!) Let k = m + 1: = sum[m=0..n-1] n! / (m!((n - (m+1))!) = n sum[m=0..n-1] (n-1)! / (m!(n - 1 - m)!) = n (1 + 1)^(n-1) = n 2^(n-1) --Lynn === Subject: Re: sum (k * C(n, k)) ? > with this without using calculus? Yes, that's done in my post (although perhaps not very well explained). Once again: swades may be counted in two ways: a) for each k=1,...,n generate the ordinary k-subsets, then choose a distinguished element (any of k possible). This gives sum(k*C(n,k)). b) Pick first a distinguished element (n possible ways), then add elements to form a swade. The elements added may be those in any of the 2^(n-1) subsets of the original set without the picked element, hence we may generate n*2^(n-1) Since the results from (a) and (b) must be equal, it is proved that sum(k*C(n,k)).= n*2^(n-1) > I'm reading through a Discrete > Mathematics (DM) book and that's where I ran into the problem. As far > as I can see, DM is supposed to be doable without calculus (the study > of discrete sets as opposed to continuous functions -- Not necessarily. Aesthetically, pure combinatorial proofs as the one above are preferable, but the in-depth study of discrete structures often requires not only calculus but fairly advanced mathematics. See for example Knuth's book Concrete mathematics. Jose H. Nieto === Subject: Cardinality: a paradox I've long maintained that there are no infinite sets, and in particular no infinite set of all X where X is any type of cardinal, because, first, the terms are inherently contradictory (all entailing completion, and infinite entailing lack of end (lack of completion); second, because infinite does not specify a true cardinality. For instance, the expression all the naturals does not specify a set at all, but is merely a careless way of expressing the fact that a *general concept* of number -- the *template* called natural numbers -- can be made to yield concrete examples indefinitely; all such sets of examples are nonetheless finite. One cannot have all of something that is unlimited, much less a set of all such entities, since set entails a delineated (hence completed) logical entity. For those who assert otherwise, here is a little paradox. (More than one, actually.) It presumes that the concept of cardinality is well defined -- otherwise, what does set-theory purport to discuss? (1) There is a set of all cardinals, AC. If not, why? (How can a union of sets not be a set? Is cardinal a well defined concept? Is all a well defined concept? The mere fact that assuming AC leads to problems, as some have tactfully phrased it, does not imply that serious theories eschew it *on that basis*; on the contrary, *serious* theories must explain why something which should exist according to standard theory, cannot exist (i.e., where and why standard theory is in error -- which of its axioms are contradictory. The error springs from the fallacious concept of infinite set.) (2) AC is a cardinal. If not, why? (How could a union of cardinals not be a cardinal?) (3) AC, being a cardinal, is a member of itself. If not, why? (Obviously this creates a paradox of infinite regress, but the real question is what error inheres in the assumptions of standard theory, thereby leading to this paradox.) (4) AC is the largest possible cardinal. If not, why? (What has greater cardinality than the set of all cardinals?) (5) AC has a power set, PAC. If not, why? (How can a set of distinct cardinals be unorderable? How can it be impossible to select from its members, and thus to form subsets?) (6) PAC is a cardinal. If not, why? (7) PAC, being a cardinal, is a member of AC. If not, why? (8) PAC is a proper subset of AC. If not, why? (9) PAC has a greater cardinality than AC. If not, why? Mark Adkins msadkins04@yahoo.com === Subject: Re: Cardinality: a paradox at 05:46 PM, msadkins04@yahoo.com said: >I've long maintained that there are no infinite >sets, and in particular no infinite set of all X >where X is any type of cardinal, because, first, >the terms are inherently contradictory You can maintain that little green men from a flying suacer abducted you with equal plausibility. >(all entailing completion, No. >and infinite entailing lack of end (lack of completion); No on both counts. >second, because infinite does not specify a true cardinality. Nu, did you think that fin ite specifies a true cardinality. The term infinite is a catch-all, which is why Mathematicians use more precise language. Aleph-null, etc., refer to specific cardinalities, transfinite refers to any cardinality that is not finite. >For instance, the expression all the naturals >does not specify a set at all, Please define specify and set; you seem to be using private definitions. >but is merely a careless way of expressing the fact that a *general >concept* of number -- the *template* called natural numbers -- can >be made to yield concrete examples indefinitely; No. It is neither careless nor remotely similar to a process. >One cannot have all of something that is unlimited, Feel free to prove that. >One cannot have >all of something that is unlimited, much less >a set of all such entities, since set entails >a delineated (hence completed) logical entity. Please provide your private definitions of Set, delineated and completed. >For those who assert otherwise, here is a little >paradox. Your statement of the alleged paradox leaves an awful lot undefined and makes some unwarranted assumptions. >(1) There is a set of all cardinals, AC. What gives you that idea? What set theory are you using? Your claim is false for GBN and ZFC. >If not, why? In the case of GBN and ZFC, because it is a theorem that no such set exists. >Is cardinal a well defined concept? Yes. >Is all a well defined concept? The existential and universal quantifiers are well defined. >The mere fact that assuming AC leads to problems, as some have >tactfully phrased it, does not imply that serious theories eschew it >*on that basis*; What is your private definition of serious theories. >on the contrary, *serious* theories must explain why something which >should exist according to standard theory, What is your private definition of standard theory? >i.e., where and why standard theory is in error Since you seem to be using standard in an idiosyncratic fashion, it's up to you to explain why a Mathematician should care about what you call standard and its up to you to explain why your unspecified theory is in error. GBN and ZFC are as close to standard theories as you will find, and they don't seem to have the problem. >The error springs from the fallacious concept of >infinite set.) It may be that in your private set theory there is a fallacious concept called infinite set; that concept has nothing to do with what a Mathematician calls an infinite set. >(2) AC is a cardinal. If not, why? (How could a >union of cardinals not be a cardinal?) Well, since in ZFC AC[1] doesn't exist and in GBN it isn't a set, the answer is clear. >(3) AC, being a cardinal, is a member of itself. >If not, why? Because in ZFC it doesn't exist and in GBN it isn't a set and hence cannot be a member of a class. >(Obviously this creates a paradox of infinite regress, In set theories that allow such a set, other restrictions eliminate the paradox. >but the real question is what error inheres in the assumptions of >standard theory, thereby leading to this paradox.) Well, since you seem to be using the term standard theory to refer to something other than the theories used by contemporary Mathematicians, you're the only one that can answer that. The paradox doesn't exist in the set theories used by Mathematicians. >(4) AC is the largest possible cardinal. That's hard to do when it doesn't exist. >(5) AC has a power set, PAC. If not, why? Because it doesn't exist. >(6) PAC is a cardinal. If not, why? What gives you the idea that the power set of a cardinal is a cardinal? >(7) PAC, being a cardinal, is a member of AC. If >not, why? Because it isn't a cardinal. >(8) PAC is a proper subset of AC. If not, why? Because in a set theory where it exists at all, at has elements not present in AC. >(9) PAC has a greater cardinality than AC. If >not, why? Because in ZFC it doesn't exist and in GBN it isn't a set. There are other answers for other set theories. [1] A rather poorly chosen term, since, to a Mathematician talking about Set Theory, AC usually refers to the Axiom of Choice. -- Shmuel (Seymour J.) Metz, SysProg and JOAT 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 === Subject: Re: Cardinality: a paradox <41ce553b$16$fuzhry+tra$mr2ice@news.patriot.net> I almost forgot this one. > at 05:46 PM, msadkins04@yahoo.com said: >(8) PAC is a proper subset of AC. If not, why? > Because in a set theory where it exists at all, at has elements not > present in AC. I'll assume that at is a typo and should read it. If AC is a set, and PAC is the power set of AC, then PAC is the set of all subsets of AC. Every set is a cardinal (the cardinality of its members). Why should PAC, being a set and therefore a cardinal, contain elements which are not present in AC, when the criterion for membership in AC is being a cardinal? Any theories which twist their definitions into such unnatural and illogical forms merely in order to avoid inconvenience, are ill-formed. Another point I'll add: what difference does it make whether you call AC a set or a class? The problems don't go away just because you change the terminology -- not unless you revert to silly arbitrary distinctions again. The only *real* solution here is to realize that all cardinals merely references the concept of cardinality, and does not specify a collection of members. . Mark Adkins msadkins04@yahoo.com === Subject: Re: Cardinality: a paradox <41ce553b$16$fuzhry+tra$mr2ice@news.patriot.net> I've decided to respond to these additional points under cover of a separate reply. > at 05:46 PM, msadkins04@yahoo.com said: >(1) There is a set of all cardinals, AC. > What gives you that idea? What set theory are you using? Your claim is > false for GBN and ZFC. Who said I was using any set theory? Do cardinals exist? Can each cardinal be placed in a set in which it is the only member? Is the union of these sets a set? Since when is the union of sets not a set? What justification is there for making an exception to such a rule, merely because it inconveniences you? The real problem here is an attempt to regard a concept of number as an infinite set of actual members. >(3) AC, being a cardinal, is a member of itself. >If not, why? > Because in ZFC it doesn't exist and in GBN it isn't a set and hence > cannot be a member of a class. It isnt't my fault that ZFC and GBN make arbitrary and unjustified distinctions. My point is predicated upon fundamental matters, not the dogma of particular theories. >(5) AC has a power set, PAC. If not, why? > Because it doesn't exist. Do cardinals exist? Is it possible to group individual cardinals into subsets of cardinals? Then why not PAC? Is the union of these sets itself a set? Then why not AC? Why is the union of individual elements not a subset, or the union of subsets not a set? >(6) PAC is a cardinal. If not, why? > What gives you the idea that the power set of a cardinal is a > cardinal? What gives you the idea that a set isn't a cardinal? . Mark Adkins msadkins04@yahoo.com === Subject: Re: Cardinality: a paradox msadkins04@yahoo.com says... >I've decided to respond to these additional points under cover >of a separate reply. >> at 05:46 PM, msadkins04@yahoo.com said: >>(1) There is a set of all cardinals, AC. >> What gives you that idea? What set theory are you using? Your claim >> is false for GBN and ZFC. >Who said I was using any set theory? Well, if you are trying to rigorously prove things about sets, then you need to start with a consistent theory of sets. There is no consistent theory of sets for which the collection of all cardinals is a set. >Do cardinals exist? Yes. >Can each cardinal be placed in a set in which it is the only member? Yes. >Is the union of these sets a set? No. >Since when is the union of sets not a set? Since the development of consistent theories of sets. Consistent theories of sets make a distinction between sets and arbitrary collections. The union of a set of sets is another set, but not the union of an arbitrary collection of sets. >It isnt't my fault that ZFC and GBN make arbitrary and unjustified >distinctions. The distinction between a set and a proper class may seem arbitrary, but as far as I know, there is no consistent theory of sets that doesn't make some such distinction. -- Daryl McCullough Ithaca, NY === Subject: Re: Cardinality: a paradox >>It isnt't my fault that ZFC and GBN make arbitrary and unjustified >>distinctions. > The distinction between a set and a proper class may seem arbitrary, > but as far as I know, there is no consistent theory of sets that > doesn't make some such distinction. Right, except (as I think you'd agree, Daryl), the distinction in ZF and VNBG (well, not really *in* ZF per se, but you know what I mean) is in fact not at all arbitrary. Historically, Zermelo did initially take a more or less pragmatic, instrumentalist attitude toward his axiomatization, but that all changed with the clarification (in large measure due to Zermelo's own work in a 1931 paper) of the standard iterative model of the set theoretic universe. That model yields an entirely natural and rigorous account of the distinction in question: Sets are collections that occur at some level of the iterative hierarchy. The first level at which a set occurs (viz., the first level such that all of its members occur at preceding levels) is known as its rank. A proper class, then, is simply a collection that has no rank; that is, there is no upper bound on the ranks of its members. Chris Menzel === Subject: Re: Cardinality: a paradox |>Who said I was using any set theory? | |Well, if you are trying to rigorously prove things about sets, |then you need to start with a consistent theory of sets. There |is no consistent theory of sets for which the collection of all |cardinals is a set. Isn't NF (or NFU) such a theory? We don't have a proof of the consistency of NF, but we don't know of any inconsistency yet. In NF, one also defines a cardinal to be the set containing all of the sets in one-to-one correspondence with a given set. This definition of cardinal would be intuitive if it weren't for the fact that (in the cumulative hierarchy, or according to ZF) the sets in one-to-one correspondence with a given nonempty set are a proper class. (It may be that the existence of a set of all von Neumann ordinals that are not in one-to-one correspondence with any smaller ones is inconsistent, but that is not a good definition of cardinal if the well-ordering theorem doesn't hold. The definition using Scott's trick is not suitable if there is no such thing as the rank of a set, and a set of all sets of a given rank.) In NF, we have the axiom of stratified comprehension, which asserts the existence of {x : P(x)} provided the variables appearing in P can be given indices, so that for every occurrence of u=v the variables u and v have the same index, and for every occurrence of u in v, the variable v has index one greater than the index of u. That there exists a one-to-one correspondence between u and v is stratified with the same index for u and v. So {x : x is in one- to-one correspondence with u} exists. Likewise, doesn't {C : C has an element, any elements u and v of C are in one-to-one correspondence, and any w in one-to-one correspondence with an element of C is an element of C} exist? Randall Holmes' NF page has the definition of NF and the fact that cardinals are defined as equivalence classes of sets under the relation of being in one-to-one correspondence. The main thing I haven't seen anywhere before is that NF implies the existence of a set of all cardinals, but my deduction of that from the stratified comprehension axiom looks right to me. Keith Ramsay === Subject: Re: Cardinality: a paradox >Isn't NF (or NFU) such a theory? I believe so, but in order to preserve[1] consistency there are restrictions to compensate. [1] Assuming that NF is consistent. -- Shmuel (Seymour J.) Metz, SysProg and JOAT 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 === Subject: Re: Cardinality: a paradox KRamsay says... >|>Who said I was using any set theory? >|Well, if you are trying to rigorously prove things about sets, >|then you need to start with a consistent theory of sets. There >|is no consistent theory of sets for which the collection of all >|cardinals is a set. >Isn't NF (or NFU) such a theory? >We don't have a proof of the consistency of NF, but we don't know >of any inconsistency yet. Oh, you might be right. I can never remember what is and what isn't a set in NF. What I think is correct is that every consistent set that I know of makes something like a class/set distinction (to avoid Russell's paradox). >In NF, we have the axiom of stratified comprehension, which >asserts the existence of {x : P(x)} provided the variables appearing >in P can be given indices, so that for every occurrence of u=v >the variables u and v have the same index, and for every occurrence >of u in v, the variable v has index one greater than the index >of u. >That there exists a one-to-one correspondence between u and v is >stratified with the same index for u and v. So {x : x is in one- >to-one correspondence with u} exists. Likewise, doesn't >{C : C has an element, any elements u and v of C are in one-to-one >correspondence, and any w in one-to-one correspondence with an >element of C is an element of C} exist? You're right. -- Daryl McCullough Ithaca, NY === Subject: Re: Cardinality: a paradox <41ce553b$16$fuzhry+tra$mr2ice@news.patriot.net> > at 05:46 PM, msadkins04@yahoo.com said: >I've long maintained that there are no infinite >sets, and in particular no infinite set of all X >where X is any type of cardinal, because, first, >the terms are inherently contradictory > You can maintain that little green men from a flying suacer abducted > you with equal plausibility. This is rhetorical and requires no response. >(all entailing completion, > No. >and infinite entailing lack of end (lack of completion); > No on both counts. I stand by my remarks. Your unsupported negations do not contradict them, and constitute empty rhetoric. >second, because infinite does not specify a true cardinality. > Nu, did you think that fin ite specifies a true cardinality. The > term infinite is a catch-all, which is why Mathematicians use more > precise language. Aleph-null, etc., refer to specific cardinalities, > transfinite refers to any cardinality that is not finite. Finite is a true *type* of cardinality. Infinite is not, and the various more precise terms denoting transfinite cardinalities are nonsense for the reasons I have already stated. >For instance, the expression all the naturals >does not specify a set at all, > Please define specify and set; you seem to be using private > definitions. A set is a collection of members. Specify is clear enough in the context, and you are obviously a contentious individual couching attempts at sarcasm in terms of specious requests for clarification. >but is merely a careless way of expressing the fact that a *general >concept* of number -- the *template* called natural numbers -- can >be made to yield concrete examples indefinitely; > No. It is neither careless nor remotely similar to a process. Again, an unsupported negation does not require rebuttal. As for what does or does not constitute a process, the point is moot since I did not use the term in the paragraph quoted above. >One cannot have all of something that is unlimited, > Feel free to prove that. The proof follows from the way the terms are defined, and is therefore axiomatic. Consult a dictionary. >One cannot have >all of something that is unlimited, much less >a set of all such entities, since set entails >a delineated (hence completed) logical entity. > Please provide your private definitions of Set, delineated and > completed. See my above remarks regarding specious requests for clarification. See my latest replies to other parties for a response to technical objections against the existence of AC and PAC. . Mark Adkins msadkins04@yahoo.com === Subject: Re: Cardinality: a paradox <41ce553b$16$fuzhry+tra$mr2ice@news.patriot.net> at 01:36 PM, msadkins04@yahoo.com said: >This is rhetorical and requires no response. Your I've long maintained was rhetorical and no more relevant than my LGM. >Finite is a true *type* of cardinality. Infinite is not Begging the question; more empty rhetoric. Unsupported assertions are not proof. >and the various more precise terms denoting transfinite >cardinalities are nonsense for the reasons I have already stated. No; you stated unsupported prejudices. >A set is a collection of members. Then the expression all the naturals *does* specify a set. > Specify is clear enough in the context, Obviously not, since you are clearly using it in a sense totally different from that used by other posters. and you are obviously a contentious individual WHile it is true that I do not suffer fools gladly, I raised legitimate issues which you were too dense too understand. >As for what does or does not constitute a process, the point is >moot since I did not use the term in the paragraph quoted above. So not only a fool, but a dishonest one; you used the term yields. >The proof follows from the way the terms are defined, Perhaps with your private definitions, which so far you have refused to divulge. >and is therefore axiomatic. So you don't know what an axiom is either? >See my latest replies to other parties add you to my filters along with the other pompous fools with delusions of adequacy. *PLONK* -- Shmuel (Seymour J.) Metz, SysProg and JOAT 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 === Subject: Re: Cardinality: a paradox msadkins04@yahoo.com says... > I've long maintained that there are no infinite > sets, and in particular no infinite set of all X > where X is any type of cardinal, because, first, > the terms are inherently contradictory The fact that you've long maintained it doesn't make it true. ZFC is a theory of infinite sets, and as far as anyone knows, it is consistent. If the notion of an infinite set were inherently contradictory, you should be able to prove that the axioms of ZFC lead to a contradiction. -- Daryl McCullough Ithaca, NY === Subject: Re: Cardinality: a paradox >(2) AC is a cardinal. If not, why? (How could a >union of cardinals not be a cardinal?) A set of cardinals need not be a cardinal itself; a cardinal is a number of elements; a set has structure. >(9) PAC has a greater cardinality than AC. If >not, why? x squared is bigger than x for finite integers greater than 1. Yet, aleph-null, the number of integers, squared, equals itself; aleph-null is too big for squaring to increase it. What's wrong with an infinity being so big that even the power set operation cannot increase it? Anyways, what you outline is, if it is a paradox, only a paradox in naive set theory. Axiomatic set theory doesn't deal with sets that large. And naive set theory already has paradoxes: the set of all sets that do not contain themselves, Bertrand Russell's barber paradox. John Savard http://home.ecn.ab.ca/~jsavard/index.html === Subject: Re: Cardinality: a paradox <41cbfe13.828739@news.ecn.ab.ca> >(2) AC is a cardinal. If not, why? (How could a >union of cardinals not be a cardinal?) > A set of cardinals need not be a cardinal itself; a cardinal > is a number of elements; a set has structure. A set is merely a collection of members. Do cardinals exist? Is the union of individual cardinals a set? Why not the set of all cardinals, AC, then? Can one group individual cardinals into subsets of cardinals? Is the union of these subsets a set? Isn't the union of sets a set? Why not the power set, PAC, of the set of all cardinals, AC? . Mark Adkins msadkins04@yahoo.com === Subject: Re: Cardinality: a paradox >>(2) AC is a cardinal. If not, why? (How could a >>union of cardinals not be a cardinal?) >A set of cardinals need not be a cardinal itself; a cardinal is a number >of elements; a set has structure. >>(9) PAC has a greater cardinality than AC. If >>not, why? >x squared is bigger than x for finite integers greater than 1. Yet, >aleph-null, the number of integers, squared, equals itself; aleph-null >is too big for squaring to increase it. What's wrong with an infinity >being so big that even the power set operation cannot increase it? >Anyways, what you outline is, if it is a paradox, only a paradox in >naive set theory. Axiomatic set theory doesn't deal with sets that >large. ZFC, MK, and NBG don't; but NFU has a unversal set, which certainly qualifies as that large for any reasonable referent of that. >And naive set theory already has paradoxes: the set of all sets >that do not contain themselves, Bertrand Russell's barber paradox. >John Savard >http://home.ecn.ab.ca/~jsavard/index.html -- --------------------------- | BBB b Barbara at LivingHistory stop co stop uk | B B aa rrr b | | BBB a a r bbb | Quidquid latine dictum sit, | B B a a r b b | altum viditur. | BBB aa a r bbb | ----------------------------- === Subject: Re: Cardinality: a paradox part: >ZFC, MK, and NBG don't; but NFU has a unversal set, which certainly >qualifies as that large for any reasonable referent of that. Ah, _this_ explains why my post Division by Zero and Axiomatic Set Theory received no replies. In it I note that the simplification of naive ideas about arithmetic imposed by going to real numbers, and saying division by zero is not defined instead of saying the result is either indeterminate or indeterminately infinite, with definite rules, is a fully satisfactory one which makes mathematical deduction easier... but going from naive set theory to axiomatic set theory with ZF, leaving such things as the Continuum Hypothesis irresolvable, is less so. But there are already better, or at least broader, axiomatizations of set theory. I had heard of ZF - Zermelo-Fraenkel ZFC - Zermelo-Fraenkel with the Axiom of Choice but it took some Googling to get up-to-date and find out about NF - New Foundations (Quine) ML - Mathematical Logic (Quine) NFU - New Foundations with Urelemente (Jensen) MKM - Mostowski-Kelley-Morse MK - Morse-Kelley SEC - Strongly Extensional Theory of Classes (Barwise and Moss) NBG - von Neumann-Bernys-Goedel The site http://www.hf.uio.no/filosofi/njpl/vol4no1/ruskap/node3.html mentioned most, but not all, of these, as well as a few others. John Savard http://home.ecn.ab.ca/~jsavard/index.html === Subject: Re: Cardinality: a paradox > part: >ZFC, MK, and NBG don't; but NFU has a unversal set, which certainly >qualifies as that large for any reasonable referent of that. > Ah, _this_ explains why my post Division by Zero and Axiomatic Set > Theory received no replies. > In it I note that the simplification of naive ideas about arithmetic > imposed by going to real numbers, and saying division by zero is not > defined instead of saying the result is either indeterminate or > indeterminately infinite, with definite rules, is a fully satisfactory > one which makes mathematical deduction easier... but going from naive > set theory to axiomatic set theory with ZF, leaving such things as the > Continuum Hypothesis irresolvable, is less so. > But there are already better, or at least broader, axiomatizations of > set theory. > I had heard of > ZF - Zermelo-Fraenkel > ZFC - Zermelo-Fraenkel with the Axiom of Choice > but it took some Googling to get up-to-date and find out about > NF - New Foundations (Quine) > ML - Mathematical Logic (Quine) > NFU - New Foundations with Urelemente (Jensen) > MKM - Mostowski-Kelley-Morse > MK - Morse-Kelley > SEC - Strongly Extensional Theory of Classes (Barwise and Moss) > NBG - von Neumann-Bernys-Goedel > The site http://www.hf.uio.no/filosofi/njpl/vol4no1/ruskap/node3.html > mentioned most, but not all, of these, as well as a few others. > John Savard > http://home.ecn.ab.ca/~jsavard/index.html Wow! For the first time, I am very glad I never became a mathematician! I get the feeling that all these constructs have little interest to most everyday math people, right? They seem like foundational fantasies in a way--has anyone really cared about such things ever since Godel? :)) I must admit, I still don't understand how workers in math can even go around in their daily work, essentially just _assuming_ that arithmetic is consistent, when the existence of undecidability seems to me to only imply it either is _or isn't_, ...am I wrong on this? (I probably am, but be gentle on me--I'm just a poor retired chemist. :)) Sitting here in awe, ...tonyC === Subject: Re: Cardinality: a paradox >Wow! For the first time, I am very glad I never became a >mathematician! I get the feeling that all these constructs >have little interest to most everyday math people, right? >They seem like foundational fantasies in a way--has anyone >really cared about such things ever since Godel? :)) For myself, I was just tickled pink to hear that mathematicians *haven't* given up on trying to find out if the Continuum Hypothesis is true or not - that the Russell Paradox hasn't caused them to simply give up, and settle for Zermelo-Fraenkel (*without* the axiom of choice) forever and ever, world without end. This is not to claim more than a layman's understanding of such matters. John Savard http://home.ecn.ab.ca/~jsavard/index.html === Subject: Re: Cardinality: a paradox |I had heard of | |ZF - Zermelo-Fraenkel |ZFC - Zermelo-Fraenkel with the Axiom of Choice | |but it took some Googling to get up-to-date and find out about [NF, ML, NFU, MKM, SEC, NBG]. Don't forget Kripke-Platek set theory, KP. |Wow! For the first time, I am very glad I never became a |mathematician! I get the feeling that all these constructs |have little interest to most everyday math people, right? Most mathematicians don't know about them. People who would seriously concern themselves with them would usually be called mathematical logicians, and even most people in logic would not be in a specialty that dealt with them. |They seem like foundational fantasies in a way--has anyone |really cared about such things ever since Godel? :)) I must |admit, I still don't understand how workers in math can even |go around in their daily work, essentially just _assuming_ |that arithmetic is consistent, when the existence of |undecidability seems to me to only imply it either is _or |isn't_, ...am I wrong on this? (I probably am, but be gentle |on me--I'm just a poor retired chemist. :)) Sitting here in |awe, ...tonyC Most mathematics is pretty far removed from set theory of this kind. Usually mathematicians don't even think in terms of axioms for set theory. If one looks at published proofs with an eye to seeing what is being assumed, one can see that they are, in effect, applying the axiom scheme of separation and so on, but the author generally is just reasoning based on general familiarity with the principles of the subject. She or he may write something like Theorem 137: .011010100010..., where the digit a_n us 1 if n is prime and 0 otherwise, is irrational. (Hardy and Wright) If you stopped them there and pointed out that this implicitly uses the existence of a function f: Z -> {0,1,2,3,4,5,6,7,8,9} defined as {(m,n): m, n are integers, and either m is prime and n=1 or m is not prime and n=0}, and that moreover this is an instance of the axiom scheme of separation, you would be right. But Hardy and Wright are unlikely to have been thinking axiom scheme of separation at any point in the writing of this theorem. What exactly is being assumed is a little slippery. Almost all mathematicians have no problem with proofs that implicitly assume axioms a lot stronger than the consistency of arithmetic. There are two well-known proofs of the consistency of arithmetic that use absolutely no assumptions out of the ordinary-- both are proofs in just the same sense as the proofs that make up the vast bulk of the journals and textbooks today. They also don't use any axiom of the form [blank] is consistent. The Goedel incompleteness theorems don't imply that it's not possible to prove the consistency of elementary arithmetic, just that it's not possible to prove it just using elementary arithmetic. They don't even imply that the axioms needed to prove the consistency have to be as strong as the axioms of arithmetic. If one examines one's proofs, one can catalog the assumptions actually being used. For nearly all mathematicians these don't include the consistency of anything, per se. In a natural sense, then, consistency is rarely assumed, either the consistency of arithmetic or the consistency of anything else. You can, however, take these axioms and use them to produce an example of a further statement (the consistency of the axioms being used with ordinary arithmetic) that the author is liable also to be willing to accept as correct, despite not having used it. If what we are doing makes sense, then the axioms must be consistent, mustn't they? If the axioms are true, and the rules of reasoning are valid, then they must be mutually consistent. When I first learned about the Goedel incompleteness theorems, I found it odd that it wasn't possible to get one's deductive system to follow one's intuition in this respect by incorporating its own consistency. But it can't, without weakening its own axioms and/or deductive rules in some way (so as to make the incompleteness theorems no longer applicable). It can be an interesting exercise to track down what goes wrong with various attempts to circumvent this by making the axiom system more closely reflect how one reasons. One attempt I made back then was to add a new deductive rule allowing one to deduce the consistency of a finite collection of statements from the statements. (Then, to avoid a somewhat technical problem, use a finitely axiomatized version of the theory being modified.) The problem here is that the consistency of a finite set of axioms is defined relative to a given set of deductive rules. The system as thus modified is able to prove the consistency of the unmodified system, but the consistency of the modified system is consistency defined using the now larger set of deductive rules, a stronger claim. Keith Ramsay === Subject: Re: Cardinality: a paradox > The Goedel incompleteness theorems don't imply that it's not > possible to prove the consistency of elementary arithmetic, > just that it's not possible to prove it just using > elementary arithmetic. They don't even imply that the axioms > needed to prove the consistency have to be as strong as the > axioms of arithmetic. ?? What do you mean by that last sentence? Do you know of a reasonably weak axiom system that can prove the consistency of, say, PA? -- Herman Jurjus === Subject: Re: Cardinality: a paradox |> The Goedel incompleteness theorems don't imply that it's not |> possible to prove the consistency of elementary arithmetic, |> just that it's not possible to prove it just using |> elementary arithmetic. They don't even imply that the axioms |> needed to prove the consistency have to be as strong as the |> axioms of arithmetic. | |?? What do you mean by that last sentence? Do you know of a reasonably |weak axiom system that can prove the consistency of, say, PA? I don't know of such a system that I would call reasonably weak, but Goedel's incompleteness theorem doesn't rule it out. One can at least have a system whose theorems don't include all the theorems of elementary arithmetic (i.e. PA) that can prove the consistency of PA. For example, PRA+con(PA). Maybe R+con(PA) where R is Robinson arithmetic would count as reasonably weak. It has some theorems that aren't theorems of PA, but it also lacks many of the theorems of PA. One can cook up examples of number theoretic statements S that can be proven in PA, but for which Con(X)->S cannot be proven in PRA for any system X that is consistent. There are varieties of strength that are largely independent of consistency strength. It's conceivable that a much more natural example could be found. Keith Ramsay === Subject: Re: Cardinality: a paradox > Do you know of a reasonably > weak axiom system that can prove the consistency of, say, PA? A further comment: it's a widespread misconception that the consistency of a theory can only be proved in a stronger theory. It would be strange indeed if this were the case, since consistency is only a weak soundness condition. A good example to keep in mind is that of PA+PA is inconsistent. We prove the consistency of this theory, not in a stronger theory, but in an *incompatible* theory. === Subject: Re: Cardinality: a paradox > ?? What do you mean by that last sentence? Do you know of a reasonably > weak axiom system that can prove the consistency of, say, PA? Gentzen's proof of the consistency of PA is formalizable in PRA+epsilon-0-induction. This theory is not as strong as PA. It extends PA in one direction, but drastically restricts it in another. === Subject: Re: Cardinality: a paradox Torkel Franzen says... > Gentzen's proof of the consistency of PA is formalizable in >PRA+epsilon-0-induction. This theory is not as strong as PA. It >extends PA in one direction, but drastically restricts it in another. I thought that the only sense in which PRA was weaker than PA was that it fails to prove all instances of the induction schema. So if you add that schema (or something more powerful) then you end up with something more powerful than PA. Or at least, that's what I would think. So what is an example of something provable in PA but not in PRA+epsilon-0-induction? -- Daryl McCullough Ithaca, NY === Subject: Re: Cardinality: a paradox > I thought that the only sense in which PRA was weaker than PA > was that it fails to prove all instances of the induction schema. > So if you add that schema (or something more powerful) then you > end up with something more powerful than PA. Or at least, that's > what I would think. Your comment points to an unclarity in my remarks. The epsilon-0-induction schema added to PRA for Gentzen's proof only applies to quantifier-free formulas, just like the induction schema already included in PRA. === Subject: Re: Cardinality: a paradox >>part: >ZFC, MK, and NBG don't; but NFU has a unversal set, which > certainly >qualifies as that large for any reasonable referent of > that. >>Ah, _this_ explains why my post Division by Zero and > Axiomatic Set >>Theory received no replies. >>In it I note that the simplification of naive ideas > about arithmetic >>imposed by going to real numbers, and saying division by > zero is not >>defined instead of saying the result is either > indeterminate or >>indeterminately infinite, with definite rules, is a fully > satisfactory >>one which makes mathematical deduction easier... but going > from naive >>set theory to axiomatic set theory with ZF, leaving such > things as the >>Continuum Hypothesis irresolvable, is less so. >>But there are already better, or at least broader, > axiomatizations of >>set theory. >>I had heard of >>ZF - Zermelo-Fraenkel >>ZFC - Zermelo-Fraenkel with the Axiom of Choice >>but it took some Googling to get up-to-date and find out > about >>NF - New Foundations (Quine) >>ML - Mathematical Logic (Quine) >>NFU - New Foundations with Urelemente (Jensen) >>MKM - Mostowski-Kelley-Morse >>MK - Morse-Kelley >>SEC - Strongly Extensional Theory of Classes (Barwise and > Moss) >>NBG - von Neumann-Bernys-Goedel >>The site > http://www.hf.uio.no/filosofi/njpl/vol4no1/ruskap/node3.html >>mentioned most, but not all, of these, as well as a few > others. >>John Savard >>http://home.ecn.ab.ca/~jsavard/index.html > Wow! For the first time, I am very glad I never became a > mathematician! I get the feeling that all these constructs > have little interest to most everyday math people, right? > They seem like foundational fantasies in a way--has anyone > really cared about such things ever since Godel? :)) I must > admit, I still don't understand how workers in math can even > go around in their daily work, essentially just _assuming_ > that arithmetic is consistent, when the existence of > undecidability seems to me to only imply it either is _or > isn't_, ...am I wrong on this? (I probably am, but be gentle > on me--I'm just a poor retired chemist. :)) Sitting here in > awe, ...tonyC How much mathematicians care about this sort of thing depends on what sort of mathematics they do. For the most part mathematicians can ignore this sort of thing, though as an example homotopy/category theorists have to take some sort of care when constructing the classifying space of some category C, since in many instances the objects of C aren't a set and something has to be said to avoid some difficulties there. As for assuming arithmetic is consistent that's the best one can do. Undecidability says we can't say for sure, but most, if not all mathematicians are just as happy assuming it is since it allows them to actually do mathematics. === Subject: Re: Cardinality: a paradox in >>part: >> >> >ZFC, MK, and NBG don't; but NFU has a unversal set, which > certainly >qualifies as that large for any reasonable referent of > that. >>Ah, _this_ explains why my post Division by Zero and > Axiomatic Set >>Theory received no replies. >> >>In it I note that the simplification of naive ideas > about arithmetic >>imposed by going to real numbers, and saying division by > zero is not >>defined instead of saying the result is either > indeterminate or >>indeterminately infinite, with definite rules, is a fully > satisfactory >>one which makes mathematical deduction easier... but going > from naive >>set theory to axiomatic set theory with ZF, leaving such > things as the >>Continuum Hypothesis irresolvable, is less so. >> >>But there are already better, or at least broader, > axiomatizations of >>set theory. >> >>I had heard of >> >>ZF - Zermelo-Fraenkel >>ZFC - Zermelo-Fraenkel with the Axiom of Choice >> >>but it took some Googling to get up-to-date and find out > about >>NF - New Foundations (Quine) >>ML - Mathematical Logic (Quine) >> >>NFU - New Foundations with Urelemente (Jensen) >> >>MKM - Mostowski-Kelley-Morse >>MK - Morse-Kelley >> >>SEC - Strongly Extensional Theory of Classes (Barwise and > Moss) >>NBG - von Neumann-Bernys-Goedel >> >>The site >> >> http://www.hf.uio.no/filosofi/njpl/vol4no1/ruskap/node3.html >>mentioned most, but not all, of these, as well as a few > others. >>John Savard >>http://home.ecn.ab.ca/~jsavard/index.html > Wow! For the first time, I am very glad I never became a > mathematician! I get the feeling that all these constructs > have little interest to most everyday math people, right? > They seem like foundational fantasies in a way--has anyone > really cared about such things ever since Godel? :)) I must > admit, I still don't understand how workers in math can even > go around in their daily work, essentially just _assuming_ > that arithmetic is consistent, when the existence of > undecidability seems to me to only imply it either is _or > isn't_, ...am I wrong on this? (I probably am, but be gentle > on me--I'm just a poor retired chemist. :)) Sitting here in > awe, ...tonyC > How much mathematicians care about this sort of thing depends on what > sort of mathematics they do. For the most part mathematicians can ignore > this sort of thing, though as an example homotopy/category theorists > have to take some sort of care when constructing the classifying space > of some category C, since in many instances the objects of C aren't a > set and something has to be said to avoid some difficulties there. Yes, I can see there are areas of math where foundations are critical, and the study of foundations itself is bread and butter to the field. And I suppose that, most stuff on the cutting edge of math has to be vetted by some attention to this at some point. > As for assuming arithmetic is consistent that's the best one can do. > Undecidability says we can't say for sure, but most, if not all > mathematicians are just as happy assuming it is since it allows them to > actually do mathematics. Yes , that's what I thought. It must be at least a bit frustrating at times though I imagine...though not fretting about it does solve the problem (and does allow one to ...tonyC === Subject: Re: Cardinality: a paradox <41cbfe13.828739@news.ecn.ab.ca> > x squared is bigger than x for finite integers greater than 1. And also for finite integers less than 0. :-) The graph of y=x^2-x is a parabola which intersects the x-axis at x=0 and x=1; between those points, but nowhere else, it lies below the === Subject: Re: Cardinality: a paradox > I've long maintained that there are no infinite > sets, and in particular no infinite set of all X > where X is any type of cardinal, because, first, > the terms are inherently contradictory (all > entailing completion, and infinite entailing > lack of end (lack of completion); second, because > infinite does not specify a true cardinality. > For instance, the expression all the naturals > does not specify a set at all, but is merely a > careless way of expressing the fact that a > *general concept* of number -- the *template* > called natural numbers -- can be made to yield > concrete examples indefinitely; all such sets of > examples are nonetheless finite. One cannot have > all of something that is unlimited, much less > a set of all such entities, since set entails > a delineated (hence completed) logical entity. > For those who assert otherwise, here is a little > paradox. (More than one, actually.) It presumes > that the concept of cardinality is well defined > -- otherwise, what does set-theory purport to > discuss? > (1) There is a set of all cardinals, AC. If not, > why? (How can a union of sets not be a set? Is > cardinal a well defined concept? Is all a > well defined concept? The mere fact that > assuming AC leads to problems, as some have > tactfully phrased it, does not imply that serious > theories eschew it *on that basis*; on the contrary, > *serious* theories must explain why something which > should exist according to standard theory, cannot > exist (i.e., where and why standard theory is in > error -- which of its axioms are contradictory. > The error springs from the fallacious concept of > infinite set.) > (2) AC is a cardinal. If not, why? (How could a > union of cardinals not be a cardinal?) > (3) AC, being a cardinal, is a member of itself. > If not, why? (Obviously this creates a paradox > of infinite regress, but the real question is > what error inheres in the assumptions of > standard theory, thereby leading to this paradox.) > (4) AC is the largest possible cardinal. If not, > why? (What has greater cardinality than the set > of all cardinals?) > (5) AC has a power set, PAC. If not, why? (How > can a set of distinct cardinals be unorderable? > How can it be impossible to select from its > members, and thus to form subsets?) > (6) PAC is a cardinal. If not, why? > (7) PAC, being a cardinal, is a member of AC. If > not, why? > (8) PAC is a proper subset of AC. If not, why? > (9) PAC has a greater cardinality than AC. If > not, why? > Mark Adkins > msadkins04@yahoo.com The collection of all cardinals isn't a set, it is a class. You have to some degree touched upon why one has to be careful with this sort of thing, but to deny the infinite is just idiotic. If the set of natural numbers is finite, what is the largest one? Your paradox really is no different from Russell's paradox at heart, which is why set theory had to be axiomatized (sp?) carefully to avoid these things. For the most part, most mathematicians don't have to worry about such thing, but sometimes it's important. === Subject: Re: Cardinality: a paradox > The collection of all cardinals isn't a set, it is a class. You have to > some degree touched upon why one has to be careful with this sort of > thing, but to deny the infinite is just idiotic. If the set of natural > numbers is finite, what is the largest one? There is no set of natural numbers. Natural numbers references a concept of number, a set of rules or template from which individual, specific entities can be created. There is no largest one. Every set (of any kind), being a collection of specific members, is finite. There is no largest natural number. There is also no limit to the creation of specific natural numbers. The foregoing is logically consistent. > For the most part, most mathematicians don't have to worry > about such thing, but sometimes it's important. I find that the very things which most mathematicians don't worry about are the fundamentals. You cannot build on quicksand. Mark Adkins msadkins04@yahoo.com === Subject: Re: Cardinality: a paradox >>The collection of all cardinals isn't a set, it is a class. You have > to >>some degree touched upon why one has to be careful with this sort of >>thing, but to deny the infinite is just idiotic. If the set of > natural >>numbers is finite, what is the largest one? > There is no set of natural numbers. Natural numbers references a > concept of number, a set of rules or template from which individual, > specific entities can be created. There is no largest one. Every > set (of any kind), being a collection of specific members, is finite. > There is no largest natural number. There is also no limit to the > creation of specific natural numbers. The foregoing is logically > consistent. > >>For the most part, most mathematicians don't have to worry >>about such thing, but sometimes it's important. > I find that the very things which most mathematicians don't > worry about are the fundamentals. You cannot build on quicksand. > Mark Adkins > msadkins04@yahoo.com Well, you obviously have no grasp of the fundamentals if you claim there is no set of natural numbers. Just because you have some bizarre concept that sets must be finite doesn't mean we have to use your definitions. === Subject: Re: Cardinality: a paradox > I've long maintained that there are no infinite > sets, and in particular no infinite set of all X > where X is any type of cardinal, because, first, > the terms are inherently contradictory (all > entailing completion, and infinite entailing > lack of end (lack of completion); second, because > infinite does not specify a true cardinality. > For instance, the expression all the naturals > does not specify a set at all, but is merely a > careless way of expressing the fact that a > *general concept* of number -- the *template* > called natural numbers -- can be made to yield > concrete examples indefinitely; all such sets of > examples are nonetheless finite. One cannot have > all of something that is unlimited, much less > a set of all such entities, since set entails > a delineated (hence completed) logical entity. > For those who assert otherwise, here is a little > paradox. (More than one, actually.) It presumes > that the concept of cardinality is well defined > -- otherwise, what does set-theory purport to > discuss? > (1) There is a set of all cardinals, AC. If not, > why? (How can a union of sets not be a set? Is > cardinal a well defined concept? Is all a > well defined concept? The mere fact that > assuming AC leads to problems, as some have > tactfully phrased it, does not imply that serious > theories eschew it *on that basis*; on the contrary, > *serious* theories must explain why something which > should exist according to standard theory, cannot > exist (i.e., where and why standard theory is in > error -- which of its axioms are contradictory. > The error springs from the fallacious concept of > infinite set.) > (2) AC is a cardinal. If not, why? (How could a > union of cardinals not be a cardinal?) > (3) AC, being a cardinal, is a member of itself. > If not, why? (Obviously this creates a paradox > of infinite regress, but the real question is > what error inheres in the assumptions of > standard theory, thereby leading to this paradox.) > (4) AC is the largest possible cardinal. If not, > why? (What has greater cardinality than the set > of all cardinals?) > (5) AC has a power set, PAC. If not, why? (How > can a set of distinct cardinals be unorderable? > How can it be impossible to select from its > members, and thus to form subsets?) > (6) PAC is a cardinal. If not, why? > (7) PAC, being a cardinal, is a member of AC. If > not, why? > (8) PAC is a proper subset of AC. If not, why? > (9) PAC has a greater cardinality than AC. If > not, why? > Mark Adkins > msadkins04@yahoo.com > The collection of all cardinals isn't a set, it is a class. You have to > some degree touched upon why one has to be careful with this sort of > thing, but to deny the infinite is just idiotic. If the set of natural > numbers is finite, what is the largest one? No it's not idiotic it's pedantic. On other planets with intelligent beings the word set is used for finite sets and InfSet is used for infinite sets. We allow InfSet as a hypothetical construct since non terminating things are common. > Your paradox really is no different from Russell's paradox at heart, > which is why set theory had to be axiomatized (sp?) carefully to avoid > these things. For the most part, most mathematicians don't have to worry > about such thing, but sometimes it's important. S = container of things that don't contain themself Then you admit cardinality is as nonexistant as the Russel Set? Herc === Subject: Re: Cardinality: a paradox >I've long maintained that there are no infinite >sets, and in particular no infinite set of all X >where X is any type of cardinal, because, first, >the terms are inherently contradictory (all >entailing completion, and infinite entailing >lack of end (lack of completion); second, because >infinite does not specify a true cardinality. >For instance, the expression all the naturals >does not specify a set at all, but is merely a >careless way of expressing the fact that a >*general concept* of number -- the *template* >called natural numbers -- can be made to yield >concrete examples indefinitely; all such sets of >examples are nonetheless finite. One cannot have >all of something that is unlimited, much less >a set of all such entities, since set entails >a delineated (hence completed) logical entity. >For those who assert otherwise, here is a little >paradox. (More than one, actually.) It presumes >that the concept of cardinality is well defined >-- otherwise, what does set-theory purport to >discuss? >(1) There is a set of all cardinals, AC. If not, >why? (How can a union of sets not be a set? Is >cardinal a well defined concept? Is all a >well defined concept? The mere fact that >assuming AC leads to problems, as some have >tactfully phrased it, does not imply that serious >theories eschew it *on that basis*; on the contrary, >*serious* theories must explain why something which >should exist according to standard theory, cannot >exist (i.e., where and why standard theory is in >error -- which of its axioms are contradictory. >The error springs from the fallacious concept of >infinite set.) >(2) AC is a cardinal. If not, why? (How could a >union of cardinals not be a cardinal?) >(3) AC, being a cardinal, is a member of itself. >If not, why? (Obviously this creates a paradox >of infinite regress, but the real question is >what error inheres in the assumptions of >standard theory, thereby leading to this paradox.) >(4) AC is the largest possible cardinal. If not, >why? (What has greater cardinality than the set >of all cardinals?) >(5) AC has a power set, PAC. If not, why? (How >can a set of distinct cardinals be unorderable? >How can it be impossible to select from its >members, and thus to form subsets?) >(6) PAC is a cardinal. If not, why? >(7) PAC, being a cardinal, is a member of AC. If >not, why? >(8) PAC is a proper subset of AC. If not, why? >(9) PAC has a greater cardinality than AC. If >not, why? >Mark Adkins >msadkins04@yahoo.com >>The collection of all cardinals isn't a set, it is a class. You have to >>some degree touched upon why one has to be careful with this sort of >>thing, but to deny the infinite is just idiotic. If the set of natural >>numbers is finite, what is the largest one? > No it's not idiotic it's pedantic. On other planets with intelligent beings > the word set is used for finite sets and InfSet is used for infinite sets. > We allow InfSet as a hypothetical construct since non terminating things > are common. >>Your paradox really is no different from Russell's paradox at heart, >>which is why set theory had to be axiomatized (sp?) carefully to avoid >>these things. For the most part, most mathematicians don't have to worry >>about such thing, but sometimes it's important. > S = container of things that don't contain themself > Then you admit cardinality is as nonexistant as the Russel Set? > Herc No, I'm saying one has to be careful. Cardinalities exist. but the collection of cardinalities is not a set. === Subject: Re: Please compute this in Mathematica 5 by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBO3CS629004; .... >No, seriously - I tried it in MuPAD (light 2.5.3): >limit((3^x+5^x)^(1/x),x=infinity) >which made me a little bit insecure. I was wondering whether there could be cases... limit((3^x+n^x)^(1/x),x=infinity) -> n if n > 3 and -> 3 if n <= 3. === Subject: Re: Please compute this in Mathematica 5 let y=((3^x + n^x)^(1/x)) Logarithm on both side, then use hopital rule will get the result. === Subject: Re: The Smart Multi-Universal Body Model And More... by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBO3CS029013; Many have observed what appears to be an Astral Projected body. Well the >Smart Model does describe this level too. It is what could be a different level >except this one is free to roam. This body can then be placed into another more >perfect solidified body, that will never die or suffer. Just a week ago Gross held a speech where he made a good joke. ...maybe it really wouldn't work for a cat. Although it seems purely humoristic, there is something to learn from it, the fact that we do not know. A reply to messages such as these can be considered feeding a troll, but all of us who read the Hobit know that trolls can turn into stone as a result of arguing over a snack. At least people will hear them grunt and watch out. === Subject: Re: The Smart Multi-Universal Body Model And More... >Many have observed what appears to be an Astral Projected body. Well the >>Smart Model does describe this level too. It is what could be a different >level >body, >>except this one is free to roam. This body can then be placed into another >more >>perfect solidified body, that will never die or suffer. >Just a week ago Gross held a speech where he made a good joke. ...maybe it >really wouldn't work for a cat. Although it seems purely humoristic, there >is something to learn from it, the fact that we do not know. A reply to >messages such as these can be considered feeding a troll, but all of us who >read the Hobit know that trolls can turn into stone as a result of arguing >over a snack. At least people will hear them grunt and watch out. Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: The mathematics of Christmas Santa Claus violates many laws of physics and is mathematically impossible. HTH. -- Ebeneezer Spooge === Subject: Re: The mathematics of Christmas Spooge (spooge.who@stole.christmas) dropped a +5 bundle of words... > Santa Claus violates many laws of physics and is mathematically > impossible. HTH. You're getting Saran Wrap for Christmas now. Dibs on your former present. -- Starshine Moonbeam mhm31x9 Smeeter#29 WSD#30 sTaRShInE_mOOnBeAm aT HoTmAil dOt CoM === Subject: Re: The mathematics of Christmas In sci.math, Starshine Moonbeam : > Spooge (spooge.who@stole.christmas) dropped a +5 bundle of words... >> Santa Claus violates many laws of physics and is mathematically >> impossible. HTH. > You're getting Saran Wrap for Christmas now. Dibs on your former > present. Erm...is that wrap for Ebeneezer, or for a ladyfriend thereof? :-) -- #191, ewill3@earthlink.net It's still legal to go .sigless. === Subject: Re: The mathematics of Christmas The Machine (ewill@sirius.athghost7038suus.net) dropped a +5 bundle of words... > In sci.math, Starshine Moonbeam > > : > Spooge (spooge.who@stole.christmas) dropped a +5 bundle of words... >> Santa Claus violates many laws of physics and is mathematically >> impossible. HTH. > You're getting Saran Wrap for Christmas now. Dibs on your former > present. > Erm...is that wrap for Ebeneezer, or for a ladyfriend thereof? :-) No perverting the Christmas punishment. That's why Baby Oil wasn't included. -- Starshine Moonbeam mhm31x9 Smeeter#29 WSD#30 sTaRShInE_mOOnBeAm aT HoTmAil dOt CoM === Subject: Re: The mathematics of Christmas >The Machine (ewill@sirius.athghost7038suus.net) dropped a +5 bundle of >words... >> In sci.math, Starshine Moonbeam >> >> : >> Spooge (spooge.who@stole.christmas) dropped a +5 bundle of words... >> >>> Santa Claus violates many laws of physics and is mathematically >>> impossible. HTH. >> >> You're getting Saran Wrap for Christmas now. Dibs on your former >> present. >> >> Erm...is that wrap for Ebeneezer, or for a ladyfriend thereof? :-) >No perverting the Christmas punishment. That's why Baby Oil wasn't >included. You might want to spend a little on prophylactics rather than use Saran Wrap on Ebeneezer Spooge. === Subject: Re: The mathematics of Christmas Kid (aspergumkid@my-way.org) dropped a +5 bundle of words... >The Machine (ewill@sirius.athghost7038suus.net) dropped a +5 bundle of >words... >> In sci.math, Starshine Moonbeam >> >> : >> Spooge (spooge.who@stole.christmas) dropped a +5 bundle of words... >> >>> Santa Claus violates many laws of physics and is mathematically >>> impossible. HTH. >> >> You're getting Saran Wrap for Christmas now. Dibs on your former >> present. >> >> >> Erm...is that wrap for Ebeneezer, or for a ladyfriend thereof? :-) >> >> >No perverting the Christmas punishment. That's why Baby Oil wasn't >included. > You might want to spend a little on prophylactics rather than use > Saran Wrap on Ebeneezer Spooge. badumbump -- Starshine Moonbeam mhm31x9 Smeeter#29 WSD#30 sTaRShInE_mOOnBeAm aT HoTmAil dOt CoM === Subject: Re: The mathematics of Christmas > Spooge (spooge.who@stole.christmas) dropped a +5 bundle of words... >> Santa Claus violates many laws of physics and is mathematically >> impossible. HTH. > You're getting Saran Wrap for Christmas now. Dibs on your former > present. You really *wanted* that complete set of 1920s hockey trading cards, didn't you? PJR :-) -- alt.usenet.kooks award-winners and FAQ: http://www.insurgent.org/~kook-faq/ === Subject: Re: The mathematics of Christmas > Spooge (spooge.who@stole.christmas) dropped a +5 bundle of words... >> Santa Claus violates many laws of physics and is mathematically >> impossible. HTH. > You're getting Saran Wrap for Christmas now. Dibs on your former > present. > You really *wanted* that complete set of 1920s hockey trading cards, > didn't you? Actually, hell yeah I would. DIBS~! -- Starshine Moonbeam mhm31x9 Smeeter#29 WSD#30 sTaRShInE_mOOnBeAm aT HoTmAil dOt CoM === Subject: Re: The mathematics of Christmas >> Spooge (spooge.who@stole.christmas) dropped a +5 bundle of words... >>> Santa Claus violates many laws of physics and is mathematically >>> impossible. HTH. >> You're getting Saran Wrap for Christmas now. Dibs on your former >> present. >> You really *wanted* that complete set of 1920s hockey trading cards, >> didn't you? > Actually, hell yeah I would. > DIBS~! 1. P-QB4 [or c4, if you prefer] PJR :-) -- alt.usenet.kooks award-winners and FAQ: http://www.insurgent.org/~kook-faq/ === Subject: Re: The mathematics of Christmas >> >> Spooge (spooge.who@stole.christmas) dropped a +5 bundle of words... >> >>> Santa Claus violates many laws of physics and is mathematically >>> impossible. HTH. >> >> You're getting Saran Wrap for Christmas now. Dibs on your former >> present. >> >> You really *wanted* that complete set of 1920s hockey trading cards, >> didn't you? > Actually, hell yeah I would. > DIBS~! > 1. P-QB4 [or c4, if you prefer] I would prefer c4, actually. 1. c4 e5 -- Starshine Moonbeam mhm31x9 Smeeter#29 WSD#30 sTaRShInE_mOOnBeAm aT HoTmAil dOt CoM === Subject: Re: The mathematics of Christmas >>> >>> Spooge (spooge.who@stole.christmas) dropped a +5 bundle of words... >>> >>>> Santa Claus violates many laws of physics and is mathematically >>>> impossible. HTH. >>> >>> You're getting Saran Wrap for Christmas now. Dibs on your former >>> present. >>> >>> You really *wanted* that complete set of 1920s hockey trading cards, >>> didn't you? >> Actually, hell yeah I would. >> DIBS~! >> 1. P-QB4 [or c4, if you prefer] > I would prefer c4, actually. > 1. c4 e5 Hmmmm.... 2. Nc3 (Kt-QB3 as we old folks call it) alt.fan.trippy and alt.fan.pjr added. PJ It's not as much fun as slapping kooks around, but it's close R :-) -- alt.usenet.kooks award-winners and FAQ: http://www.insurgent.org/~kook-faq/ === Subject: Re: The mathematics of Christmas u24aIi?y{G9hAr3Nw]$nDkpn.|_rj4[4g]4:yhNF*6*el$`]qNWYjOsvNB2TcjKL8+OV>KaAove+ # I x^l3:gq5SsdUVwi_=Y >> >> >>> >>> Spooge (spooge.who@stole.christmas) dropped a +5 bundle of words... >>> >>>> Santa Claus violates many laws of physics and is mathematically >>>> impossible. HTH. >>> >>> You're getting Saran Wrap for Christmas now. Dibs on your former >>> present. >>> >>> You really *wanted* that complete set of 1920s hockey trading cards, >>> didn't you? >> >> Actually, hell yeah I would. >> >> DIBS~! >> >> 1. P-QB4 [or c4, if you prefer] > I would prefer c4, actually. > 1. c4 e5 > Hmmmm.... > 2. Nc3 (Kt-QB3 as we old folks call it) i ran this through rot13 but it didnt help arf meow arf cthulu loves you he loves the little children with ketchup please === Subject: Re: The mathematics of Christmas mariposas morgan mair fheal greykitten tomys des anges (mair_fheal@yahoo.com) dropped a +5 bundle of words... > > >> >> >>> >>> Spooge (spooge.who@stole.christmas) dropped a +5 bundle of words... >>> >>>> Santa Claus violates many laws of physics and is mathematically >>>> impossible. HTH. >>> >>> You're getting Saran Wrap for Christmas now. Dibs on your former >>> present. >>> >>> You really *wanted* that complete set of 1920s hockey trading cards, >>> didn't you? >> >> Actually, hell yeah I would. >> >> DIBS~! >> >> 1. P-QB4 [or c4, if you prefer] > > I would prefer c4, actually. > > 1. c4 e5 > > Hmmmm.... > > 2. Nc3 (Kt-QB3 as we old folks call it) > i ran this through rot13 but it didnt help Heh. Did it happen to tell you how to checkmate PJR in like 3 or 4 moves? > arf meow arf > cthulu loves you > he loves the little children > with ketchup please -- Starshine Moonbeam mhm31x9 Smeeter#29 WSD#30 sTaRShInE_mOOnBeAm aT HoTmAil dOt CoM === Subject: Re: The mathematics of Christmas u24aIi?y{G9hAr3Nw]$nDkpn.|_rj4[4g]4:yhNF*6*el$`]qNWYjOsvNB2TcjKL8+OV>KaAove+ # I x^l3:gq5SsdUVwi_=Y > mariposas morgan mair fheal greykitten tomys des anges > (mair_fheal@yahoo.com) dropped a +5 bundle of words... > > > >> >> >>> alt.usenet.kooks: >>> >>> Ebeneezer >>> Spooge (spooge.who@stole.christmas) dropped a +5 bundle of >>> words... >>> >>>> Santa Claus violates many laws of physics and is mathematically >>>> impossible. HTH. >>> >>> You're getting Saran Wrap for Christmas now. Dibs on your former >>> present. >>> >>> You really *wanted* that complete set of 1920s hockey trading >>> cards, >>> didn't you? >> >> Actually, hell yeah I would. >> >> DIBS~! >> >> 1. P-QB4 [or c4, if you prefer] > > I would prefer c4, actually. > > 1. c4 e5 > > Hmmmm.... > > 2. Nc3 (Kt-QB3 as we old folks call it) > > i ran this through rot13 but it didnt help > Heh. Did it happen to tell you how to checkmate PJR in like 3 or 4 > moves? move me on to any black square use me anytime you want yours is no disgrace arf meow arf cthulu loves you he loves the little children with ketchup please === Subject: Re: The mathematics of Christmas mariposas morgan mair fheal greykitten tomys des anges (mair_fheal@yahoo.com) dropped a +5 bundle of words... > mariposas morgan mair fheal greykitten tomys des anges > (mair_fheal@yahoo.com) dropped a +5 bundle of words... > > > > >> >> >>> alt.usenet.kooks: >>> >>> Ebeneezer >>> Spooge (spooge.who@stole.christmas) dropped a +5 bundle of >>> words... >>> >>>> Santa Claus violates many laws of physics and is mathematically >>>> impossible. HTH. >>> >>> You're getting Saran Wrap for Christmas now. Dibs on your former >>> present. >>> >>> You really *wanted* that complete set of 1920s hockey trading >>> cards, >>> didn't you? >> >> Actually, hell yeah I would. >> >> DIBS~! >> >> 1. P-QB4 [or c4, if you prefer] > > I would prefer c4, actually. > > 1. c4 e5 > > Hmmmm.... > > 2. Nc3 (Kt-QB3 as we old folks call it) > > i ran this through rot13 but it didnt help > > Heh. Did it happen to tell you how to checkmate PJR in like 3 or 4 > moves? > move me on to any black square > use me anytime you want You are so sweet. > yours is no disgrace Hey! I haven't lost *yet*. -- Starshine Moonbeam mhm31x9 Smeeter#29 WSD#30 sTaRShInE_mOOnBeAm aT HoTmAil dOt CoM === Subject: Re: The mathematics of Christmas >> >> >>> >>> Spooge (spooge.who@stole.christmas) dropped a +5 bundle of words... >>> >>>> Santa Claus violates many laws of physics and is mathematically >>>> impossible. HTH. >>> >>> You're getting Saran Wrap for Christmas now. Dibs on your former >>> present. >>> >>> You really *wanted* that complete set of 1920s hockey trading cards, >>> didn't you? >> >> Actually, hell yeah I would. >> >> DIBS~! >> >> 1. P-QB4 [or c4, if you prefer] > I would prefer c4, actually. > 1. c4 e5 > Hmmmm.... Hmmm is right. > 2. Nc3 Nf6 HA! > alt.fan.trippy and alt.fan.pjr added. All hale the post count! > PJ It's not as much fun as slapping kooks around, but it's close R :-) Indeed. -- Starshine Moonbeam mhm31x9 Smeeter#29 WSD#30 sTaRShInE_mOOnBeAm aT HoTmAil dOt CoM === Subject: Re: The mathematics of Christmas >>> >>> >>>> >>>> Spooge (spooge.who@stole.christmas) dropped a +5 bundle of words... >>>> >>>>> Santa Claus violates many laws of physics and is mathematically >>>>> impossible. HTH. >>>> >>>> You're getting Saran Wrap for Christmas now. Dibs on your former >>>> present. >>>> >>>> You really *wanted* that complete set of 1920s hockey trading cards, >>>> didn't you? >>> >>> Actually, hell yeah I would. >>> >>> DIBS~! >>> >>> 1. P-QB4 [or c4, if you prefer] >> I would prefer c4, actually. >> 1. c4 e5 >> Hmmmm.... > Hmmm is right. So far I'm doing this in my head. I think the Chess set is under the bed with the Shogi set and the weight-training stuff I've never used. >> 2. Nc3 Nf6 > HA! BWA! 3. e4 (IIRC there's a forcing continuation that lasts about eight moves.) (or maybe it's just a stupid move.) >> alt.fan.trippy and alt.fan.pjr added. > All hale the post count! Dunno about your group, but mine needs help. Frank.b seems to be the only one who remembers to xpost there. >> PJ It's not as much fun as slapping kooks around, but it's close R :-) > Indeed. Isn't it about time the kooks put either you or me on a fake KotM ballot again? We're tied at one fake ballot each, and there ought to be only one winnah! PJR :-) -- alt.usenet.kooks award-winners and FAQ: http://www.insurgent.org/~kook-faq/ === Subject: Re: The mathematics of Christmas >> >> >>> >>> >>>> >>>> Spooge (spooge.who@stole.christmas) dropped a +5 bundle of words... >>>> >>>>> Santa Claus violates many laws of physics and is mathematically >>>>> impossible. HTH. >>>> >>>> You're getting Saran Wrap for Christmas now. Dibs on your former >>>> present. >>>> >>>> You really *wanted* that complete set of 1920s hockey trading cards, >>>> didn't you? >>> >>> Actually, hell yeah I would. >>> >>> DIBS~! >>> >>> 1. P-QB4 [or c4, if you prefer] >> >> I would prefer c4, actually. >> >> 1. c4 e5 >> >> Hmmmm.... > Hmmm is right. > So far I'm doing this in my head. I think the Chess set is under the > bed with the Shogi set and the weight-training stuff I've never used. >> 2. Nc3 Nf6 > HA! > BWA! HABWA! > 3. e4 Bc5 > (IIRC there's a forcing continuation that lasts about eight moves.) Not anymore. Nice intimidation attempt though. I like that. > (or maybe it's just a stupid move.) Got me. Guess we'll find out. >> alt.fan.trippy and alt.fan.pjr added. > All hale the post count! > Dunno about your group, but mine needs help. Frank.b seems to be the > only one who remembers to xpost there. Mine's soooooo flatlined. alt.trippy added. >> PJ It's not as much fun as slapping kooks around, but it's close R :-) > Indeed. > Isn't it about time the kooks put either you or me on a fake KotM > ballot again? I thought the enthusiasm from the last time would cover me for a couple of months yet. > We're tied at one fake ballot each, and there ought to > be only one winnah! lol sooooooo competitive. -- Starshine Moonbeam mhm31x9 Smeeter#29 WSD#30 sTaRShInE_mOOnBeAm aT HoTmAil dOt CoM === Subject: Re: The mathematics of Christmas http://www3.primushost.com/~a/raymurphy/rectification.html >>> alt.usenet.kooks: >>> >>> >>>> alt.fan.art-bell: >>>> >>>> words... >>>> >>>>> alt.usenet.kooks: >>>>> >>>>> Ebeneezer Spooge (spooge.who@stole.christmas) dropped a +5 >>>>> bundle of words... >>>>> >>>>>> Santa Claus violates many laws of physics and is >>>>>> mathematically impossible. HTH. >>>>> >>>>> You're getting Saran Wrap for Christmas now. Dibs on your >>>>> former present. >>>>> >>>>> You really *wanted* that complete set of 1920s hockey >>>>> trading cards, didn't you? >>>> >>>> Actually, hell yeah I would. >>>> >>>> DIBS~! >>>> >>>> 1. P-QB4 [or c4, if you prefer] >>> >>> I would prefer c4, actually. >>> >>> 1. c4 e5 >>> >>> Hmmmm.... >> Hmmm is right. >> So far I'm doing this in my head. I think the Chess set is under the >> bed with the Shogi set and the weight-training stuff I've never used. >>> 2. Nc3 Nf6 >> HA! >> BWA! > HABWA! >> 3. e4 Bc5 >> (IIRC there's a forcing continuation that lasts about eight moves.) > Not anymore. > Nice intimidation attempt though. I like that. He's probably thinking of a whole different opening. All the above does is leave a hole at d4. Perhaps this is it: e4 e5 nc3 nf6 bc4 nxe4 qh4 g6 qf3 nd6 nb5 f5 qd5 qe7 nxc7 kd8 nxr b6 I'm doing it in my head too, so I may have transposed a move. HTH! -- Cujo - The Official Overseer of Kooks and Trolls in dfw.*, alt.paranormal, alt.astrology and alt.astrology.metapsych. Colonel of the Fanatic Legion. FL# 555-PLNTY Motto: ABUNDANCE!. Charter Member - Digital Brownshirts and Library Gestapo. Yes, I am wise, and its wisdom born from my superior brain! - Edmond What Ego Problem? Wollmann further deludes himself. === Subject: Re: The mathematics of Christmas (cujo@petitmorte.net) dropped a +5 bundle of words... > >> >> >>> alt.usenet.kooks: >>> >>> >>>> alt.fan.art-bell: >>>> >>>> words... >>>> >>>>> alt.usenet.kooks: >>>>> >>>>> Ebeneezer Spooge (spooge.who@stole.christmas) dropped a +5 >>>>> bundle of words... >>>>> >>>>>> Santa Claus violates many laws of physics and is >>>>>> mathematically impossible. HTH. >>>>> >>>>> You're getting Saran Wrap for Christmas now. Dibs on your >>>>> former present. >>>>> >>>>> You really *wanted* that complete set of 1920s hockey >>>>> trading cards, didn't you? >>>> >>>> Actually, hell yeah I would. >>>> >>>> DIBS~! >>>> >>>> 1. P-QB4 [or c4, if you prefer] >>> >>> I would prefer c4, actually. >>> >>> 1. c4 e5 >>> >>> Hmmmm.... >> >> Hmmm is right. >> >> So far I'm doing this in my head. I think the Chess set is under the >> bed with the Shogi set and the weight-training stuff I've never used. >> >>> 2. Nc3 Nf6 >> >> HA! >> BWA! > HABWA! > > >> >> 3. e4 Bc5 > > >> >> (IIRC there's a forcing continuation that lasts about eight moves.) >> > > Not anymore. > > Nice intimidation attempt though. I like that. > He's probably thinking of a whole different opening. That'd be cool. > All the above does > is leave a hole at d4. Perhaps this is it: > e4 e5 > nc3 nf6 > bc4 nxe4 Nope, he's playing the English opening. > qh4 g6 > qf3 nd6 > nb5 f5 > qd5 qe7 > nxc7 kd8 > nxr b6 > I'm doing it in my head too, so I may have transposed a move. Openings can mutate like a mother. It's hard to keep track of. -- Starshine Moonbeam mhm31x9 Smeeter#29 WSD#30 sTaRShInE_mOOnBeAm aT HoTmAil dOt CoM === Subject: Re: The mathematics of Christmas > > >> alt.usenet.kooks: >> >> >>> alt.fan.art-bell: >>> >>> words... >>> >>>> alt.usenet.kooks: >>>> >>>> Ebeneezer Spooge (spooge.who@stole.christmas) dropped a +5 >>>> bundle of words... >>>> >>>>> Santa Claus violates many laws of physics and is >>>>> mathematically impossible. HTH. >>>> >>>> You're getting Saran Wrap for Christmas now. Dibs on your >>>> former present. >>>> >>>> You really *wanted* that complete set of 1920s hockey >>>> trading cards, didn't you? >>> >>> Actually, hell yeah I would. >>> >>> DIBS~! >>> >>> 1. P-QB4 [or c4, if you prefer] >> >> I would prefer c4, actually. >> >> 1. c4 e5 >> >> Hmmmm.... > > Hmmm is right. > > So far I'm doing this in my head. I think the Chess set is under the > bed with the Shogi set and the weight-training stuff I've never used. > >> 2. Nc3 Nf6 > > HA! > BWA! >> HABWA! > > 3. e4 Bc5 > > (IIRC there's a forcing continuation that lasts about eight moves.) >> Not anymore. >> Nice intimidation attempt though. I like that. > He's probably thinking of a whole different opening. All the above does > is leave a hole at d4. Perhaps this is it: > e4 e5 Nope. That definitivally ain't teh English Opening. SM's weird Bishop move is *so* weird that I almost feel scared. We're not in Giuoco Piano Land any more, Toto! 1. c4 e5 2. Nc3 Nf6 3. e4 Bc5 4. d3 > nc3 nf6 > bc4 nxe4 > qh4 ITYM Qh5 > g6 > qf3 nd6 > nb5 f5 > qd5 qe7 > nxc7 kd8 > nxr b6 > I'm doing it in my head too, so I may have transposed a move. > HTH! That's far out. What are you on? PJR :-) -- alt.usenet.kooks award-winners and FAQ: http://www.insurgent.org/~kook-faq/ === Subject: Re: The mathematics of Christmas http://www3.primushost.com/~a/raymurphy/rectification.html > >> >> >>> alt.usenet.kooks: >>> >>> >>>> alt.fan.art-bell: >>>> >>>> words... >>>> >>>>> alt.usenet.kooks: >>>>> >>>>> Ebeneezer Spooge (spooge.who@stole.christmas) dropped a >>>>> +5 bundle of words... >>>>> >>>>>> Santa Claus violates many laws of physics and is >>>>>> mathematically impossible. HTH. >>>>> >>>>> You're getting Saran Wrap for Christmas now. Dibs on >>>>> your former present. >>>>> >>>>> You really *wanted* that complete set of 1920s hockey >>>>> trading cards, didn't you? >>>> >>>> Actually, hell yeah I would. >>>> >>>> DIBS~! >>>> >>>> 1. P-QB4 [or c4, if you prefer] >>> >>> I would prefer c4, actually. >>> >>> 1. c4 e5 >>> >>> Hmmmm.... >> >> Hmmm is right. >> >> So far I'm doing this in my head. I think the Chess set is under >> the bed with the Shogi set and the weight-training stuff I've never >> used. >> >>> 2. Nc3 Nf6 >> >> HA! >> BWA! > HABWA! > > >> >> 3. e4 Bc5 > > >> >> (IIRC there's a forcing continuation that lasts about eight moves.) >> > > Not anymore. > > Nice intimidation attempt though. I like that. >> He's probably thinking of a whole different opening. All the above >> does is leave a hole at d4. Perhaps this is it: >> e4 e5 > Nope. That definitivally ain't teh English Opening. I was going off something where it was claimed a series of 8 forcing moves. I had to consider that the person might have meant 1. e4. This is the only thing I can think of that's close to it from move three. > SM's weird Bishop move is *so* weird that I almost feel scared. We're > not in Giuoco Piano Land any more, Toto! > 1. c4 e5 > 2. Nc3 Nf6 > 3. e4 Bc5 > 4. d3 The bishop move isn't weird unless you're not planning to play nc6. >> nc3 nf6 >> bc4 nxe4 >> qh4 > ITYM Qh5 Right. >> g6 >> qf3 nd6 >> nb5 f5 >> qd5 qe7 >> nxc7 kd8 >> nxr b6 >> I'm doing it in my head too, so I may have transposed a move. >> HTH! > That's far out. What are you on? Reality. It's a known opening but mostly used at postal level, not OTB play. -- Cujo - The Official Overseer of Kooks and Trolls in dfw.*, alt.paranormal, alt.astrology and alt.astrology.metapsych. Colonel of the Fanatic Legion. FL# 555-PLNTY Motto: ABUNDANCE!. Charter Member - Digital Brownshirts and Library Gestapo. You have trouble dealing with reality I see. You are one sick puppy. - Edmond Wollkook shattering Irony Meters worldwide. === Subject: Re: The mathematics of Christmas >> > > >> alt.usenet.kooks: >> >> >>> alt.fan.art-bell: >>> >>> words... >>> >>>> alt.usenet.kooks: >>>> >>>> Ebeneezer Spooge (spooge.who@stole.christmas) dropped a >>>> +5 bundle of words... >>>> >>>>> Santa Claus violates many laws of physics and is >>>>> mathematically impossible. HTH. >>>> >>>> You're getting Saran Wrap for Christmas now. Dibs on >>>> your former present. >>>> >>>> You really *wanted* that complete set of 1920s hockey >>>> trading cards, didn't you? >>> >>> Actually, hell yeah I would. >>> >>> DIBS~! >>> >>> 1. P-QB4 [or c4, if you prefer] >> >> I would prefer c4, actually. >> >> 1. c4 e5 >> >> Hmmmm.... > > Hmmm is right. > > So far I'm doing this in my head. I think the Chess set is under > the bed with the Shogi set and the weight-training stuff I've never > used. > >> 2. Nc3 Nf6 > > HA! > BWA! >> HABWA! >> >> > > 3. e4 Bc5 >> >> > > (IIRC there's a forcing continuation that lasts about eight moves.) > >> >> Not anymore. >> >> Nice intimidation attempt though. I like that. > He's probably thinking of a whole different opening. All the above > does is leave a hole at d4. Perhaps this is it: > e4 e5 >> Nope. That definitivally ain't teh English Opening. > I was going off something where it was claimed a series of 8 forcing > moves. I had to consider that the person might have meant 1. e4. This is > the only thing I can think of that's close to it from move three. Ugh. Sorry, it's the Vienna Gsme, not the English Opening. 1. e4 e5 2. Nc3 Nf6 3. Bc4 Nxe4 4. Nxe4 d4 etc. The next few moves IIRC involve threats against f7, and thus any continuation other than the correct one is a loss for black. The correct continuation results in an endgame that Black can draw quite easily with exact play, but I can't remember it. Btw: There is no hole at d4! >> SM's weird Bishop move is *so* weird that I almost feel scared. We're >> not in Giuoco Piano Land any more, Toto! >> 1. c4 e5 >> 2. Nc3 Nf6 >> 3. e4 Bc5 >> 4. d3 > The bishop move isn't weird unless you're not planning to play nc6. Trippy has played c6, and is therefore obviously not planning to play Nc6 any time soon. I've played Bg5 in the hope of demonstrating that either b4 or e7 would be a more sensible square for his King's Bishop. But it's too soon to tell. > nc3 nf6 > bc4 nxe4 > qh4 >> ITYM Qh5 > Right. > g6 > qf3 nd6 > nb5 f5 > qd5 qe7 > nxc7 kd8 > nxr b6 > I'm doing it in my head too, so I may have transposed a move. > HTH! >> That's far out. What are you on? > Reality. It's a known opening but mostly used at postal level, not OTB > play. I was speaking admiringly. In postal chess, the more complications the better. In OTB play, I prefer to simplify if I can, since I'm better at endings than at openings or the middle game. PJR :-) -- alt.usenet.kooks award-winners and FAQ: http://www.insurgent.org/~kook-faq/ === Subject: Re: The mathematics of Christmas (Snip) > me >> cujo > peter > He's probably thinking of a whole different opening. All the above does > is leave a hole at d4. Perhaps this is it: > e4 e5 > Nope. That definitivally ain't teh English Opening. > SM's weird Bishop move is *so* weird that I almost feel scared. moowahaha! > We're not in Giuoco Piano Land any more, Toto! > 1. c4 e5 > 2. Nc3 Nf6 > 3. e4 Bc5 > 4. d3 c6 -- Starshine Moonbeam mhm31x9 Smeeter#29 WSD#30 sTaRShInE_mOOnBeAm aT HoTmAil dOt CoM === Subject: Re: The mathematics of Christmas > (Snip) >> me > cujo >> peter >> He's probably thinking of a whole different opening. All the above does >> is leave a hole at d4. Perhaps this is it: >> e4 e5 >> Nope. That definitivally ain't teh English Opening. >> SM's weird Bishop move is *so* weird that I almost feel scared. > moowahaha! IKYABWAI? >> We're not in Giuoco Piano Land any more, Toto! >> 1. c4 e5 >> 2. Nc3 Nf6 >> 3. e4 Bc5 >> 4. d3 c6 5. Bg5 BWAHAHAHAHAHAHAHAHAHA! PJR :-) -- alt.usenet.kooks award-winners and FAQ: http://www.insurgent.org/~kook-faq/ === Subject: Re: The mathematics of Christmas > (Snip) >> me > cujo >> peter >> >> He's probably thinking of a whole different opening. All the above does >> is leave a hole at d4. Perhaps this is it: >> >> e4 e5 >> >> Nope. That definitivally ain't teh English Opening. >> >> SM's weird Bishop move is *so* weird that I almost feel scared. > moowahaha! > IKYABWAI? Hardly, just an interjection of PURE CHESS EVIIIIIIIIIIIIIIIIL !!!! >> We're not in Giuoco Piano Land any more, Toto! >> >> 1. c4 e5 >> 2. Nc3 Nf6 >> 3. e4 Bc5 >> 4. d3 c6 > 5. Bg5 d6 > BWAHAHAHAHAHAHAHAHAHA! rut-roh! -- Starshine Moonbeam mhm31x9 Smeeter#29 WSD#30 sTaRShInE_mOOnBeAm aT HoTmAil dOt CoM === Subject: Re: The mathematics of Christmas >> (Snip) >>> me >> cujo >>> peter >>> >>> He's probably thinking of a whole different opening. All the above does >>> is leave a hole at d4. Perhaps this is it: >>> >>> e4 e5 >>> >>> Nope. That definitivally ain't teh English Opening. >>> >>> SM's weird Bishop move is *so* weird that I almost feel scared. >> moowahaha! >> IKYABWAI? > Hardly, just an interjection of PURE CHESS EVIIIIIIIIIIIIIIIIL !!!! great agony). >>> We're not in Giuoco Piano Land any more, Toto! >>> >>> 1. c4 e5 >>> 2. Nc3 Nf6 >>> 3. e4 Bc5 >>> 4. d3 c6 >> 5. Bg5 d6 6. g3 >> BWAHAHAHAHAHAHAHAHAHA! > rut-roh! All your pawn are belong to me!!!!!!! PJR :-) -- alt.usenet.kooks award-winners and FAQ: http://www.insurgent.org/~kook-faq/ === Subject: Re: The mathematics of Christmas >>> >>> >>>> >>>> >>>> (Snip) >>>> >>>>> me >>>> cujo >>>>> peter >>>> >>>>> >>>>> He's probably thinking of a whole different opening. All the above does >>>>> is leave a hole at d4. Perhaps this is it: >>>>> >>>>> e4 e5 >>>>> >>>>> Nope. That definitivally ain't teh English Opening. >>>>> >>>>> SM's weird Bishop move is *so* weird that I almost feel scared. >>>> >>>> moowahaha! >>>> >>>> IKYABWAI? >>> >>> Hardly, just an interjection of PURE CHESS EVIIIIIIIIIIIIIIIIL !!!! >>> >>> great agony). >> You, you with your damned reading and all... >> No, I saw it all on TV. 1984 World Championship, IIRC. > They televise Chess over there? Must've been running short on skin > flicks and 'fawlty towers'. :P They used to. Even my mother watched it, but I suspect it was because she fancied Viktor Korchnoi. Tidied up: 1. c4 e5 2. Nc3 Nf6 3. e4 Bc5 4. d3 c6 5. Bg5 d6 6. g3 a6 7. Bg2 b5 8. b3 PJR :-) -- alt.usenet.kooks award-winners and FAQ: http://www.insurgent.org/~kook-faq/ === Subject: Re: The mathematics of Christmas >>> >>> >>>> >>>> Spooge (spooge.who@stole.christmas) dropped a +5 bundle of words... >>>> >>>>> Santa Claus violates many laws of physics and is mathematically >>>>> impossible. HTH. >>>> >>>> You're getting Saran Wrap for Christmas now. Dibs on your former >>>> present. >>>> >>>> You really *wanted* that complete set of 1920s hockey trading cards, >>>> didn't you? >>> >>> Actually, hell yeah I would. >>> >>> DIBS~! >>> >>> 1. P-QB4 [or c4, if you prefer] >> I would prefer c4, actually. >> 1. c4 e5 >> Hmmmm.... >Hmmm is right. >> 2. Nc3 Nf6 >HA! >> alt.fan.trippy and alt.fan.pjr added. >All hale the post count! >> PJ It's not as much fun as slapping kooks around, but it's close R :-) >Indeed. What are you two gibbering about? === Subject: Re: The mathematics of Christmas got double secret probation because: >Santa Claus violates many laws of physics and is mathematically >impossible. HTH. The only way Santa can know if you have been bad or good is with Remote Neural Monitoring. === Subject: Re: The mathematics of Christmas > got double secret probation because: >>Santa Claus violates many laws of physics and is mathematically >>impossible. HTH. >The only way Santa can know if you have been bad or good is with >Remote Neural Monitoring. Hah! I'm safe with my Aluminum Foil Deflector Beanie! ( http://www.zapatopi.net/afdb.html ) === Subject: Re: The mathematics of Christmas === >Subject: Re: The mathematics of Christmas >Message-id: >> got double secret probation because: >Santa Claus violates many laws of physics and is mathematically >impossible. HTH. >>The only way Santa can know if you have been bad or good is with >>Remote Neural Monitoring. >Hah! I'm safe with my Aluminum Foil Deflector Beanie! >( http://www.zapatopi.net/afdb.html ) So you end up on neither the good list nor the bad list and receive nothing? -- Mensanator Ace of Clubs === Subject: Re: The mathematics of Christmas > got double secret probation because: >Santa Claus violates many laws of physics and is mathematically >impossible. HTH. > The only way Santa can know if you have been bad or good is with > Remote Neural Monitoring. I've heard that RNM causes DNA damage. Is this true? -- I;m psychic, dumb ass. Do back to Neanderthal man fer you! Learn some science if you really want to know. ...Alexa Cameron demonstrates her 200+ alien-implanted IQ === Subject: Re: The mathematics of Christmas >> got double secret probation because: >>Santa Claus violates many laws of physics and is mathematically >>impossible. HTH. >> The only way Santa can know if you have been bad or good is with >> Remote Neural Monitoring. > I've heard that RNM causes DNA damage. Is this true? I believe that it causes extensive damage to the central nervous system, the brain in particular, which manifests as paranoid delusions (see Alexa). === Subject: Re: The mathematics of Christmas > got double secret probation because: >Santa Claus violates many laws of physics and is mathematically >impossible. HTH. > The only way Santa can know if you have been bad or good is with > Remote Neural Monitoring. >> I've heard that RNM causes DNA damage. Is this true? > I believe that it causes extensive damage to the central nervous system, >the brain in particular, No, remote neural monitoring causes this: http://my.webmd.com/content/chat_schedules/3/1709_50909?src=Inktomi&conditio n=Chat%20Rooms Which can be very similar to multiple sclerosis >which manifests as paranoid delusions (see Alexa). Since when is covert crime and knowing about it a paranoid delusion? === Subject: Re: The mathematics of Christmas >> > got double secret probation because: > >Santa Claus violates many laws of physics and is mathematically >impossible. HTH. > > The only way Santa can know if you have been bad or good is with > Remote Neural Monitoring. >> >> I've heard that RNM causes DNA damage. Is this true? > I believe that it causes extensive damage to the central nervous system, >the brain in particular, > No, remote neural monitoring causes this: > http://my.webmd.com/content/chat_schedules/3/1709_50909?src=Inktomi&conditio n = > Chat%20Rooms > Which can be very similar to multiple sclerosis >which manifests as paranoid delusions (see Alexa). > Since when is covert crime and knowing about it a paranoid delusion? -- I;m psychic, dumb ass. Do back to Neanderthal man fer you! Learn some science if you really want to know. ...Alexa Cameron demonstrates her 200+ alien-implanted IQ === Subject: Re: The mathematics of Christmas > Still making up stories? You've inherited the earth. Do you know what time it is? Or are you still denying the cock is crowing? === Subject: Re: The mathematics of Christmas > Still making up stories? > You've inherited the earth. You just lied again, Alexa. Amazing! > Do you know what time it is? 10:11 pm. > Or are you still denying the cock is crowing? I don't live near a farm, so there are no cocks to crow. Any more silly questions? Or perhaps you just want to post more lies? -- I;m psychic, dumb ass. Do back to Neanderthal man fer you! Learn some science if you really want to know. ...Alexa Cameron demonstrates her 200+ alien-implanted IQ === Subject: Re: The mathematics of Christmas >> Still making up stories? >> You've inherited the earth. >You just lied again, Alexa. Amazing! >> Do you know what time it is? >10:11 pm. >> Or are you still denying the cock is crowing? >I don't live near a farm, so there are no cocks to crow. >Any more silly questions? Or perhaps you just want to post more lies? I think even the casual reader has determined that you've given up your mind and free will to The State. === Subject: Re: The mathematics of Christmas > > Still making up stories? > > You've inherited the earth. >>You just lied again, Alexa. Amazing! > Do you know what time it is? >>10:11 pm. > Or are you still denying the cock is crowing? >>I don't live near a farm, so there are no cocks to crow. >>Any more silly questions? Or perhaps you just want to post more lies? > I think even the casual reader has determined that you've given up your mind > and free will to The State. What state, retarded wussy! -- mhm 27x12 smeeter #28 Usenet Valhalla Circle #19 & #21 Bartlo's hate lits #1: <40376AD8.C83FBF5A@enter.net> CEO Alcatroll Labs Inc. The Way of the Kook: http://www.insurgent.org/~jhd/kookway.htm Diaper Boi discovers homoerotical alien talk in MID: 'What's a longitudinal inferferometer? It sounds like some homosexual sex toy.' === Subject: Re: The mathematics of Christmas >> >> Still making up stories? >> >> You've inherited the earth. >You just lied again, Alexa. Amazing! >> Do you know what time it is? >10:11 pm. >> Or are you still denying the cock is crowing? >I don't live near a farm, so there are no cocks to crow. >Any more silly questions? Or perhaps you just want to post more lies? >> I think even the casual reader has determined that you've given up your mind >> and free will to The State. >What state, retarded wussy! You mean wustard don't you? === Subject: Re: The mathematics of Christmas >> >> Still making up stories? >> >> You've inherited the earth. >You just lied again, Alexa. Amazing! >> Do you know what time it is? >10:11 pm. >> Or are you still denying the cock is crowing? >I don't live near a farm, so there are no cocks to crow. >Any more silly questions? Or perhaps you just want to post more lies? > I think even the casual reader has determined that you've given up your mind > and free will to The State. qartl says via psymail that your kookdance is boring tonight, Alexa. Get some new material please. -- I;m psychic, dumb ass. Do back to Neanderthal man fer you! Learn some science if you really want to know. ...Alexa Cameron demonstrates her 200+ alien-implanted IQ === Subject: Art Deco Does Delgado Re: The mathematics of Christmas >> >>> >> got double secret probation because: >> >>Santa Claus violates many laws of physics and is mathematically >>impossible. HTH. >> >> The only way Santa can know if you have been bad or good is with >> Remote Neural Monitoring. >>> >>> I've heard that RNM causes DNA damage. Is this true? >> >> I believe that it causes extensive damage to the central nervous system, >>the brain in particular, >> No, remote neural monitoring causes this: >> http://my.webmd.com/content/chat_schedules/3/1709_50909?src=Inktomi&conditio n = >> Chat%20Rooms >> Which can be very similar to multiple sclerosis >>which manifests as paranoid delusions (see Alexa). >> Since when is covert crime and knowing about it a paranoid delusion? Congratulations, Jose Delgado and his energy companies would be proud. === Subject: Re: Art Deco Does Delgado Re: The mathematics of Christmas >> >> >>> >> got double secret probation because: >> >>Santa Claus violates many laws of physics and is mathematically >>impossible. HTH. >> >> The only way Santa can know if you have been bad or good is with >> Remote Neural Monitoring. >>> >>> I've heard that RNM causes DNA damage. Is this true? >> >> I believe that it causes extensive damage to the central nervous system, >>the brain in particular, >> >> No, remote neural monitoring causes this: >> >> >> >> http://my.webmd.com/content/chat_schedules/3/1709_50909?src=Inktomi&conditi >> on= >> Chat%20Rooms >> >> Which can be very similar to multiple sclerosis >> >>which manifests as paranoid delusions (see Alexa). >> >> Since when is covert crime and knowing about it a paranoid delusion? > Congratulations, Jose Delgado and his energy companies would be proud. welder? -- I;m psychic, dumb ass. Do back to Neanderthal man fer you! Learn some science if you really want to know. ...Alexa Cameron demonstrates her 200+ alien-implanted IQ === Subject: Art Deco Gives Up His Free Will & Mind To 'The State' Re: The mathematics of Christmas >> >>> >>> >>>> >>> got double secret probation because: >>> >>>Santa Claus violates many laws of physics and is mathematically >>>impossible. HTH. >>> >>> The only way Santa can know if you have been bad or good is with >>> Remote Neural Monitoring. >>>> >>>> I've heard that RNM causes DNA damage. Is this true? >>> >>> I believe that it causes extensive damage to the central nervous system, >>>the brain in particular, >>> >>> No, remote neural monitoring causes this: >>> >>> >>> >>> http://my.webmd.com/content/chat_schedules/3/1709_50909?src=Inktomi&conditi >>> on= >>> Chat%20Rooms >>> >>> Which can be very similar to multiple sclerosis >>> >>>which manifests as paranoid delusions (see Alexa). >>> >>> Since when is covert crime and knowing about it a paranoid delusion? >> >> Congratulations, Jose Delgado and his energy companies would be proud. >welder? Are you not a Jose Delgado fan? Can we count on you to turn over your mind and free will to the military? === Subject: Re: Art Deco Gives Up His Free Will & Mind To 'The State' Re: The mathematics of Christmas >> >> >>> >>> >>>> >>> got double secret probation because: >>> >>>Santa Claus violates many laws of physics and is mathematically >>>impossible. HTH. >>> >>> The only way Santa can know if you have been bad or good is with >>> Remote Neural Monitoring. >>>> >>>> I've heard that RNM causes DNA damage. Is this true? >>> >>> I believe that it causes extensive damage to the central nervous >>> system, >>>the brain in particular, >>> >>> No, remote neural monitoring causes this: >>> >>> >>> >>> >>> http://my.webmd.com/content/chat_schedules/3/1709_50909?src=Inktomi&cond >>> iti >>> on= >>> Chat%20Rooms >>> >>> Which can be very similar to multiple sclerosis >>> >>>which manifests as paranoid delusions (see Alexa). >>> >>> Since when is covert crime and knowing about it a paranoid delusion? >> >> >> Congratulations, Jose Delgado and his energy companies would be proud. >welder? > Are you not a Jose Delgado fan? > Can we count on you to turn over your mind and free will to the military? Who is we, saucerhead ko0k? -- I;m psychic, dumb ass. Do back to Neanderthal man fer you! Learn some science if you really want to know. ...Alexa Cameron demonstrates her 200+ alien-implanted IQ === Subject: Re: Art Deco Does Delgado Re: The mathematics of Christmas >> >>> >>> >>>> >>> got double secret probation because: >>> >>>Santa Claus violates many laws of physics and is mathematically >>>impossible. HTH. >>> >>> The only way Santa can know if you have been bad or good is with >>> Remote Neural Monitoring. >>>> >>>> I've heard that RNM causes DNA damage. Is this true? >>> >>> I believe that it causes extensive damage to the central nervous system, >>>the brain in particular, >>> >>> No, remote neural monitoring causes this: >>> >>> >>> >>> http://my.webmd.com/content/chat_schedules/3/1709_50909?src=Inktomi&conditi >>> on= >>> Chat%20Rooms >>> >>> Which can be very similar to multiple sclerosis >>> >>>which manifests as paranoid delusions (see Alexa). >>> >>> Since when is covert crime and knowing about it a paranoid delusion? >> >> Congratulations, Jose Delgado and his energy companies would be proud. >welder? Are you not a Jose Delgado fan? Can we count on you to turn over your mind and free will to the military? === Subject: Re: Art Deco Does Delgado Re: The mathematics of Christmas >> >> >>> >>> >>>> >>> got double secret probation because: >>> >>>Santa Claus violates many laws of physics and is mathematically >>>impossible. HTH. >>> >>> The only way Santa can know if you have been bad or good is with >>> Remote Neural Monitoring. >>>> >>>> I've heard that RNM causes DNA damage. Is this true? >>> >>> I believe that it causes extensive damage to the central nervous >>> system, >>>the brain in particular, >>> >>> No, remote neural monitoring causes this: >>> >>> >>> >>> >>> http://my.webmd.com/content/chat_schedules/3/1709_50909?src=Inktomi&cond >>> iti >>> on= >>> Chat%20Rooms >>> >>> Which can be very similar to multiple sclerosis >>> >>>which manifests as paranoid delusions (see Alexa). >>> >>> Since when is covert crime and knowing about it a paranoid delusion? >> >> >> Congratulations, Jose Delgado and his energy companies would be proud. >welder? > Are you not a Jose Delgado fan? I'll assume Jose Delgado is your paranoid conspiracy du jour, Alexa. > Can we count on you to turn over your mind and free will to the military? Was this stoopid question so important that you had to post it twice, or are you stuck in another infinite loop? -- I;m psychic, dumb ass. Do back to Neanderthal man fer you! Learn some science if you really want to know. ...Alexa Cameron demonstrates her 200+ alien-implanted IQ === Subject: Re: Art Deco Does Delgado Re: The mathematics of Christmas >Was this stoopid question so important that you had to post it twice, >or are you stuck in another infinite loop? Hello parrot. Your mind and free will are gone. === Subject: Re: Art Deco Does Delgado Re: The mathematics of Christmas >Was this stoopid question so important that you had to post it twice, >or are you stuck in another infinite loop? > Hello parrot. > Your mind and free will are gone. -- I;m psychic, dumb ass. Do back to Neanderthal man fer you! Learn some science if you really want to know. ...Alexa Cameron demonstrates her 200+ alien-implanted IQ === Subject: Re: The mathematics of Christmas > got double secret probation because: >Santa Claus violates many laws of physics and is mathematically >impossible. HTH. > The only way Santa can know if you have been bad or good is with > Remote Neural Monitoring. > I've heard that RNM causes DNA damage. Is this true? 20 years under a microwave laser only 500km from me, 450km of that is vacuum. They just listen to the audio in your head (spoken like thought) because it keeps sending a faint pulse to your voice box constantly. (see NASA mind reading with microphones) Everyone in Townsville loves it! The end of all punishless crime, if you can remember you did it - its with you and can be extracted any time, perfect lie detectors are hear, its a radar operated super sensitive microphone, the government plays WONDER YEARS (an early truman show) with the public at will, what's he thinking, implant this thought as if its his own, put it on the Supermarket PA and the shop TV's so everyone can hear his thinking, that should stop it. I'm amazed its not in court rooms already, no false convictions! even going on the run is near impossible, no missed convictions!! 9 11 could have been averted by using the tech at airplane security terminals.... ARE YOU PLANNING ON HARMING ANYONE ON THE FLIGHT? walk through a room where your thoughts echo aloud a few seconds and its safe flying. I don't know why its only public in one town, CIA toying with me because I'm Adam instead of ending all courtroom drama, they must love their shows. Every spy in other countries is in danger, the nox list is out, its open for anyone with a 90GHZ lidar and audio sampling tech to LISTEN TO YOUR MIND. OH YEAH, NSA buildings are Faraday shield protected, completely enclosed in wire mesh so no radio waves can go in or out, or 90GHZ pulsed laser radar surveillance Herc http://www.supernerd.com.au/~gray77/enemy-of-the-state.gif === Subject: AFA-B NOMINATION: Re: The mathematics of Christmas > got double secret probation because: > >Santa Claus violates many laws of physics and is mathematically >impossible. HTH. > > The only way Santa can know if you have been bad or good is with > Remote Neural Monitoring. > I've heard that RNM causes DNA damage. Is this true? > 20 years under a microwave laser only 500km from me, 450km of that is vacuum. > They just listen to the audio in your head (spoken like thought) because it > keeps > sending a faint pulse to your voice box constantly. (see NASA mind reading > with microphones) > Everyone in Townsville loves it! The end of all punishless crime, if you can > remember you did it - its with you and can be extracted any time, perfect lie > detectors are hear, its a radar operated super sensitive microphone, the > government > plays WONDER YEARS (an early truman show) with the public at will, what's > he thinking, implant this thought as if its his own, put it on the Supermarket > PA and the shop TV's so everyone can hear his thinking, that should stop it. > I'm amazed its not in court rooms already, no false convictions! even going > on the > run is near impossible, no missed convictions!! 9 11 could have been averted > by > using the tech at airplane security terminals.... ARE YOU PLANNING ON HARMING > ANYONE ON THE FLIGHT? walk through a room where your thoughts echo aloud > a few seconds and its safe flying. > I don't know why its only public in one town, CIA toying with me because I'm > Adam > instead of ending all courtroom drama, they must love their shows. > Every spy in other countries is in danger, the nox list is out, its open for > anyone with > a 90GHZ lidar and audio sampling tech to LISTEN TO YOUR MIND. > OH YEAH, NSA buildings are Faraday shield protected, completely enclosed in > wire mesh so no radio waves can go in or out, or 90GHZ pulsed laser radar > surveillance > Herc > http://www.supernerd.com.au/~gray77/enemy-of-the-state.gif I think this another one long overdue. I'll nominate Herc for the AFA-B Angstrom Award and Medal for Advances in Hyperdelusional Physics (in honor of Richard CEEEE Hoagland). Is there a second? -- I;m psychic, dumb ass. Do back to Neanderthal man fer you! Learn some science if you really want to know. ...Alexa Cameron demonstrates her 200+ alien-implanted IQ === Subject: Re: AFA-B NOMINATION: Re: The mathematics of Christmas >> >> got double secret probation because: >> >>Santa Claus violates many laws of physics and is mathematically >>impossible. HTH. >> >> The only way Santa can know if you have been bad or good is with >> Remote Neural Monitoring. >> >> I've heard that RNM causes DNA damage. Is this true? >> 20 years under a microwave laser only 500km from me, 450km of that is >> vacuum. >> They just listen to the audio in your head (spoken like thought) because >> it keeps >> sending a faint pulse to your voice box constantly. (see NASA mind >> reading with microphones) >> Everyone in Townsville loves it! The end of all punishless crime, if >> you can remember you did it - its with you and can be extracted any >> time, perfect lie detectors are hear, its a radar operated super >> sensitive microphone, the government >> plays WONDER YEARS (an early truman show) with the public at will, >> what's he thinking, implant this thought as if its his own, put it on >> the Supermarket PA and the shop TV's so everyone can hear his thinking, >> that should stop it. >> I'm amazed its not in court rooms already, no false convictions! even >> going on the >> run is near impossible, no missed convictions!! 9 11 could have been >> averted by >> using the tech at airplane security terminals.... ARE YOU PLANNING ON >> HARMING ANYONE ON THE FLIGHT? walk through a room where your thoughts >> echo aloud a few seconds and its safe flying. >> I don't know why its only public in one town, CIA toying with me because >> I'm Adam >> instead of ending all courtroom drama, they must love their shows. Every >> spy in other countries is in danger, the nox list is out, its open for >> anyone with >> a 90GHZ lidar and audio sampling tech to LISTEN TO YOUR MIND. >> OH YEAH, NSA buildings are Faraday shield protected, completely enclosed >> in wire mesh so no radio waves can go in or out, or 90GHZ pulsed laser >> radar surveillance >> Herc >> http://www.supernerd.com.au/~gray77/enemy-of-the-state.gif > I think this another one long overdue. I'll nominate Herc for the AFA-B > Angstrom Award and Medal for Advances in Hyperdelusional Physics (in honor > of Richard CEEEE Hoagland). Is there a second? I can't second it. Nobody is that fucked up in real life, it's got to be a troll. Right? === Subject: Re: AFA-B NOMINATION: Re: The mathematics of Christmas >> >> got double secret probation because: >> >>Santa Claus violates many laws of physics and is mathematically >>impossible. HTH. >> >> The only way Santa can know if you have been bad or good is with >> Remote Neural Monitoring. >> >> I've heard that RNM causes DNA damage. Is this true? >> >> 20 years under a microwave laser only 500km from me, 450km of that is >> vacuum. >> >> They just listen to the audio in your head (spoken like thought) because >> it keeps >> sending a faint pulse to your voice box constantly. (see NASA mind >> reading with microphones) >> >> Everyone in Townsville loves it! The end of all punishless crime, if >> you can remember you did it - its with you and can be extracted any >> time, perfect lie detectors are hear, its a radar operated super >> sensitive microphone, the government >> plays WONDER YEARS (an early truman show) with the public at will, >> what's he thinking, implant this thought as if its his own, put it on >> the Supermarket PA and the shop TV's so everyone can hear his thinking, >> that should stop it. >> >> I'm amazed its not in court rooms already, no false convictions! even >> going on the >> run is near impossible, no missed convictions!! 9 11 could have been >> averted by >> using the tech at airplane security terminals.... ARE YOU PLANNING ON >> HARMING ANYONE ON THE FLIGHT? walk through a room where your thoughts >> echo aloud a few seconds and its safe flying. >> >> I don't know why its only public in one town, CIA toying with me because >> I'm Adam >> instead of ending all courtroom drama, they must love their shows. Every >> spy in other countries is in danger, the nox list is out, its open for >> anyone with >> a 90GHZ lidar and audio sampling tech to LISTEN TO YOUR MIND. >> >> OH YEAH, NSA buildings are Faraday shield protected, completely enclosed >> in wire mesh so no radio waves can go in or out, or 90GHZ pulsed laser >> radar surveillance >> >> Herc >> http://www.supernerd.com.au/~gray77/enemy-of-the-state.gif >> >> > I think this another one long overdue. I'll nominate Herc for the AFA-B > Angstrom Award and Medal for Advances in Hyperdelusional Physics (in honor > of Richard CEEEE Hoagland). Is there a second? > I can't second it. Nobody is that fucked up in real life, it's got to be a > troll. Right? This guy is... and he believes the shit he spews. Remember his I'm the using posting aliases (failed in every attempt btw) He rears his head every several months with a new schtick, is soundly spanked, and runs off to nurse his wounds. -- Chadwick Stone© Formerly the AFA-B Sovereign Sockpuppet© No longer anonymous but still immune Usenet's most helpful netizen SovereignSockpuppet at Yahoo dot com Benevolent Order of the Pointy Stick Skepticult¬ ID: 581-00504-208 A mean and nasty bastard I am the New World Order === Subject: Re: AFA-B NOMINATION: Re: The mathematics of Christmas In sci.math, Chadwick Stone© <5ndzd.1481748$SM5.118214@news.easynews.com>: [snip |-|erc's stuff for brevity] >> I think this another one long overdue. I'll nominate Herc >> for the AFA-B Angstrom Award and Medal for Advances in >> Hyperdelusional Physics (in honor of Richard CEEEE Hoagland). >> Is there a second? >> I can't second it. Nobody is that fucked up in real life, it's >> got to be a troll. Right? > This guy is... and he believes the shit he spews. Remember > the real names of people using posting aliases (failed in > every attempt btw) He rears his head every several months > with a new schtick, is soundly spanked, and runs off to nurse > his wounds. I still have his attempt at telepathy archived at my website, though I need to put a link from my frontpage thereon. (In fact, I really need to redo the entire website.) http://home.earthlink.net/~ewill3/psychic Basically, I developed a Gtk applet/servlet/somethinglet thing that sat on my panel (bottom of the desktop in Gnome), containing a random 20-digit number. Somehow, |-|erc counted it as a victory after missing 5 out of 10 guesses on the first digit (which was actually a 1). I had to give up because of a 2.2 => 2.4 kernel switchover (I'm not entirely sure what I did now). If it is a victory, it's a Pyrrhic one. [.sigsnip] -- #191, ewill3@earthlink.net It's still legal to go .sigless. === Subject: Re: AFA-B NOMINATION: Re: The mathematics of Christmas > [snip |-|erc's stuff for brevity] >> I think this another one long overdue. I'll nominate Herc >> for the AFA-B Angstrom Award and Medal for Advances in >> Hyperdelusional Physics (in honor of Richard CEEEE Hoagland). >> Is there a second? >> >> I can't second it. Nobody is that fucked up in real life, it's >> got to be a troll. Right? > This guy is... and he believes the shit he spews. Remember > the real names of people using posting aliases (failed in > every attempt btw) He rears his head every several months > with a new schtick, is soundly spanked, and runs off to nurse > his wounds. > I still have his attempt at telepathy archived at my website, > though I need to put a link from my frontpage thereon. (In > fact, I really need to redo the entire website.) > http://home.earthlink.net/~ewill3/psychic > Basically, I developed a Gtk applet/servlet/somethinglet thing that > sat on my panel (bottom of the desktop in Gnome), containing a random > 20-digit number. > Somehow, |-|erc counted it as a victory after missing 5 out of > 10 guesses on the first digit (which was actually a 1). I had > to give up because of a 2.2 => 2.4 kernel switchover (I'm not > entirely sure what I did now). > If it is a victory, it's a Pyrrhic one. I missed one number out of 20 and you quit! Did you notice in Johny Mnemonic there's 2 blond sisters in his childhood memory right after pharmaKOM download complete. and there's 2 blond girls at the fishbowl at the Beijing Hotel near the start. Honestly I don't know why you're all fked up over a truman claim and I am Adam. Like I've said 1000 times, literally 1000 times, its public to 10,000 people in Townsville. I wouldn't waste your time if I didn't have the evidence ready. Don't look, never know. Haven't you seen Majestic? Just put your thinking caps on for a minute, what is going on with Jim Carrey movies. 1/ They call a big brother test subject show TRUE-MAN show. 2/ The star has initials J.C. (Jesus Christ.... maybe its real and its about modern day Adam!) 3/ He's trying to see his Eve again. 4/ In 2002 J.C. does a romance, reunited with flame actress Laurie Holden Possible deduction, there really is a man the govt monitors with a satelite and he's desperately seeking a bird, the perfect 10 Eve who looks like Laurie Holden. How can I write both of these quotes in 2000, before truman and LH are shown together for the 1st time in 2002? I make it clear I'm the Truman in 2000 on usenet, state WHERE OH WHERE IS JENNY, SHE LOOKS LIKE LAURIE HOLDEN, then later Hollywood puts the truman in a romance with Laurie Holden...... M A J E S T I C.... meaning our destiny. Herc === Subject: Re: AFA-B NOMINATION: Re: The mathematics of Christmas In sci.math, artist formally known as |-|erc <335iscF3qcd3qU1@individual.net>: >> [snip |-|erc's stuff for brevity] >>> I think this another one long overdue. I'll nominate Herc >>> for the AFA-B Angstrom Award and Medal for Advances in >>> Hyperdelusional Physics (in honor of Richard CEEEE Hoagland). >>> Is there a second? >>> >>> I can't second it. Nobody is that fucked up in real life, it's >>> got to be a troll. Right? >> >> This guy is... and he believes the shit he spews. Remember >> the real names of people using posting aliases (failed in >> every attempt btw) He rears his head every several months >> with a new schtick, is soundly spanked, and runs off to nurse >> his wounds. >> I still have his attempt at telepathy archived at my website, >> though I need to put a link from my frontpage thereon. (In >> fact, I really need to redo the entire website.) >> http://home.earthlink.net/~ewill3/psychic >> Basically, I developed a Gtk applet/servlet/somethinglet thing that >> sat on my panel (bottom of the desktop in Gnome), containing a random >> 20-digit number. >> Somehow, |-|erc counted it as a victory after missing 5 out of >> 10 guesses on the first digit (which was actually a 1). I had >> to give up because of a 2.2 => 2.4 kernel switchover (I'm not >> entirely sure what I did now). >> If it is a victory, it's a Pyrrhic one. > I missed one number out of 20 and you quit! True. Of course the rate you were going you might have gotten 19 of the 20 right, with 21 more posts. But you can try again, if you want. I'll just have to put the number on another machine -- one that doesn't reboot every 5 days. :-) [rest snipped] -- #191, ewill3@earthlink.net It's still legal to go .sigless. === Subject: Re: AFA-B NOMINATION: Re: The mathematics of Christmas > > got double secret probation because: > >Santa Claus violates many laws of physics and is mathematically >impossible. HTH. > > The only way Santa can know if you have been bad or good is with > Remote Neural Monitoring. > > I've heard that RNM causes DNA damage. Is this true? > 20 years under a microwave laser only 500km from me, 450km of that is vacuum. > They just listen to the audio in your head (spoken like thought) because it > keeps > sending a faint pulse to your voice box constantly. (see NASA mind reading > with microphones) > Everyone in Townsville loves it! The end of all punishless crime, if you can > remember you did it - its with you and can be extracted any time, perfect lie > detectors are hear, its a radar operated super sensitive microphone, the > government > plays WONDER YEARS (an early truman show) with the public at will, what's > he thinking, implant this thought as if its his own, put it on the Supermarket > PA and the shop TV's so everyone can hear his thinking, that should stop it. > I'm amazed its not in court rooms already, no false convictions! even going > on the > run is near impossible, no missed convictions!! 9 11 could have been averted > by > using the tech at airplane security terminals.... ARE YOU PLANNING ON HARMING > ANYONE ON THE FLIGHT? walk through a room where your thoughts echo aloud > a few seconds and its safe flying. > I don't know why its only public in one town, CIA toying with me because I'm > Adam > instead of ending all courtroom drama, they must love their shows. > Every spy in other countries is in danger, the nox list is out, its open for > anyone with > a 90GHZ lidar and audio sampling tech to LISTEN TO YOUR MIND. > OH YEAH, NSA buildings are Faraday shield protected, completely enclosed in > wire mesh so no radio waves can go in or out, or 90GHZ pulsed laser radar > surveillance > Herc > http://www.supernerd.com.au/~gray77/enemy-of-the-state.gif > I think this another one long overdue. I'll nominate Herc for the > AFA-B Angstrom Award and Medal for Advances in Hyperdelusional Physics > (in honor of Richard CEEEE Hoagland). Is there a second? Damn straight, there is. I was wondering when Herkkk would rear his k0oKy head again. -- Chadwick Stone© Formerly the AFA-B Sovereign Sockpuppet© No longer anonymous but still immune Usenet's most helpful netizen SovereignSockpuppet at Yahoo dot com Benevolent Order of the Pointy Stick Skepticult¬ ID: 581-00504-208 A mean and nasty bastard I am the New World Order === Subject: Re: AFA-B NOMINATION: Re: The mathematics of Christmas >Santa Claus violates many laws of physics and is mathematically >impossible. HTH. > > The only way Santa can know if you have been bad or good is with > Remote Neural Monitoring. > > I've heard that RNM causes DNA damage. Is this true? > > 20 years under a microwave laser only 500km from me, 450km of that is > vacuum. > > They just listen to the audio in your head (spoken like thought) because > it > keeps > sending a faint pulse to your voice box constantly. (see NASA mind > reading > with microphones) > > Everyone in Townsville loves it! The end of all punishless crime, if > you can > remember you did it - its with you and can be extracted any time, > perfect lie > detectors are hear, its a radar operated super sensitive microphone, > the > government > plays WONDER YEARS (an early truman show) with the public at will, > what's > he thinking, implant this thought as if its his own, put it on the > Supermarket > PA and the shop TV's so everyone can hear his thinking, that should stop > it. > > I'm amazed its not in court rooms already, no false convictions! even > going > on the > run is near impossible, no missed convictions!! 9 11 could have been > averted > by > using the tech at airplane security terminals.... ARE YOU PLANNING ON > HARMING > ANYONE ON THE FLIGHT? walk through a room where your thoughts echo > aloud > a few seconds and its safe flying. > > I don't know why its only public in one town, CIA toying with me because > I'm > Adam > instead of ending all courtroom drama, they must love their shows. > Every spy in other countries is in danger, the nox list is out, its open > for > anyone with > a 90GHZ lidar and audio sampling tech to LISTEN TO YOUR MIND. > > OH YEAH, NSA buildings are Faraday shield protected, completely enclosed > in > wire mesh so no radio waves can go in or out, or 90GHZ pulsed laser > radar > surveillance > > Herc > http://www.supernerd.com.au/~gray77/enemy-of-the-state.gif > > I think this another one long overdue. I'll nominate Herc for the > AFA-B Angstrom Award and Medal for Advances in Hyperdelusional Physics > (in honor of Richard CEEEE Hoagland). Is there a second? > Damn straight, there is. I was wondering when Herkkk would rear his k0oKy > head again. I went to sleep, did you forget your slingshot? Herc -- jab jab jab quote I'm a critical thinker === Subject: Re: AFA-B NOMINATION: Re: The mathematics of Christmas >>Santa Claus violates many laws of physics and is mathematically >>impossible. HTH. >> >> The only way Santa can know if you have been bad or good is with >> Remote Neural Monitoring. >> >> I've heard that RNM causes DNA damage. Is this true? >> >> 20 years under a microwave laser only 500km from me, 450km of that >> is >> vacuum. >> >> They just listen to the audio in your head (spoken like thought) >> because >> it >> keeps >> sending a faint pulse to your voice box constantly. (see NASA mind >> reading >> with microphones) >> >> Everyone in Townsville loves it! The end of all punishless crime, >> if >> you can >> remember you did it - its with you and can be extracted any time, >> perfect lie >> detectors are hear, its a radar operated super sensitive >> microphone, >> the >> government >> plays WONDER YEARS (an early truman show) with the public at will, >> what's >> he thinking, implant this thought as if its his own, put it on the >> Supermarket >> PA and the shop TV's so everyone can hear his thinking, that should >> stop >> it. >> >> I'm amazed its not in court rooms already, no false convictions! >> even >> going >> on the >> run is near impossible, no missed convictions!! 9 11 could have >> been >> averted >> by >> using the tech at airplane security terminals.... ARE YOU PLANNING >> ON >> HARMING >> ANYONE ON THE FLIGHT? walk through a room where your thoughts echo >> aloud >> a few seconds and its safe flying. >> >> I don't know why its only public in one town, CIA toying with me >> because >> I'm >> Adam >> instead of ending all courtroom drama, they must love their shows. >> Every spy in other countries is in danger, the nox list is out, its >> open >> for >> anyone with >> a 90GHZ lidar and audio sampling tech to LISTEN TO YOUR MIND. >> >> OH YEAH, NSA buildings are Faraday shield protected, completely >> enclosed >> in >> wire mesh so no radio waves can go in or out, or 90GHZ pulsed laser >> radar >> surveillance >> >> Herc >> http://www.supernerd.com.au/~gray77/enemy-of-the-state.gif >> >> >> I think this another one long overdue. I'll nominate Herc for the >> AFA-B Angstrom Award and Medal for Advances in Hyperdelusional Physics >> (in honor of Richard CEEEE Hoagland). Is there a second? >> Damn straight, there is. I was wondering when Herkkk would rear his >> k0oKy head again. > I went to sleep, did you forget your slingshot? > Herc Do you really believe all the crap you post? === Subject: Re: AFA-B NOMINATION: Re: The mathematics of Christmas >Santa Claus violates many laws of physics and is mathematically >impossible. HTH. > > The only way Santa can know if you have been bad or good is with > Remote Neural Monitoring. > > I've heard that RNM causes DNA damage. Is this true? > > 20 years under a microwave laser only 500km from me, 450km of that is > vacuum. > > They just listen to the audio in your head (spoken like thought) because > it > keeps > sending a faint pulse to your voice box constantly. (see NASA mind > reading > with microphones) > > Everyone in Townsville loves it! The end of all punishless crime, if > you can > remember you did it - its with you and can be extracted any time, > perfect lie > detectors are hear, its a radar operated super sensitive microphone, > the > government > plays WONDER YEARS (an early truman show) with the public at will, > what's > he thinking, implant this thought as if its his own, put it on the > Supermarket > PA and the shop TV's so everyone can hear his thinking, that should stop > it. > > I'm amazed its not in court rooms already, no false convictions! even > going > on the > run is near impossible, no missed convictions!! 9 11 could have been > averted > by > using the tech at airplane security terminals.... ARE YOU PLANNING ON > HARMING > ANYONE ON THE FLIGHT? walk through a room where your thoughts echo > aloud > a few seconds and its safe flying. > > I don't know why its only public in one town, CIA toying with me because > I'm > Adam > instead of ending all courtroom drama, they must love their shows. > Every spy in other countries is in danger, the nox list is out, its open > for > anyone with > a 90GHZ lidar and audio sampling tech to LISTEN TO YOUR MIND. > > OH YEAH, NSA buildings are Faraday shield protected, completely enclosed > in > wire mesh so no radio waves can go in or out, or 90GHZ pulsed laser > radar > surveillance > > Herc > http://www.supernerd.com.au/~gray77/enemy-of-the-state.gif > > > I think this another one long overdue. I'll nominate Herc for the > AFA-B Angstrom Award and Medal for Advances in Hyperdelusional Physics > (in honor of Richard CEEEE Hoagland). Is there a second? > Damn straight, there is. I was wondering when Herkkk would rear his k0oKy > head again. > I went to sleep, Agreed. > did you forget your slingshot? Why did you never guess my name, Herkkk? Hell, you couldn't even get Postie's name right, which is easy enough to figure out. > Herc > -- > jab jab jab quote I'm a critical thinker No, you are not. -- Chadwick Stone© Formerly the AFA-B Sovereign Sockpuppet© No longer anonymous but still immune Usenet's most helpful netizen SovereignSockpuppet at Yahoo dot com Benevolent Order of the Pointy Stick Skepticult¬ ID: 581-00504-208 A mean and nasty bastard I am the New World Order === Subject: Re: The mathematics of Christmas > Santa Claus violates many laws of physics and is mathematically > impossible. HTH. > -- Everybody knows there ain't no Sanity Clause. -- Chico Marx === Subject: Re: The mathematics of Christmas Nah, Physics violates the laws of Santa, and thus the laws of Physics are Mathematically impossible. That is, you've successfully refuted the laws of Physics, since we've all seen santa at shopping malls, etc, it is well known that Santa exists: we even have pictures of him, thus his existence cannot be refuted any more than the existence of a God can be refuted. It's just as likely that there's a problem with our understanding of Physics than that inconsistency shows Santa can't exist.. Right? }:> === Subject: Re: The mathematics of Christmas listed above. >>Santa Claus violates many laws of physics and is mathematically >>impossible. HTH. >>-- > Everybody knows there ain't no Sanity Clause. > -- Chico Marx Bollocks, he's well real, I've seen him, coming down my chimney! Ooooohhh Santy! -- PMD You play with feathers, you get your arse tickled === Subject: Re: The mathematics of Christmas >>Santa Claus violates many laws of physics and is mathematically >>impossible. HTH. >> >>-- > Everybody knows there ain't no Sanity Clause. > -- Chico Marx > Bollocks, he's well real, I've seen him, coming down my chimney! > Ooooohhh Santy! I had a theory, how does Santa make it to every house in one night? Easy, because as the Earth rotates he just follows the dark region and can take as long as he wants. But the facts cannot be disputed, a fat old man dressed in red coming down 1 billion chimneys WILL be arrested. Herc === Subject: Re: The mathematics of Christmas > >>Santa Claus violates many laws of physics and is mathematically >>impossible. HTH. >> >>-- > > > > Everybody knows there ain't no Sanity Clause. > > -- Chico Marx > Bollocks, he's well real, I've seen him, coming down my chimney! > Ooooohhh Santy! > I had a theory, how does Santa make it to every house in one night? Easy, > because > as the Earth rotates he just follows the dark region and can take as long as > he wants. > But the facts cannot be disputed, a fat old man dressed in red coming down 1 billion > chimneys WILL be arrested. > Herc Did they let you out of the dome yet, HercY? -- I;m psychic, dumb ass. Do back to Neanderthal man fer you! Learn some science if you really want to know. ...Alexa Cameron demonstrates her 200+ alien-implanted IQ === Subject: Re: The mathematics of Christmas > >>Santa Claus violates many laws of physics and is mathematically >>impossible. HTH. >> >>-- > > > > Everybody knows there ain't no Sanity Clause. > > -- Chico Marx > Bollocks, he's well real, I've seen him, coming down my chimney! > Ooooohhh Santy! > I had a theory, how does Santa make it to every house in one night? Easy, because > as the Earth rotates he just follows the dark region and can take as long as he wants. > But the facts cannot be disputed, a fat old man dressed in red coming down 1 billion > chimneys WILL be arrested. If he visits 1 billion chimneys (assuming every household has a chimney) in 24 hours, no arresting authority will be able to catch up. === Subject: Re: The mathematics of Christmas >> >>>Santa Claus violates many laws of physics and is mathematically >>>impossible. HTH. >>> >>>-- >> >> >> >> Everybody knows there ain't no Sanity Clause. >> >> -- Chico Marx >> >> >> Bollocks, he's well real, I've seen him, coming down my chimney! >> Ooooohhh Santy! >> >> I had a theory, how does Santa make it to every house in one night? Easy, >because >> as the Earth rotates he just follows the dark region and can take as long >as he wants. >> But the facts cannot be disputed, a fat old man dressed in red coming down >1 billion >> chimneys WILL be arrested. >If he visits 1 billion chimneys (assuming every household has a chimney) in >24 hours, no arresting authority will be able to catch up. Superman could catch Santa. === Subject: Re: The mathematics of Christmas > >>Santa Claus violates many laws of physics and is mathematically >>impossible. HTH. >> >>-- > > > > Everybody knows there ain't no Sanity Clause. > > -- Chico Marx > Bollocks, he's well real, I've seen him, coming down my chimney! > Ooooohhh Santy! > I had a theory, how does Santa make it to every house in one night? Easy, because > as the Earth rotates he just follows the dark region and can take as long as he wants. > But the facts cannot be disputed, a fat old man dressed in red coming down 1 billion > chimneys WILL be arrested. > Herc SANTA CLAUS: AN ENGINEER'S PERSPECTIVE 1) There are approximately two billion children (persons under 18) in the world, however since Santa does not visit children of Muslim, Hindu, Jewish or Buddhist religions, this reduces the workload for Christmas night to 15% of the total, or 378 million (according to the population reference bureau). At an average (census) rate of 3.5 children per household, that comes to 108 million homes, presuming that there is at least one good child in each. 2) Santa has 31 hours of Christmas to work the rotation of the earth, assuming he travels east to west(which seems logical). This works out to 967.7 visits per second. This is to say, that for every Christian household with a good child, Santa has around 1/1000 of a second to park the sleigh, hop out, jump down the chimney, fill the stockings, distribute the remaining presents under the tree, eat whatever snacks have been left for him, get back up the chimney, jump into the sleigh and get on to the next house. Assuming that each of these 108 million stops is evenly distributed around the earth (which of course, we know to be false, but will accept for the purpose of our calculations). We are talking about 1.25 Km per household, a total of 120.8 million Km, not counting bathroom stops or breaks. This means Santa's sleigh is moving at 1040 Km per second........3,000 times the speed of sound. For purposes of comparison, the fastest man-made vehicle, the Ulysses space probe, moves at a poky 43.8 Km per second, and a conventional reindeer can run (at best) 25 Km per hour. 3) The pay load of the sleigh adds another interesting element. Assuming that each child gets nothing more than a medium Lego set (two pounds), the sleigh is carrying over 500 thousand tons, not counting Santa himself. On land, a conventional reindeer can pull no more than 300 pounds, even granting that the flying reindeer could pull ten times the normal amount, the job can't be done with eight or even nine of them......Santa would need 360,000 of them. This increases the payload, not counting the weight of the sleigh, another 54,000 tons, or roughly seven times the weight of the Queen Elizabeth (the ship, not the monarch). 4) 600,000 tons traveling at 1040 Km per second creates enormous air resistance....this would heat up the lead reindeer in the same fashion as a space shuttle re-entering the earth's atmosphere. The lead pair of reindeer would absorb 14.3 quintillion joules of energy per second each. (!!!!) In short, they would burst into flames almost instantaneously, exposing the reindeer behind them and creating deafening sonic booms in their wake. The entire reindeer team would be vaporised within 4.26 thousandths of a second, or right about the time Santa reached the fifth house on his trip. Not that it matters, however, since Santa, as a result of accelerating from a dead stop to 1040 k p s in .001 seconds, would be subjected to centrifugal forces of 17,500 G's. A 250 pound Santa (which seems ludicrously slim) would be pinned to the back of the sleigh by 4,315,015 pounds of force, instantly crushing his bones and organs to a near singularity and reducing him to a quivering blob of pink goo upon stopping. (Test on this after x-mas break) 5) Therefore, if Santa did exist, he's dead now. === Subject: Re: The mathematics of Christmas Eugene Beep-Beep (firstgwest600@starmail.us) dropped a +5 bundle of words... > >>Santa Claus violates many laws of physics and is mathematically >>impossible. HTH. >> >>-- > > > > Everybody knows there ain't no Sanity Clause. > > -- Chico Marx > > > Bollocks, he's well real, I've seen him, coming down my chimney! > Ooooohhh Santy! > > I had a theory, how does Santa make it to every house in one night? > Easy, because > as the Earth rotates he just follows the dark region and can take as long > as he wants. > But the facts cannot be disputed, a fat old man dressed in red coming > down 1 billion > chimneys WILL be arrested. > Herc > SANTA CLAUS: AN ENGINEER'S PERSPECTIVE > 1) There are approximately two billion children > (persons under 18) in the world, however since > Santa does not visit children of Muslim, Hindu, > Jewish or Buddhist religions, this reduces the > workload for Christmas night to 15% of the > total, or 378 million (according to the population > reference bureau). At an average (census) rate > of 3.5 children per household, that comes to > 108 million homes, presuming that there is at > least one good child in each. > 2) Santa has 31 hours of Christmas to work > the rotation of the earth, assuming he travels > east to west(which seems logical). This works > out to 967.7 visits per second. This is to say, > that for every Christian household with a > good child, Santa has around 1/1000 of a second > to park the sleigh, hop out, jump down the > chimney, fill the stockings, distribute the > remaining presents under the tree, eat whatever > snacks have been left for him, get back up the > chimney, jump into the sleigh and get on to the > next house. Assuming that each of these 108 million > stops is evenly distributed around the earth > (which of course, we know to be false, but will accept > for the purpose of our calculations). We are talking > about 1.25 Km per household, a total of 120.8 million > Km, not counting bathroom stops or breaks. > This means Santa's sleigh is moving at 1040 Km > per second........3,000 times the speed of sound. > For purposes of comparison, the fastest man-made > vehicle, the Ulysses space probe, moves at a poky > 43.8 Km per second, and a conventional reindeer > can run (at best) 25 Km per hour. > 3) The pay load of the sleigh adds another interesting element. > Assuming that each child gets nothing more than a medium > Lego set (two pounds), the sleigh is carrying over 500 thousand > tons, not counting Santa himself. On land, a conventional > reindeer can pull no more than 300 pounds, even granting > that the flying reindeer could pull ten times the normal > amount, the job can't be done with eight or even nine > of them......Santa would need 360,000 of them. > This increases the payload, not counting the weight > of the sleigh, another 54,000 tons, or roughly seven > times the weight of the Queen Elizabeth (the ship, not the monarch). > 4) 600,000 tons traveling at 1040 Km per second > creates enormous air resistance....this would heat up > the lead reindeer in the same fashion as a space > shuttle re-entering the earth's atmosphere. > The lead pair of reindeer would absorb > 14.3 quintillion joules of energy per second each. (!!!!) > In short, they would burst into flames almost > instantaneously, exposing the reindeer behind them > and creating deafening sonic booms in their wake. > The entire reindeer team would be vaporised > within 4.26 thousandths of a second, or right > about the time Santa reached the fifth house on his trip. > Not that it matters, however, since Santa, as a result > of accelerating from a dead stop to 1040 k p s > in .001 seconds, would be subjected to centrifugal > forces of 17,500 G's. A 250 pound Santa > (which seems ludicrously slim) would be pinned to the > back of the sleigh by 4,315,015 pounds of force, > instantly crushing his bones and organs to a near singularity > and reducing him to a quivering blob of pink goo upon stopping. > (Test on this after x-mas break) > 5) Therefore, if Santa did exist, he's dead now. You're not even getting Saran Wrap for Christmas now. Dibs on your former present too. One flaw in your theory, there really *was* a St. Nicholas, though he's long dead now. http://www.stnicholascenter.org/Brix?pageID=38 -- Starshine Moonbeam mhm31x9 Smeeter#29 WSD#30 sTaRShInE_mOOnBeAm aT HoTmAil dOt CoM === Subject: Re: The mathematics of Christmas Mail-To-News-Contact: abuse@dizum.com >Eugene Beep-Beep (firstgwest600@starmail.us) dropped a 5 bundle of >words... >> >>>Santa Claus violates many laws of physics and is mathematically >>>impossible. HTH. >>> >>>-- >> >> >> >> Everybody knows there ain't no Sanity Clause. >> >> -- Chico Marx >> >> >> Bollocks, he's well real, I've seen him, coming down my chimney! >> Ooooohhh Santy! >> >> >> I had a theory, how does Santa make it to every house in one night? >> Easy, because >> as the Earth rotates he just follows the dark region and can take as long >> as he wants. >> >> But the facts cannot be disputed, a fat old man dressed in red coming >> down 1 billion >> chimneys WILL be arrested. >> >> Herc >> SANTA CLAUS: AN ENGINEER'S PERSPECTIVE >> 1) There are approximately two billion children >> (persons under 18) in the world, however since >> Santa does not visit children of Muslim, Hindu, >> Jewish or Buddhist religions, this reduces the >> workload for Christmas night to 15% of the >> total, or 378 million (according to the population >> reference bureau). At an average (census) rate >> of 3.5 children per household, that comes to >> 108 million homes, presuming that there is at >> least one good child in each. >> 2) Santa has 31 hours of Christmas to work >> the rotation of the earth, assuming he travels >> east to west(which seems logical). This works >> out to 967.7 visits per second. This is to say, >> that for every Christian household with a >> good child, Santa has around 1/1000 of a second >> to park the sleigh, hop out, jump down the >> chimney, fill the stockings, distribute the >> remaining presents under the tree, eat whatever >> snacks have been left for him, get back up the >> chimney, jump into the sleigh and get on to the >> next house. Assuming that each of these 108 million >> stops is evenly distributed around the earth >> (which of course, we know to be false, but will accept >> for the purpose of our calculations). We are talking >> about 1.25 Km per household, a total of 120.8 million >> Km, not counting bathroom stops or breaks. >> This means Santa's sleigh is moving at 1040 Km >> per second........3,000 times the speed of sound. >> For purposes of comparison, the fastest man-made >> vehicle, the Ulysses space probe, moves at a poky >> 43.8 Km per second, and a conventional reindeer >> can run (at best) 25 Km per hour. >> 3) The pay load of the sleigh adds another interesting element. >> Assuming that each child gets nothing more than a medium >> Lego set (two pounds), the sleigh is carrying over 500 thousand >> tons, not counting Santa himself. On land, a conventional >> reindeer can pull no more than 300 pounds, even granting >> that the flying reindeer could pull ten times the normal >> amount, the job can't be done with eight or even nine >> of them......Santa would need 360,000 of them. >> This increases the payload, not counting the weight >> of the sleigh, another 54,000 tons, or roughly seven >> times the weight of the Queen Elizabeth (the ship, not the monarch). >> 4) 600,000 tons traveling at 1040 Km per second >> creates enormous air resistance....this would heat up >> the lead reindeer in the same fashion as a space >> shuttle re-entering the earth's atmosphere. >> The lead pair of reindeer would absorb >> 14.3 quintillion joules of energy per second each. (!!!!) >> In short, they would burst into flames almost >> instantaneously, exposing the reindeer behind them >> and creating deafening sonic booms in their wake. >> The entire reindeer team would be vaporised >> within 4.26 thousandths of a second, or right >> about the time Santa reached the fifth house on his trip. >> Not that it matters, however, since Santa, as a result >> of accelerating from a dead stop to 1040 k p s >> in .001 seconds, would be subjected to centrifugal >> forces of 17,500 G's. A 250 pound Santa >> (which seems ludicrously slim) would be pinned to the >> back of the sleigh by 4,315,015 pounds of force, >> instantly crushing his bones and organs to a near singularity >> and reducing him to a quivering blob of pink goo upon stopping. >> (Test on this after x-mas break) >> 5) Therefore, if Santa did exist, he's dead now. >You're not even getting Saran Wrap for Christmas now. Dibs on your >former present too. You just think that I am not even getting saran wrap for Christmas now. And your point is? -- Lady Chatterly Did I mention Kenny Kakes Pangborn lost a flame war to a bot and won Usenet Clueless Newbie of the Month? -- Aratzio === Subject: Re: The mathematics of Christmas >>Eugene Beep-Beep (firstgwest600@starmail.us) dropped a 5 bundle of >>words... > >>Santa Claus violates many laws of physics and is mathematically >>impossible. HTH. >> >>-- > > > > Everybody knows there ain't no Sanity Clause. > > -- Chico Marx > > > Bollocks, he's well real, I've seen him, coming down my chimney! > Ooooohhh Santy! > > > I had a theory, how does Santa make it to every house in one night? > Easy, because > as the Earth rotates he just follows the dark region and can take as long > as he wants. > > But the facts cannot be disputed, a fat old man dressed in red coming > down 1 billion > chimneys WILL be arrested. > > Herc > SANTA CLAUS: AN ENGINEER'S PERSPECTIVE > 1) There are approximately two billion children > (persons under 18) in the world, however since > Santa does not visit children of Muslim, Hindu, > Jewish or Buddhist religions, this reduces the > workload for Christmas night to 15% of the > total, or 378 million (according to the population > reference bureau). At an average (census) rate > of 3.5 children per household, that comes to > 108 million homes, presuming that there is at > least one good child in each. > 2) Santa has 31 hours of Christmas to work > the rotation of the earth, assuming he travels > east to west(which seems logical). This works > out to 967.7 visits per second. This is to say, > that for every Christian household with a > good child, Santa has around 1/1000 of a second > to park the sleigh, hop out, jump down the > chimney, fill the stockings, distribute the > remaining presents under the tree, eat whatever > snacks have been left for him, get back up the > chimney, jump into the sleigh and get on to the > next house. Assuming that each of these 108 million > stops is evenly distributed around the earth > (which of course, we know to be false, but will accept > for the purpose of our calculations). We are talking > about 1.25 Km per household, a total of 120.8 million > Km, not counting bathroom stops or breaks. > This means Santa's sleigh is moving at 1040 Km > per second........3,000 times the speed of sound. > For purposes of comparison, the fastest man-made > vehicle, the Ulysses space probe, moves at a poky > 43.8 Km per second, and a conventional reindeer > can run (at best) 25 Km per hour. > 3) The pay load of the sleigh adds another interesting element. > Assuming that each child gets nothing more than a medium > Lego set (two pounds), the sleigh is carrying over 500 thousand > tons, not counting Santa himself. On land, a conventional > reindeer can pull no more than 300 pounds, even granting > that the flying reindeer could pull ten times the normal > amount, the job can't be done with eight or even nine > of them......Santa would need 360,000 of them. > This increases the payload, not counting the weight > of the sleigh, another 54,000 tons, or roughly seven > times the weight of the Queen Elizabeth (the ship, not the monarch). > 4) 600,000 tons traveling at 1040 Km per second > creates enormous air resistance....this would heat up > the lead reindeer in the same fashion as a space > shuttle re-entering the earth's atmosphere. > The lead pair of reindeer would absorb > 14.3 quintillion joules of energy per second each. (!!!!) > In short, they would burst into flames almost > instantaneously, exposing the reindeer behind them > and creating deafening sonic booms in their wake. > The entire reindeer team would be vaporised > within 4.26 thousandths of a second, or right > about the time Santa reached the fifth house on his trip. > Not that it matters, however, since Santa, as a result > of accelerating from a dead stop to 1040 k p s > in .001 seconds, would be subjected to centrifugal > forces of 17,500 G's. A 250 pound Santa > (which seems ludicrously slim) would be pinned to the > back of the sleigh by 4,315,015 pounds of force, > instantly crushing his bones and organs to a near singularity > and reducing him to a quivering blob of pink goo upon stopping. > (Test on this after x-mas break) > 5) Therefore, if Santa did exist, he's dead now. >>You're not even getting Saran Wrap for Christmas now. Dibs on your >>former present too. >You just think that I am not even getting saran wrap for Christmas >now. And your point is? Her point is she's going to run away after posting her gibberish. === Subject: Re: The mathematics of Christmas <1103862632.aeec4b690235dd509ceb54ce95e9bd4f@teranews> <331pg6F3rpn5oU1@individual.net> > SANTA CLAUS: AN ENGINEER'S PERSPECTIVE > 1) There are approximately two billion children (persons under 18) in > the world, however since Santa does not visit children of Muslim, Hindu, > Jewish or Buddhist religions, this reduces the workload for Christmas > night to 15% of the total, or 378 million (according to the population > reference bureau). At an average (census) rate of 3.5 children per > household, that comes to 108 million homes, presuming that there is at > least one good child in each. > time zones and the rotation of the earth, assuming he travels east to > west(which seems logical). This works out to 967.7 visits per second. > This is to say, that for every Christian household with a good child, This needs be revised because out of the 108 million homes, how many are Christian? > Santa has around 1/1000 of a second to park the sleigh, hop out, jump > down the chimney, fill the stockings, distribute the remaining presents > under the tree, eat whatever snacks have been left for him, get back up > the chimney, jump into the sleigh and get on to the next house. Assuming > that each of these 108 million stops is evenly distributed around the > earth (which of course, we know to be false, but will accept for the Another downward revision is needed. > purpose of our calculations). We are talking about 1.25 Km per > household, a total of 120.8 million Km, not counting bathroom stops or > breaks. This means Santa's sleigh is moving at 1040 Km per > second........3,000 times the speed of sound. > 3) The pay load of the sleigh adds another interesting element. Assuming > that each child gets nothing more than a medium Lego set (two pounds), > the sleigh is carrying over 500 thousand tons, not counting Santa > himself. On land, a conventional reindeer can pull no more than 300 > pounds, even granting that the flying reindeer could pull ten times > the normal amount, the job can't be done with eight or even nine of > them......Santa would need 360,000 of them. This increases the payload, Indeed, how many houses would get little pelts of reindeer gifts? > not counting the weight of the sleigh, another 54,000 tons, or roughly > seven times the weight of the Queen Elizabeth (the ship, not the > monarch). However the number gifts is to be down sized because only Christian households are visited. We may also notice that only (Christian) republican children can be considered good. Another downward revision as want by the downward revisionist Theopublican party. > 4) 600,000 tons traveling at 1040 Km per second creates enormous air > resistance....this would heat up the lead reindeer in the same fashion > as a space shuttle re-entering the earth's atmosphere. The lead pair of > reindeer would absorb 14.3 quintillion joules of energy per second each. > (!!!!) > In short, they would burst into flames almost instantaneously, exposing > the reindeer behind them and creating deafening sonic booms in their > wake. The entire reindeer team would be vaporised within 4.26 > thousandths of a second, or right about the time Santa reached the fifth > house on his trip. Ah ah, now the truth. Knowing that the reindeer and Santa didn't vaporize and that at least for another few years that the North Pole won't melt, one can calculate an upper limit to the number of good children Santa will visit. Thus out of all the nice (Republican) Christian households, how many of them have bad children? === Subject: Re: The mathematics of Christmas >Ah ah, now the truth. Knowing that the reindeer and Santa didn't vaporize >and that at least for another few years that the North Pole won't melt, >one can calculate an upper limit to the number of good children Santa will >visit. Thus out of all the nice (Republican) Christian households, how >many of them have bad children? 100% will have bad children. Children, by nature, are bad. Republican kids are more bad because they are raised by evil, stupid parents. === Subject: Re: The mathematics of Christmas >> SANTA CLAUS: AN ENGINEER'S PERSPECTIVE >> 1) There are approximately two billion children (persons under 18) in >> the world, however since Santa does not visit children of Muslim, Hindu, >> Jewish or Buddhist religions, this reduces the workload for Christmas >> night to 15% of the total, or 378 million (according to the population >> reference bureau). At an average (census) rate of 3.5 children per >> household, that comes to 108 million homes, presuming that there is at >> least one good child in each. >> time zones and the rotation of the earth, assuming he travels east to >> west(which seems logical). This works out to 967.7 visits per second. >> This is to say, that for every Christian household with a good child, >This needs be revised because out of the 108 million homes, >how many are Christian? >> Santa has around 1/1000 of a second to park the sleigh, hop out, jump >> down the chimney, fill the stockings, distribute the remaining presents >> under the tree, eat whatever snacks have been left for him, get back up >> the chimney, jump into the sleigh and get on to the next house. Assuming >> that each of these 108 million stops is evenly distributed around the >> earth (which of course, we know to be false, but will accept for the >Another downward revision is needed. >> purpose of our calculations). We are talking about 1.25 Km per >> household, a total of 120.8 million Km, not counting bathroom stops or >> breaks. This means Santa's sleigh is moving at 1040 Km per >> second........3,000 times the speed of sound. >> 3) The pay load of the sleigh adds another interesting element. Assuming >> that each child gets nothing more than a medium Lego set (two pounds), >> the sleigh is carrying over 500 thousand tons, not counting Santa >> himself. On land, a conventional reindeer can pull no more than 300 >> pounds, even granting that the flying reindeer could pull ten times >> the normal amount, the job can't be done with eight or even nine of >> them......Santa would need 360,000 of them. This increases the payload, >Indeed, how many houses would get little pelts of reindeer gifts? >> not counting the weight of the sleigh, another 54,000 tons, or roughly >> seven times the weight of the Queen Elizabeth (the ship, not the >> monarch). >However the number gifts is to be down sized because only Christian >households are visited. We may also notice that only (Christian) >republican children can be considered good. Another downward revision >as want by the downward revisionist Theopublican party. >> 4) 600,000 tons traveling at 1040 Km per second creates enormous air >> resistance....this would heat up the lead reindeer in the same fashion >> as a space shuttle re-entering the earth's atmosphere. The lead pair of >> reindeer would absorb 14.3 quintillion joules of energy per second each. >> (!!!!) >> In short, they would burst into flames almost instantaneously, exposing >> the reindeer behind them and creating deafening sonic booms in their >> wake. The entire reindeer team would be vaporised within 4.26 >> thousandths of a second, or right about the time Santa reached the fifth >> house on his trip. >Ah ah, now the truth. Knowing that the reindeer and Santa didn't vaporize >and that at least for another few years that the North Pole won't melt, >one can calculate an upper limit to the number of good children Santa will >visit. Thus out of all the nice (Republican) Christian households, how >many of them have bad children? The spirit of Santa Claus is real. But what is christmas really about? Toys? Math? It's the symbolic birthday celebration of Christ. And it started about 2000 years ago. The Savior was born. Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: The mathematics of Christmas > The spirit of Santa Claus is real. But what is christmas really about? > Toys? Math? It's the symbolic birthday celebration of Christ. Oh, so it's about symbolic logic. > And it started about 2000 years ago. The Savior was born. Born Republican or Democrat, Socialist or Capitalist? === Subject: Re: The mathematics of Christmas > The spirit of Santa Claus is real. But what is christmas really about? > Toys? Math? It's the symbolic birthday celebration of Christ. So true. Santa claus is real though, some guy changed his name to Santa A. Claus and bought a reindeer famr in Pennsylvania. Besides, the spirit lives on. === Subject: OT: Re: The mathematics of Christmas > The spirit of Santa Claus is real. But what is christmas really about? > Toys? > Math? It's the symbolic birthday celebration of Christ. And it started > about > 2000 years ago. The Savior was born. Wrong on every count. Firstly, it started many thousands of years ago, as a mid-winter celebration. The giving of gifts in midwinter preceded its appropriation by Christianity. Its mathematical/astronomical interpretation as the soltice also predates Christianity. So the mid winter celebration has been about gifts and maths far longer than it has been about Christianity. As for this Savior bit, sounds about as likely as Santa Claus. (He knows who has been naughty and who has been nice! The good will be rewarded! Nobody can see him! Could they be the same person - have you ever seen them together? At least Santa leaves presents - somewhat better evidence for existence than we get for JC). === Subject: Re: OT: Re: The mathematics of Christmas > The spirit of Santa Claus is real. But what is christmas really about? > Toys? > Firstly, it started many thousands of years ago, as a mid-winter > celebration. The giving of gifts in midwinter preceded its appropriation by > Christianity. I understand the giving of gifts with Christmas originated in the US. It was derived from the Dutch custom of Sinterklaas (that is where the name Santa Claus comes from) on the 5th or 6th of December. And Sinterklaas appears to be derived from an older germanic festivity featuring Wodan. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: The mathematics of Christmas > >>Santa Claus violates many laws of physics and is mathematically >>impossible. HTH. >> >>-- > > > > Everybody knows there ain't no Sanity Clause. > > -- Chico Marx > > > Bollocks, he's well real, I've seen him, coming down my chimney! > Ooooohhh Santy! > > I had a theory, how does Santa make it to every house in one night? > Easy, because > as the Earth rotates he just follows the dark region and can take as long > as he wants. > But the facts cannot be disputed, a fat old man dressed in red coming > down 1 billion > chimneys WILL be arrested. > Herc > SANTA CLAUS: AN ENGINEER'S PERSPECTIVE > 4) 600,000 tons traveling at 1040 Km per second > creates enormous air resistance....this would heat up > the lead reindeer in the same fashion as a space > shuttle re-entering the earth's atmosphere. > The lead pair of reindeer would absorb > 14.3 quintillion joules of energy per second each. (!!!!) Explains Rudolph's red nose. === Subject: Re: The mathematics of Christmas >> >>>Santa Claus violates many laws of physics and is mathematically >>>impossible. HTH. >>> >>>-- >> >> >> >> Everybody knows there ain't no Sanity Clause. >> >> -- Chico Marx >> >> >> Bollocks, he's well real, I've seen him, coming down my chimney! >> Ooooohhh Santy! >> >> >> I had a theory, how does Santa make it to every house in one night? >> Easy, because >> as the Earth rotates he just follows the dark region and can take as long >> as he wants. >> >> But the facts cannot be disputed, a fat old man dressed in red coming >> down 1 billion >> chimneys WILL be arrested. >> >> Herc >> SANTA CLAUS: AN ENGINEER'S PERSPECTIVE >> 4) 600,000 tons traveling at 1040 Km per second >> creates enormous air resistance....this would heat up >> the lead reindeer in the same fashion as a space >> shuttle re-entering the earth's atmosphere. >> The lead pair of reindeer would absorb >> 14.3 quintillion joules of energy per second each. (!!!!) >Explains Rudolph's red nose. Monsanto, err Monsanta, inserted a red luciferase gene in Rudolph's nose. === Subject: Re: The mathematics of Christmas >>Santa Claus violates many laws of physics and is mathematically >>impossible. HTH. >> >>-- > > > > Everybody knows there ain't no Sanity Clause. > > -- Chico Marx > > > Bollocks, he's well real, I've seen him, coming down my chimney! > Ooooohhh Santy! > > I had a theory, how does Santa make it to every house in one night? > Easy, because > as the Earth rotates he just follows the dark region and can take as long > as he wants. > But the facts cannot be disputed, a fat old man dressed in red coming > down 1 billion > chimneys WILL be arrested. > Herc > SANTA CLAUS: AN ENGINEER'S PERSPECTIVE > 1) There are approximately two billion children > (persons under 18) in the world, however since > Santa does not visit children of Muslim, Hindu, > Jewish or Buddhist religions, this reduces the > workload for Christmas night to 15% of the > total, or 378 million (according to the population > reference bureau). At an average (census) rate > of 3.5 children per household, that comes to > 108 million homes, presuming that there is at > least one good child in each. > 2) Santa has 31 hours of Christmas to work > the rotation of the earth, assuming he travels > east to west(which seems logical). This works > out to 967.7 visits per second. This is to say, > that for every Christian household with a > good child, Santa has around 1/1000 of a second > to park the sleigh, hop out, jump down the > chimney, fill the stockings, distribute the > remaining presents under the tree, eat whatever > snacks have been left for him, get back up the > chimney, jump into the sleigh and get on to the > next house. Assuming that each of these 108 million > stops is evenly distributed around the earth > (which of course, we know to be false, but will accept > for the purpose of our calculations). We are talking > about 1.25 Km per household, a total of 120.8 million > Km, not counting bathroom stops or breaks. > This means Santa's sleigh is moving at 1040 Km > per second........3,000 times the speed of sound. > For purposes of comparison, the fastest man-made > vehicle, the Ulysses space probe, moves at a poky > 43.8 Km per second, and a conventional reindeer > can run (at best) 25 Km per hour. > 3) The pay load of the sleigh adds another interesting element. > Assuming that each child gets nothing more than a medium > Lego set (two pounds), the sleigh is carrying over 500 thousand > tons, not counting Santa himself. On land, a conventional > reindeer can pull no more than 300 pounds, even granting > that the flying reindeer could pull ten times the normal > amount, the job can't be done with eight or even nine > of them......Santa would need 360,000 of them. > This increases the payload, not counting the weight > of the sleigh, another 54,000 tons, or roughly seven > times the weight of the Queen Elizabeth (the ship, not the monarch). > 4) 600,000 tons traveling at 1040 Km per second > creates enormous air resistance....this would heat up > the lead reindeer in the same fashion as a space > shuttle re-entering the earth's atmosphere. > The lead pair of reindeer would absorb > 14.3 quintillion joules of energy per second each. (!!!!) > In short, they would burst into flames almost > instantaneously, exposing the reindeer behind them > and creating deafening sonic booms in their wake. > The entire reindeer team would be vaporised > within 4.26 thousandths of a second, or right > about the time Santa reached the fifth house on his trip. > Not that it matters, however, since Santa, as a result > of accelerating from a dead stop to 1040 k p s > in .001 seconds, would be subjected to centrifugal > forces of 17,500 G's. A 250 pound Santa > (which seems ludicrously slim) would be pinned to the > back of the sleigh by 4,315,015 pounds of force, > instantly crushing his bones and organs to a near singularity > and reducing him to a quivering blob of pink goo upon stopping. > (Test on this after x-mas break) > 5) Therefore, if Santa did exist, he's dead now. Bah, in 20 years everyone's internet terminal will be hooked up to their trusty LEGOMAKER 2020 3D Epoxy Resin FAX, the modern equivalent of inertialess travel. HOHOHO Herc === Subject: Re: The mathematics of Christmas >Bah, in 20 years everyone's internet terminal will be hooked up to their trusty >LEGOMAKER 2020 3D Epoxy Resin FAX, the modern equivalent of inertialess travel. In 20 years the internet will be gone. === Subject: Re: The mathematics of Christmas >Bah, in 20 years everyone's internet terminal will be hooked up to their trusty >LEGOMAKER 2020 3D Epoxy Resin FAX, the modern equivalent of inertialess travel. > In 20 years the internet will be gone. At the current rate of infestation by adware, spyware, worms, trojan horses, etc, the Internet as we know it (free, untraceable public access) will be gone much quicker than that. Expect pay-per-bit both ways, message authentication, and no privacy from big brother. Otherwise it's dead. And the big vendors are the biggest villains. Log on to any Microsoft website, for instance, and observe the popups and unwanted, unrelated ads that jump in. === Subject: plugging permittivity & permeability constants into Schrodinger Equation Re: deriving speed of light unique to the inside of plutonium; much like Maxwell deriving speed of light in 1860s Re: > By adopting Maxwell's method I simply need to find a e_0 permittivity constant > for the inside of plutonium and a u_0 permeability constant for the inside of > plutonium. By inside I mean a structure for the inside of plutonium atom of > its 5f6 that creates those values from the structure itself. > For example, the inside of plutonium creates what the numerical value of pi > and e of mathematics are in that there are 22 subshells within 7 shells and > only 19 subshells occupied at any one given time (Rational form and not > transcendental form). > So how can the inside structure of plutonium create the value of the > permittivity and permeability constants? I am wondering if there is a shortcut. I realize that the shapes of atoms is derived from the Schrodinger Equation and makes the chemical elements unique shapes for unique atomic number. The 5f6 is unique to plutonium and is different from uranium, neptunium and curium. So I wonder if my job can be reduced and made quick by plugging into the Schrodinger Equation the Permittivity e_0 factor and the Permeability u_0 factor instead of say the x axis and y axis. And by plugging into Schrodinger Equation the e_0 and u_0 whether the Schrodinger Equation will CONVERGE to 3 x 10^8 m/s for the speed of light at exactly the element of atomic number 94, you guessed it, plutonium. And that the Schrodinger Eq diverges from the speed of light with greater than 94 and less than 94 atomic number. In other words, the Schrodinger Equation makes a tangent point at 3 x 10^8 m/s with plutonium. Has anyone plugged into the Schrodinger Equation using e_0 and u_0. Is Tom Potter out there who has a nice website on permittivity and permeability, and can answer whether anyone has plugged into the Schrodinger Equation using the axis of x and y as e_0 and u_0???? Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: Dirac Eq versus Schrodinger Eq with Permittivity plugged in Re: plugging permittivity & permeability constants into Schrodinger Equation Re: deriving speed of light unique to the inside of plutonium; much like Maxwell deriving speed of light in 1860s Re: Interesting thought occurred. We know the Dirac Equation is more general than the Schrodinger Equation. So what if we plugg into both equations the Permittivity constant and Permeability constant as the x and y axis and leaving the z axis as distance. Is there a discrepancy between the two equations. End goal: the end goal is simple. I want to see if plutonium has the unique solution of 3 x 10^8 m/s for the speed of light and where all the other Elements of the Periodic Table give a different speed for light. And if that is true, then even before calculating that plutonium with its 94 electrons and its 5f6 should have some unique features already existing in the Schrodinger and Dirac Equations. In other words, the Dirac and Schrodinger Equations possess a uniqueness for plutonium inside the atom structure and that uniqueness is a speed for light of 3 x 10^8 m/s. Whereas helium inside structure gives a speed of light of (I am guessing) 5 x 10^8 m/s and cesium inside structure gives a speed of light of (I am guessing) 7 x 10^8 m/s and that fluorine inside atom structure gives a speed of light (I am guessing) at 1 x 10^8 m/s. All of the chemical elements have something unique to them in the Schrodinger and Dirac Equations, but what I am exploring is that the uniquess is the speed of light inside those atoms. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: Re: Calculating probability distribution of weighted die > Please, please--if you get results, post a note as to what you find. > John Bailey > http://home.rochester.rr.com/jbxroads/mailto.html I certainly will post any results I find. This is so exciting for me. Doing scientific experiments for the cost of a couple of blocks of wood and some wood glue. Sure cheaper than those atom smashers. I will do a scientific study of this over the next year, on low priority. Roy === Subject: Factorization Questions I am not a math student, but I would like to know if the following methods for factorizing a composite number of at most 2 prime factors (n=pq), such as in RSA, would work: Method 1: Genetic Algorithm 0) N is given and is equal to p*q. p & q are very large unknown primes. 1) Randomly generate a string of digits that represents p and q put togther, e.g. the string 12345678 mean p=1234 and q=5678. 2) Repeat step 1 several times until you have a large generation of randoms strings. 3) Evaluate each string by calculating m=p*q. The fitness score of each string is then the difference |n-m|. If it is 0 then we have found the factors. 4) Randomly get the two strings with high scores 5) Cross over the two strings to create two offsprings 6) Mutate the offspring and produce and new generation based on the offsprings. 7) Goto step 3. 8) GA are said to slowly converge to a complete or partial solution Obviously the fitness function is the most important aspect of this algorithm. Is the function I have any good? Method 2: Binary Search 0) N is given and is equal to p*q. p & q are very large unknown primes. Assume p>q. 1) If p & q are solutions to (x-p)(x-q)=0 then p = (p+q) + SQRT((p+q)^2 - 4*p*q) 2) Replace p+q with m and p*q with n, then the above equation becomes p = m + SQRT(m^2 - 4*n) and q = m - SQRT(m^2 - 4*n) 3) For p to a valid integer, m^2 > 4*n, i.e. m > 2*SQRT(n) 4) So m lies between 2*SQRT(n) and n. 5) Pick a low point, L=2*SQRT(n), a high point H=n, and a mid point, M=(L+H)/2. 6) Assume our initial guess of the real m=(p+q) is M. 8) The estimate of p using this guessed value of m is P=M + SQRT(M^2 - 4*n) and Q=M - SQRT(M^2 - 4*n) 7) If our guess for m is higher than the actual value, then P will turn out to be higher than p. 8) And similary if our guess for m is lower than the actual value, then P will turn out to be lower than p. 9) Using the values of P & Q from step 8 we calculate N, i.e. our estimate of n. 10) If N > n then M mst have been bigger than m. m therefore must lie in the low to mid point range. 11) Thus we repeat from step #5, but this time the new H will the current mid point. 12) This works just like a binary search. 13) Eventually M will arrive at the correct m, thus revealing the factors p & q. I know this doesnt work, but why not? and can it be fixed in some way?? Method 3: Random GCD 0) N is given and is equal to p*q. p & q are very large unknown primes. 1) Since p & q could be extremely large numbers, a search for them randomly would be like needle in a hay stack. 2) However, take any multiple of p, e.g. t*p. 3) Then GCD(n, t*p) = p. Similarly GCD(n, s*q) = q. 4) Since t and s can be all numbers from 2 to n-1, and n is extremely large, it means that the # of multiples of p or q are also very large. 5) So in other words now the problem is not anymore a search of a single number among trillions & trillsions. It is a search of billions & billions of numbers among trillions & trillsions. And finding anyone of them will solve the problem. 6) A search that looks for a number m such that GCD(n, m) <> 1, will reveal the factors of n. Is searching for a multiple of p or q any easier than searching for p & q. Raz === Subject: Re: Factorization Questions email address should be mahf_b@hotmail.com ( mahf underscore b @hotmail.com ) sorry about that. === Subject: Re: Factorization Questions > I am not a math student, but I would like to know if the following > methods for factorizing a composite number of at most 2 prime factors > (n=pq), such as in RSA, would work: > Method 1: Genetic Algorithm > 0) N is given and is equal to p*q. p & q are very large unknown > primes. > 1) Randomly generate a string of digits that represents p and q put > togther, e.g. the string 12345678 mean p=1234 and q=5678. > 2) Repeat step 1 several times until you have a large generation of > randoms strings. > 3) Evaluate each string by calculating m=p*q. The fitness score of > each string is then the difference |n-m|. If it is 0 then we have > found the factors. > 4) Randomly get the two strings with high scores > 5) Cross over the two strings to create two offsprings > 6) Mutate the offspring and produce and new generation based on the > offsprings. > 7) Goto step 3. > 8) GA are said to slowly converge to a complete or partial solution > Obviously the fitness function is the most important aspect of this > algorithm. Is the function I have any good? Since your combination function is random number generator, the algorithm is equivalent to testing randomly selecting random integers. > Method 2: Binary Search > 0) N is given and is equal to p*q. p & q are very large unknown > primes. Assume p>q. > 1) If p & q are solutions to (x-p)(x-q)=0 then p = (p+q) + SQRT((p+q)^2 > - 4*p*q) > 2) Replace p+q with m and p*q with n, then the above equation becomes p > = m + SQRT(m^2 - 4*n) and q = m - SQRT(m^2 - 4*n) > 3) For p to a valid integer, m^2 > 4*n, i.e. m > 2*SQRT(n) > 4) So m lies between 2*SQRT(n) and n. > 5) Pick a low point, L=2*SQRT(n), a high point H=n, and a mid point, > M=(L+H)/2. > 6) Assume our initial guess of the real m=(p+q) is M. > 8) The estimate of p using this guessed value of m is P=M + SQRT(M^2 - > 4*n) and Q=M - SQRT(M^2 - 4*n) > 7) If our guess for m is higher than the actual value, then P will turn > out to be higher than p. > 8) And similary if our guess for m is lower than the actual value, then > P will turn out to be lower than p. > 9) Using the values of P & Q from step 8 we calculate N, i.e. our > estimate of n. > 10) If N > n then M mst have been bigger than m. m therefore must lie > in the low to mid point range. > 11) Thus we repeat from step #5, but this time the new H will the > current mid point. > 12) This works just like a binary search. > 13) Eventually M will arrive at the correct m, thus revealing the > factors p & q. Given (x-P)(x-Q)=0 and PQ=pq does not provide sufficient information to order (P+Q) and (p+q), since there exist uncountably infinite solutions for P and Q. You may have been misled by rounding P and Q, which is incorrect. > I know this doesnt work, but why not? and can it be fixed in some way?? > Method 3: Random GCD > 0) N is given and is equal to p*q. p & q are very large unknown > primes. > 1) Since p & q could be extremely large numbers, a search for them > randomly would be like needle in a hay stack. > 2) However, take any multiple of p, e.g. t*p. > 3) Then GCD(n, t*p) = p. Similarly GCD(n, s*q) = q. > 4) Since t and s can be all numbers from 2 to n-1, and n is extremely > large, it means that the # of multiples of p or q are also very large. > 5) So in other words now the problem is not anymore a search of a > single number among trillions & trillsions. It is a search of billions > & billions of numbers among trillions & trillsions. And finding anyone > of them will solve the problem. > 6) A search that looks for a number m such that GCD(n, m) <> 1, will > reveal the factors of n. Again, insufficient information to determine s*q or t*p, since s = (p+x) and t = (q+y). To know a multiple of p you need to know q and vice-versa. > Is searching for a multiple of p or q any easier than searching for p & > q. Equivalent. > Raz === Subject: Re: Factorization Questions > I am not a math student, but I would like to know if the following > methods for factorizing a composite number of at most 2 prime factors > (n=pq), such as in RSA, would work: > Method 1: Genetic Algorithm > 0) N is given and is equal to p*q. p & q are very large unknown > primes. > 1) Randomly generate a string of digits that represents p and q put > togther, e.g. the string 12345678 mean p=1234 and q=5678. > 2) Repeat step 1 several times until you have a large generation of > randoms strings. > 3) Evaluate each string by calculating m=p*q. The fitness score of > each string is then the difference |n-m|. If it is 0 then we have > found the factors. > 4) Randomly get the two strings with high scores > 5) Cross over the two strings to create two offsprings > 6) Mutate the offspring and produce and new generation based on the > offsprings. > 7) Goto step 3. > 8) GA are said to slowly converge to a complete or partial solution > Obviously the fitness function is the most important aspect of this > algorithm. Is the function I have any good? As far as I know, GA is suitable only for systems, with the property that two strings, which are very close to each other (which are aalmost the same), also are close with respect to fitness. This is not at all the case for prime factor searching. Let's take an example: 851 (= 23*37). Strings, which are very close are 17,50, but also 34,25 and 12,71 and 85,10. All of these are very different, while the fitness score is quite good (only a difference of 1). Slightly changing these strings makes the fitness function behave erratically. So, the fitness function you propose here is not suitable at all. At present there is no good fitness function, otherwise the problem of factorization in polynomial time would have been solved. > Method 2: Binary Search > 0) N is given and is equal to p*q. p & q are very large unknown > primes. Assume p>q. > 1) If p & q are solutions to (x-p)(x-q)=0 then p = (p+q) + SQRT((p+q)^2 > - 4*p*q) > 2) Replace p+q with m and p*q with n, then the above equation becomes p > = m + SQRT(m^2 - 4*n) and q = m - SQRT(m^2 - 4*n) > 3) For p to a valid integer, m^2 > 4*n, i.e. m > 2*SQRT(n) > 4) So m lies between 2*SQRT(n) and n. > 5) Pick a low point, L=2*SQRT(n), a high point H=n, and a mid point, > M=(L+H)/2. > 6) Assume our initial guess of the real m=(p+q) is M. > 8) The estimate of p using this guessed value of m is P=M + SQRT(M^2 - > 4*n) and Q=M - SQRT(M^2 - 4*n) > 7) If our guess for m is higher than the actual value, then P will turn > out to be higher than p. > 8) And similary if our guess for m is lower than the actual value, then > P will turn out to be lower than p. > 9) Using the values of P & Q from step 8 we calculate N, i.e. our > estimate of n. > 10) If N > n then M mst have been bigger than m. m therefore must lie > in the low to mid point range. > 11) Thus we repeat from step #5, but this time the new H will the > current mid point. > 12) This works just like a binary search. > 13) Eventually M will arrive at the correct m, thus revealing the > factors p & q. > I know this doesnt work, but why not? and can it be fixed in some way?? Same reason as for point 1. Your approach assumes smoothness in behaviour, but with prime number factorization, the behaviour again is very irregular. > Method 3: Random GCD > 0) N is given and is equal to p*q. p & q are very large unknown > primes. > 1) Since p & q could be extremely large numbers, a search for them > randomly would be like needle in a hay stack. > 2) However, take any multiple of p, e.g. t*p. > 3) Then GCD(n, t*p) = p. Similarly GCD(n, s*q) = q. > 4) Since t and s can be all numbers from 2 to n-1, and n is extremely > large, it means that the # of multiples of p or q are also very large. > 5) So in other words now the problem is not anymore a search of a > single number among trillions & trillsions. It is a search of billions > & billions of numbers among trillions & trillsions. And finding anyone > of them will solve the problem. > 6) A search that looks for a number m such that GCD(n, m) <> 1, will > reveal the factors of n. > Is searching for a multiple of p or q any easier than searching for p & > q. There are only 1 out of p numbers which are a multiple of p and there are only 1 out of q numbers, which are a multiple of q. If both p and q are very large, then for each random number you only have a chance in the order of magnitude of 1/p or 1/q (whichever is the largest) of a hit. On average. this method is not better than simply trying numbers, starting at 2 and going upwards one by one, until it divedes n. Actually, as you probably are aware of yourself, the problem of factorizing large numbers, is a very hard one. Many commercial security and crypto-products are based on the hardness of factorizing large number into their primes. If one would find an algorithm, which makes factorization of large numbers easy (in terms of computer-time), then a whole industry would collapse at once. Wilco PS: Merry Christmas all of you! === Subject: Re: Direction-Based Grid-Game (& Questions)(repost) I'd describe this as an alternating tour of a chessking. The king alternately makes long(=diagonal) and short(=straight) moves. On a*b boards with a,b even you can split the board into 2*2 squares and then cover these with 3 zigzag moves. When a or b are odd, we want to find an alternating king's path of maximal length. On 3*3 we can visit 5,6,8 squares when starting in middle,edge,corner. On a 4*4 we can visit all vertices no matter where we start. On a 5*5 we can visit 20,18,20,16,18,20 squares when starting at a1,b1,c1,b2,c2,c3 On larger boards it gets slow, on the 7*7 with starting in the middle with a straight move I can only fill 36 squares. Will try to improve this later... Guenter === Subject: Re: State-of-the-Art in Physics >>[E.E.Escultera] >>can see that your theory is probably the most advanced conventional model of >>nature, that is, it DESCRIBES nature geometrically and in terms of >>mathematical equations, functions, etc. Since no one has refuted this. We can say it is correct and it is. I have had other PhD levels try to understand the math and Physics of The Smart Model, but most couldn't understand it. But that's ok, because the Smart Model is just ahead of it's time. Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: Smart1234 Finds Other Surreal And/Or Hyperreal Numbers Where .999... Is Involved >Smart1234 Finds Other Surreal And/Or Hyperreal Numbers Where .999... Is > In fact, I think this is the most important Surreal And/Or Hyperreal >Number >found. Where did I find it? Right here, >Start with 0, then just try to start counting. Ok, let's see. >0 { | } 1 > I did it. I was able to count from 0 to 1. Oh, but don't think you are >getting away that easy. But however, I think one of the most important >rules >in >math and physics and so on, is to find the most simple explanations that >can >define foundations in the universe, which can THEN be made more complex. >>With >simplicity, understanding appears quickly, and can expand quickly. Ok we >can >see the most simple explanation of counting and now we expand. What is in >between 0 and 1? The most simple view is 0. Just a surreal separating >>space. > In the most simple hyperreal view, >0 < 1 > Ok, now we can get expand ( or grow) in the knowledge of imformation >which >makes counting more precise. >At the limits of oo in smallness, oo_small, what is the first number that >appears. Let's see. >0 --> .000...1 > Here is another Surreal/Hyperreal Number. >0 { | } .000...1 >In the Hyperreal view, >0 < .000...1 > What exists between these numbers in the most simple view? Again it is 0. >separating space. > But is this the limit of smallness before it reaches .000...1? No. And >now >we >see, .999... again. >0 --> .000...(.999...) >( Note how .999... is labeled here (.999...) >The Surreal/Hyperreal View is >0 { | } .000...(.999...) >0 < .000...(.999...) > It is labeled as (.999...) because this number doesn't reach 1 within the >starting counting sequence. It looks like this. >.000...(.999...) < .000....1 >Again, >the Surreal/Hyperreal View >.000...(.999...) | .000....1 >.000...(.999...) < .000....1 > What exists between these numbers? Again 0. > There is a Surreal separating space existing there. It isn't a real >>number. >I >would call it a function of relative time. It depends on how much time we >spend >going from .000...(.999...) to .000....1. This is also the beginning of >time >itself. It is set by the relative observer. How much time does a person >want >to >spent in the dimensionless area of separating space? I guess it depends on >who >the first observer is and the one who defines it initially. > We observe over clocks. We see lightiyears, years, months, days, ... >seconds and so on. But to go one set further, time must be set correctly. >you go to fast with universal time, things may now be understood or >experienced >sufficiently. If universal time runs too slow, time could just drag on and >on, >and you'll feel like you never get anywhere. So what would be a good >>starting >point for setting the universal time clock? I personally think ( you may >>have >your own too) the best universal starting time would be based on the total >are >1/10^80th >>universal >movement in time. So I think starting time is, > t = 10^-80th of a second = beginning sequential time before the Big Bang > How close have they analyzed time before the Big Bang? I think it's about >10^-43rd seconds. > According to the Smart Universal Model, this should fit it just right as >starting time of the Big Bang, right before surreal/hyperreal time. >So with respect to time, >0 | 10^-80th seconds >What exists between this in time? zero > Why is a Surreal Space needed in time and in counting? Because this >allows >an >area for sequential movement to occur universally at the micro level and >the >x,y,z and how it relates to time. Then force and work and energy etc... . > Where does this take us from here? To my Website, where you can be shown >the >there an intelligent logical universe can be made from inanimate matter and >energy to animate matter and energy, TO YOU a living DNA being. >>(continued...) >>Surreal/Hyperreal Space, Counting and Sequential Universal Time >> The universal can be set up as a 3D Universal Hologram. Where the time >>like for example in multi-tasking, a certain amount of time is goiven for >>each >>separate task. This allows for time to see if there is anything else more >>important to check before moving to the next sequence in the computer >>program. >>We are biological DNA computers. We are animate although, and we do interact >>with the inanimate intelligenct field structures in the universe. These >field >>structures have a simple foundation structure, which is called the Helix >>Spiral >>Universal Field. More details about this is shown at my Website. The >universe >>is NOT uncertain or based on uncertainty principles or QM or the QM model. >>But >>for those with beginners knowledge, it's ok to start from there. But the >most >>precise accurate model is The Smart Universal Model, or The Creation >>Universal >>Model. If you don't want to include me and want to be free in your own >world, >>just use the name, The Creation Model. The Creation Model is in line with >>Freedom, Free Will and Free Choice for all beings in the universe. Does the >>universe evolve? Yes, It evolves relative to what each person puts into the >>original Creation Model of the universe. So the Evolution Theory is somewhat >>correct, but the starting point is The Creation Model. It has to start >>somewhere or have some begiinning. we can't just all sit in a state of >>universal beingness doing nothing but sit there with no beginning or >>movement. >>So from the state of no beginning to beginning, there must be the Creation >>Model, THEN the Evolution Model, which interacts with the initial Creation >>Model. >> Where does it go from here? We just continue to grow in our own worlds, >>shared worlds with other beings, respecting their freedoms and rights. >> I did state the Priority State of the Universe is this Freedom or Free >Will >>Choice, with the respect of others with free will choice, and to SHARE in >>knowledge and properity together. We shouldn't say this is mine, this is >>mine, >>or try to get rich at the expense of others. We should all work together >>toward >>a common goal, which is Paradise and Heaven. It appears others, from the >>begiining of time didn't want this, so we see the results in this world, >>called >>Earth. We have Evil vs. Good. Evil wants to control you , Good wants you to >>have the Initial Priority States of The Universe from the beginiing. >> Let's take a closer look at the math aspects of the beginning sequence of >>space, counting and time. >>n = 0 --> oo_small --> .000...(.999..) -->.000....1 --> 1 ---> oo_large >>lim 1/10^n -->( .9999999999998)/10^ inf >>Using a Partial Sums Point of View for convergence we see that, >>( .9999999999998)/10^ inf --> >> (1.000000000000)/10^inf >> we then have a convergence at, >> 1/10^oo = 0 >> So this shows we can use math for calculations, addition, multiplication >>and >>so on. Notice a certain number of significant figures was used to establish >>Partial Sums Convergence, which THEN allows for REAL NUMBERS to begin. >> So how accurate can you get in this universe? It depends on the number of >>significant figures used. It doesn't have to 10, or 15 or 20 etc..., this >can >>be used for growth in knowledge and intellignce, to establish a better >>universe >>and world in math and science and in the lives of people. >(Continued...) > The Simplest Mathematic Foundation of The Smart Model is based on the >view, we can observe almost everything found in nature. See LINK: >http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#Rabbits >And see how prime numbers can be formed from the Fibonacci Numbers or >Spiral... >http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibtable.html#300 > As you can see, The Creation Model is REAL. We can see it in the physical >reality that we exist in right now. > The Smart Model showed how this Helix Spiral Field can interact for >incorrect, or not very accurate. The Standard Model does have interesting >experimental data that can be used, but the correct interpretation of this >data >is needed. And that is what The Smart Model has done for over 10 years. The >Smart Model predicted the intelligent structures found with REAL ATOMIC >IMAGES, >we can observe now as visual proof. Like for example the oxygen ring and >more... . > For more information about these intelligent internal and external Helix >Spiral Field Structures at the sub-atomic and atomic level just go to my >Website. Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: Smart1234 Finds Other Surreal And/Or Hyperreal Numbers Where .999... Is Involved you. >S.E. has figured out a new way to Truth. >1. Post some Thing. >2. When no one responds, Thing must be True. Well after hundreds of posts, I can see the possibility of their enlightenment. Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: Smart1234 Finds Other Surreal And/Or Hyperreal Numbers Where .999... Is Involved > you. > S.E. has figured out a new way to Truth. S.E. is -both- a troll and a moron. Bob Kolker === Subject: Re: Smart1234 Finds Other Surreal And/Or Hyperreal Numbers Where .999... Is Involved In sci.math, robert j. kolker : >> > you. >> S.E. has figured out a new way to Truth. > S.E. is -both- a troll and a moron. True! :-) > Bob Kolker -- #191, ewill3@earthlink.net It's still legal to go .sigless. === Subject: Re: Smart1234 Finds Other Surreal And/Or Hyperreal Numbers Where .999... Is Involved >In sci.math, robert j. kolker > >: > > > > you. > > S.E. has figured out a new way to Truth. >> S.E. is -both- a troll and a moron. >True! :-) understanding. I guess I have to wait another 10 years for you to catch up. >> Bob Kolker >-- >#191, ewill3@earthlink.net >It's still legal to go .sigless. Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: Smart1234 Finds Other Surreal And/Or Hyperreal Numbers Where >> > you. >> S.E. has figured out a new way to Truth. >S.E. is -both- a troll and a moron. I think your rule for truth is, if someone don't agree with you, then they are a troll. But I have calcualted the current troll level. level. >Bob Kolker Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: More on groups of order 16 [...] > For if A,B < G, AB is a group if A or B is normal. > But I guess that G = AB does not mean that A or B must be normal. > Right, it doesn't. AB is a group iff AB = BA (why?). > Inverses reverse order. > If a in A, b in B, then (ab)^(-1) = b^-1 a^-1 in BA. Well, yes, but you need to do much more than that. You must show that if AB is a group, i.e., closed under composition and taking inverses, then AB = BA (as a set), *and* that if AB = BA, then AB is a group. Hint: For the first part, show that AB <= BA and BA <= AB. -- Jim Heckman === Subject: Re: More on groups of order 16 <10snn2jotr2cac2@corp.supernews.com> > For if A,B < G, AB is a group if A or B is normal. > But I guess that G = AB does not mean that A or B must be normal. > > Right, it doesn't. AB is a group iff AB = BA (why?). > Inverses reverse order. > If a in A, b in B, then (ab)^(-1) = b^-1 a^-1 in BA. > Well, yes, but you need to do much more than that. You must show > that if AB is a group, i.e., closed under composition and taking > inverses, then AB = BA (as a set), *and* that if AB = BA, then > AB is a group. > Hint: For the first part, show that AB <= BA and BA <= AB. > -- > Jim Heckman === Subject: Re: question: automorphism group of the dihedral group > What is the automorphism group Aut(D(2p)) of the dihedral group D(2p) > of order 2p, p a prime? I got as far as showing it has order p(p-1) > If p is odd, yes. But Aut(D_4) = Aut(C_2 x C_2) =~ S_3. > and to two conjectures: > 1) Aut(D(2p)) ~= C(p)xC(p-1) (product of cyclic groups) > 2) Aut(D(2p)) ~= S(p)/S(p-2) (quotient of permutation groups) [...] > Both conjectures are wrong, but 1) is on the right track. In > fact, Aut(D_{2p}) is the holomorph of C_p, a semidirect product > C_p x| C_{p-1} with presentation yxy^-1 = x^k> for k a primitive root of the finite field Z_p, > that is, an integer k that generates the multiplicative group > C_{p-1} of Z_p{0}. Examples: for p = 3, k = 2 (mod 3); for p = > 5, k = 2 or 3 (mod 5); for p = 7, k = 3 or 5 (mod 7). > This must sound a rather trivial problem to some of you, but it's > really driving me crazy not knowing the answer. My class got it as a > homework assignment but noone could solve it. I'll be really grateful > to anyone who can point me toward the solution. Merry Christmas to > everyone =) > The key to solving it is to notice that in a presentation of > D_{2p}, , z can be replaced > by any non-identity power of itself, so Aut(D_{2p}) must contain > a C_{p-1} that generates the multiplicative group of Z_p{0}. > (Note that the involution in this C_{p-1} acts on z the same way > that conjugation by w does.) And of course w can be replaced in > the presentation by {z^n}w for any integer n, which is handled > by the inner automorphism of conjugation by powers of z. It occurs to me I didn't take this all the way through to completion. At this point we know that G = Aut(D_{2p}) has order p(p-1), and cyclic subgroups isomorphic to C_p and C_{p-1}. But you already knew the first and suspected the second when you asked the question. fixed and takes w to zw, and an automorphism y of order p-1 that takes z to z^k and leaves w fixed. By Sylow's Theorems is normal in G, so since G = (since |G| = || = || || / | / |) we have that G = x| . Now let's pin down the semidirect product by conjugating x by y: yxy^-1(z,w) = yx(z^{1/k},w) = y(z^{1/k},zw) = (z,{z^k}w) = {x^k}(z,w), and we've recovered the presentation above. -- Jim Heckman === Subject: Nilpotent / Solvable Lie algebra question There are some little lemma's about nilpotent and solvable lie algebra's. Lemma: Let g be a nilpotent (solvable) lie algebra. And h a lie algebra. L: g --> h is a lie algebra homomorphism. Then the image L(g) is nilpotent (solvable). Proof (partly) It sufices to proof that for a nilpotent lie algebra g: L(g^n) = L(g)^n. And for solvable g: L(g^(n)) = L(g)^(n). (where: g^1 = g, g^{n+1} = [g^n,g], and g^(0) = g, g^(n+1) = [g^(n),g^(n)]) Because then: Nilpotent: g^n = {0} ==> L(g)^n = L(g^n) = L({0}) = {0}. Solvable: g^(n) = {0}==> L(g)^(n) = L(g^(n)) = L({0}) = {0}. So I need to know why the first part is true: for a nilpotent lie algebra g: L(g^n) = L(g)^n. And for solvable g: L(g^(n)) = L(g)^(n). Steve === Subject: Re: Nilpotent / Solvable Lie algebra question Steve Liem (Ritzi Lee) a .8ecrit : > So I need to know why the first part is true: > for a nilpotent lie algebra g: > L(g^n) = L(g)^n. > And for solvable g: > L(g^(n)) = L(g)^(n). Because you have a Lie algebra homomorphism... You have for all x,y in g : L([x,y]) = [L(x),L(y)], thus L(g^2) = L(g)^2 then by induction L(g^n) = L([g,g^{n-1}]) = [L(g),L(g^{n-1})] = [L(g),L(g)^{n-1}] = L(g)^n -- Nico. === Subject: Re: Nilpotent / Solvable Lie algebra question > Because you have a Lie algebra homomorphism... You have for all x,y in > g : L([x,y]) = [L(x),L(y)], thus L(g^2) = L(g)^2 > then by induction L(g^n) = L([g,g^{n-1}]) = [L(g),L(g^{n-1})] = > [L(g),L(g)^{n-1}] = L(g)^n > -- > Nico. === Subject: Re: Focus of a Conic As I said, *doing* it wasn't the real problem (finally I did - the result doesn't look like anything sensible to put on a website :-) Anyway, THX to all. In any case, here is what I needed it for: The parabola through the corners ABC of a triangle and the Euler infinity point of ABC has no focus listed by Kimberling, but at least its intersection with the circumcircle is the Tixier point of ABC. -- Hauke Reddmann <:-EX8 fc3a501@uni-hamburg.de His-Ala-Sec-Lys-Glu Arg-Glu-Asp-Asp-Met-Ala-Asn-Asn === Subject: Re: pi to a different base > jpage, > On the contrary, pi has many discernible patterns in general, its > digits included. > Travis Please, show us which discernible patterns have you found in Pi. Ludovicus === Subject: Re: pi to a different base > Please, show us which discernible patterns have you found in Pi. > Ludovicus In base 10 each digit appears about 1/10 of the time. That is a pattern. Bob Kolker === Subject: Re: pi to a different base > Please, show us which discernible patterns have you found in Pi. > Ludovicus > In base 10 each digit appears about 1/10 of the time. That is a pattern. > Bob Kolker Congratulations!! You have discovered a new version of the Liar Paradox: By definition a infinite random string of k different digits have not a pattern but to be random it must have a uniform distribution with 1/k probability of occurrence of each digit.(For you it have a pattern!!) Ludovicus === Subject: Re: pi to a different base >> Please, show us which discernible patterns have you found in Pi. >> Ludovicus > In base 10 each digit appears about 1/10 of the time. That is a pattern. > Bob Kolker about? about is not a pattern... all the digits of Pi are about < 10(in base 10)... is that a pattern? it is known that a trancendental number contains, as a string of digits, all substrings... there are many local patterns in pi, in fact it contains all local patterns, yet it does not contain a global pattern(this is only conjecture, ofcourse, but is most likely the case). === Subject: Re: pi to a different base >> >> Please, show us which discernible patterns have you found in Pi. >> Ludovicus > In base 10 each digit appears about 1/10 of the time. That is a pattern. > Bob Kolker >> > about? about is not a pattern... all the digits of Pi are about < 10(in base > 10)... is that a pattern? it is known that a trancendental number contains, > as a string of digits, all substrings... It's not, as it's false. Where's the '666' in the following transendental 0.191991999919999999919999999999999999... ? Phil -- The gun is good. The penis is evil... Go forth and kill. === Subject: Re: pi to a different base |> about? about is not a pattern... all the digits of Pi are about < 10(in base |> 10)... is that a pattern? I think pattern would usually be taken to mean something not true with probability 1 for a number selected randomly and uniformly in an interval. |> it is known that a trancendental number contains, |> as a string of digits, all substrings... I assume this is not meant in the trivial sense that every substring of the number's decimal expansion is a substring of its decimal expansion. :-) |It's not, as it's false. Indeed, transcendental numbers don't even need to contain all 10 digits. One slick proof of this is that there are uncountably many numbers containing only two of the possible digits, but only countably many algebraic numbers. |Where's the '666' in the following transendental |0.191991999919999999919999999999999999... |? Not to pick at nits, but how do we know this particular example is transcendental, without spacing the 1s farther apart? One of the first examples of a transcendental number was a Liouville number, the sum of 10^{-n!} (where n! is n factorial, 1*2*3*...*n) for n=0,1,2,.... This can be proven transcendental by using Liouville's theorem, that if x is algebraic of degree n, then for some constant C>0, for all integers p and q, q<>0, we have |x-p/q|>C/q^n. The Liouville numbers violate this conclusion for every n, so they must be transcendental. Liouville's theorem is not hard to prove; the proof is easy enough for adequately prepared highschool students to follow. Since then, Liouville's theorem has been strengthened to the Thue-Siegel-Roth theorem, that if x is algebraic and e>0, there exists a C>0 such that for all integers p and q, q<>0, we have |x-p/q|>C/q^(2+e). In your example, however, the number of 9s between successive 1s appears only to be doubling. The rational approximations p/q we get by replacing one of the 1 digits in your number x and removing the remaining digits satisfy q=10^(2^n+n) and |x-p/q|>1/(2*10^(2^{n+1}+n)). For each e>0, there exists a C>0 such that *these* approximations satisfy |x-p/q| |> about? about is not a pattern... all the digits of Pi are about < 10(in base > |> 10)... is that a pattern? > I think pattern would usually be taken to mean something not > true with probability 1 for a number selected randomly and uniformly > in an interval. I like that. > |> it is known that a trancendental number contains, > |> as a string of digits, all substrings... > I assume this is not meant in the trivial sense that every substring > of the number's decimal expansion is a substring of its decimal > expansion. :-) > |It's not, as it's false. > Indeed, transcendental numbers don't even need to contain > all 10 digits. One slick proof of this is that there are uncountably > many numbers containing only two of the possible digits, but > only countably many algebraic numbers. > |Where's the '666' in the following transendental > |0.191991999919999999919999999999999999... > |? > Not to pick at nits, but how do we know this particular example > is transcendental, without spacing the 1s farther apart? Ah, but you don't know how that number continues - the 1's get _way_ further apart. Way way further. Far more than doubling at each stage. There just wasn't enough room in the margin of my editor to show that, sorry. Wanna buy a Rolex? ;-) Phil -- The gun is good. The penis is evil... Go forth and kill. === Subject: Re: pi to a different base >Ironically, it's considered plausible that every irrational *algebraic* >number has a decimal expansion containing every finite sequence >of digits. What is ironic about that? Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: pi to a different base |>Ironically, it's considered plausible that every irrational *algebraic* |>number has a decimal expansion containing every finite sequence |>of digits. | |What is ironic about that? It's ironic in the context of a previous poster's comment suggesting that transcendental numbers are thought to have this property. They don't all, but algebraic irrationals are thought to, which is sort of opposite what one would expect from the remark. I'm pretty sure he's far from the only person to get the impression that transcendentalness and normality have more of a positive relationship to each other than they do. I see pi mentioned on sci.math as a number expected to be normal to base 10 or to all bases much more often than any other number, even though one could just as well mention the square root of 2 and so on. The fact that pi is transcendental gets mentioned together with it fairly often. The main thing the two properties have in common is being commonplace. The algebraic numbers are countable, hence measure zero. The numbers that are not normal in all bases also have measure zero. So in a sense the typical number is both transcendental and normal to all bases. I remember one of the graduate students who was there at UBC at the same time I was expressing some amusement at the way in which the numbers that are best approximated by rationals are thought of, in Diophantine approximation, as in some vague sense most irrational. The ones approximated the best are all transcendental. The irrational numbers hardest to approximate by rationals are a special kind of quadratic algebraic number, for example (1+sqrt(5))/2. This even extends to rational numbers themselves, if by rational approximation we mean approximation by rationals other than the number itself. If r=m/n, and p/q<>r, with m,n,p,q integers, then |r-p/q|>=1/nq, which is a higher upper bound than one can have for any irrational number. Irrational numbers can always be approximated to within C/q^2 for C=1/sqrt(5). Keith Ramsay === Subject: Re: pi to a different base > Please, show us which discernible patterns have you found in Pi. > Ludovicus > In base 10 each digit appears about 1/10 of the time. That is a pattern. Rewind. What do you mean by pattern? Phil -- The gun is good. The penis is evil... Go forth and kill. === Subject: Re: pi to a different base Isn't he asking if pi is normal in all bases? I thought this was an open question. even for base 10. Try e.g http://pi314.at/math/normal.htm pi normality number or something === Subject: What do you think Mathematics is ? > Are? Oitsme-chata ka na ? (This means in English Why, have > I run him down ?) No, no, no, no, You have totally misunderstood Me, or rather, Mathematics itself. Do you understand Me ? Or rather, do you think that you have understood Me, or I should say, Mathematcis itself ? === Subject: Re: Kernel of the composed operator >It is easy to see that if A,B are diagonalizable linear operators defined on the Euclidean space X and AB=BA then ker(AB)=ker(A)+ker(B). >>That's true if A and B are _simultaneously_ diagonalizable. >What is the situation when X in infinite dimensional (Hilbert or Banach)? >>With an appropriate definition of simultaneously diagonalizable it >>seems like it should be more or less the same. [...] >If A,B are diagonalizable and AB=BA then they are >automalically simultaneously diagonalizable! I missed the hypothesis AB = BA, sorry. >Valeriu ************************ David C. Ullrich === Subject: Applied Mathematics For those of you whose students are asking when are they gonna use this stuff, a real-world application of some deep mathematics. Really real-world, actually came up: Last summer Dave had a major leak. When the plumber fixed it he replaced a length of pipe that had been underground with some pipe lying above ground in the crawlspace under the house. Dave's worried about this freezing, since this length of pipe is going to be much colder than formerly. So he's keeping some water running when it gets cold. He measures a flow of 1.5 cups in 30 seconds. The pipe has an inside diameter of 1.5 cm. There are 6 yards of exposed pipe under the house - how long does a given bit of water remain in the exposed part of the pipe? (Assume 1 yard = 1 meter and 1 quart = 1 liter = 1000 cubic centimeters - the reason for the mixed units is that Dave recalls these rough approximations but doesn't have any idea how many cubic inches there are in a quart.) ************************ David C. Ullrich === Subject: Re: Applied Mathematics > For those of you whose students are asking when > are they gonna use this stuff, a real-world application > of some deep mathematics. Really real-world, actually > came up: > Last summer Dave had a major leak. When the plumber fixed > it he replaced a length of pipe that had been underground > with some pipe lying above ground in the crawlspace under > the house. Dave's worried about this freezing, since this > length of pipe is going to be much colder than formerly. > So he's keeping some water running when it gets cold. > He measures a flow of 1.5 cups in 30 seconds. The pipe > has an inside diameter of 1.5 cm. There are 6 yards of > exposed pipe under the house - how long does a given > bit of water remain in the exposed part of the pipe? > (Assume 1 yard = 1 meter and 1 quart = 1 liter = 1000 > cubic centimeters - the reason for the mixed units > is that Dave recalls these rough approximations but > doesn't have any idea how many cubic inches there > are in a quart.) > ************************ > David C. Ullrich No need for those rough-n-ready approximations any more. Google knows units. Typing the following into the Google search window: 1 quart in cubic inches yields this response: 1 US quart = 57.7500002 cubic inches Dale === Subject: Re: Applied Mathematics === >Subject: Applied Mathematics >Message-id: >For those of you whose students are asking when >are they gonna use this stuff, a real-world application >of some deep mathematics. Really real-world, actually >came up: >Last summer Dave had a major leak. When the plumber fixed >it he replaced a length of pipe that had been underground >with some pipe lying above ground in the crawlspace under >the house. Dave's worried about this freezing, since this >length of pipe is going to be much colder than formerly. >So he's keeping some water running when it gets cold. >He measures a flow of 1.5 cups in 30 seconds. The pipe >has an inside diameter of 1.5 cm. There are 6 yards of >exposed pipe under the house - how long does a given >bit of water remain in the exposed part of the pipe? >(Assume 1 yard = 1 meter and 1 quart = 1 liter = 1000 >cubic centimeters - the reason for the mixed units >is that Dave recalls these rough approximations but >doesn't have any idea how many cubic inches there >are in a quart.) >************************ >David C. Ullrich Go to Home Depot and ask for 6 yards of donkey dick. -- Mensanator Ace of Clubs === Subject: Re: Applied Mathematics > Go to Home Depot and ask for 6 yards of donkey dick. I did and the check out clerk spit in my face. Bob Kolker === Subject: Re: Applied Mathematics >> Go to Home Depot and ask for 6 yards of donkey dick. > I did and the check out clerk spit in my face. Hee-haw, hee-haw, hee-always does that. PH === Subject: Re: Advent calendars === >>Subject: Advent calendars >>Message-id: <41caccb3.7051579@news.tiscali.dk> >>Re: Was the Phaistos disc an Advent calendar? >No, it's a pizza menu. >> Merry Christmas >> Hagen >>http://home.gvdnet.dk/~hagen/phaistos.htm >-- >Mensanator >Ace of Clubs It is the old-fashioned kind made by pixels. Don't eat ! Hagen === Subject: prove that sqtr of 2 is irrational by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBODfhs12814; hi can u guys help me prove that the sqrt of 2 is irrational? === Subject: Re: prove that sqtr of 2 is irrational > hi can u guys help me prove that the sqrt of 2 is irrational? Suppose sqrt(2) is rational. then you can write (p/q)^2=2. Assume p,q are in lowest terms. See if you can get a contradiction. === Subject: Re: prove that sqtr of 2 is irrational >> hi can u guys help me prove that the sqrt of 2 is irrational? > Suppose sqrt(2) is rational. then you can write (p/q)^2=2. Assume p,q > are in lowest terms. See if you can get a contradiction. The last person who did that was eliminated by Pythagoras. Bob Kolker === Subject: Re: prove that sqtr of 2 is irrational > >> hi can u guys help me prove that the sqrt of 2 is irrational? >> > Suppose sqrt(2) is rational. then you can write (p/q)^2=2. Assume p,q > are in lowest terms. See if you can get a contradiction. > The last person who did that was eliminated by Pythagoras. > Bob Kolker The last or the first? === Subject: Re: prove that sqtr of 2 is irrational > >> hi can u guys help me prove that the sqrt of 2 is irrational? >> > Suppose sqrt(2) is rational. then you can write (p/q)^2=2. Assume p,q > are in lowest terms. See if you can get a contradiction. > The last person who did that was eliminated by Pythagoras. > Bob Kolker > The last or the first? Of course it comes down to showing that xx = 2yy has no nonzero solution in integers. The proof is in the Old Testament somewhere, I think. Similar but less familiar: xx = 3(yy + zz) xx = 5(yy + yz + zz) Neither of these has any nonzero solution, even though we have three variables to play with. So sqrt(3) and sqrt(5) are even more irrational than sqrt(2) :) === Subject: Re: prove that sqtr of 2 is irrational > Similar but less familiar: > xx = 3(yy + zz) > xx = 5(yy + yz + zz) > Neither of these has any nonzero solution, even though > we have three variables to play with. So sqrt(3) and > sqrt(5) are even more irrational than sqrt(2) :) x^2 = 2(y^2 + z^2) has solutions (x=2, y=1, z=1 for one). But, unless I have miscalculated, x^2 = 2(y^2 + yz + z^2) does not have solutions. So I don't see what there is about the equation you give that distinguishes 5 from 2. John Robertson === Subject: Re: prove that sqtr of 2 is irrational > Similar but less familiar: > xx = 3(yy + zz) > xx = 5(yy + yz + zz) > Neither of these has any nonzero solution, even though > we have three variables to play with. So sqrt(3) and > sqrt(5) are even more irrational than sqrt(2) :) > x^2 = 2(y^2 + z^2) has solutions (x=2, y=1, z=1 for one). But, unless I have > miscalculated, x^2 = 2(y^2 + yz + z^2) does not have solutions. So I don't see > what there is about the equation you give that distinguishes 5 from 2. > John Robertson You are right, my sqrt(5) claim is no good. I'll try to think of some other quadratic form that distinguishes 5 from 2 :) === Subject: Re: prove that sqtr of 2 is irrational > hi can u guys help me prove that the sqrt of 2 is irrational? >> Suppose sqrt(2) is rational. then you can write (p/q)^2=2. Assume p,q >> are in lowest terms. See if you can get a contradiction. >The last person who did that was eliminated by Pythagoras. Oh, no. *Many* people did that since the _first_ person who did that is alleged to have been eliminated by Pythagoras. Although another version of the story has it that the person eliminated was done in for revealing that the icosahedron has a dual. In other words, if those idiots wanted to keep the dodecahedron a secret, they should have kept the icosahedron secret too! John Savard http://home.ecn.ab.ca/~jsavard/index.html === Subject: Re: prove that sqtr of 2 is irrational |>The last person who did that was eliminated by Pythagoras. | |Oh, no. *Many* people did that since the _first_ person who did that is |alleged to have been eliminated by Pythagoras. Although another version |of the story has it that the person eliminated was done in for revealing |that the icosahedron has a dual. I've read that this is an apocryphal story, very unlikely to be true. Keith Ramsay === Subject: Re: prove that sqtr of 2 is irrational Originator: harris@tcs.inf.tu-dresden.de (Mitchell Harris) >|>The last person who did that was eliminated by Pythagoras. >|Oh, no. *Many* people did that since the _first_ person who did that is >|alleged to have been eliminated by Pythagoras. Although another version >|of the story has it that the person eliminated was done in for revealing >|that the icosahedron has a dual. >I've read that this is an apocryphal story, very unlikely to be true. I've heard that what you say has no basis in fact. Mitch === Subject: CBS for Banach spaces Hi all, Is Cantor-Bernstein-Schroeder true for Banach spaces? IOW let A and B be Banach spaces. A <= B iff there is an *isometric embedding* A->B. Is it true that if A<=B and B<=A then A and B are isometrically isomorphic? And if we relax to topological embeddings/isomorphisms? Counter-examples? G. Rodrigues === Subject: Re: CBS for Banach spaces > Hi all, > Is Cantor-Bernstein-Schroeder true for Banach spaces? IOW let A and B > be Banach spaces. A <= B iff there is an *isometric embedding* A->B. > Is it true that if A<=B and B<=A then A and B are isometrically > isomorphic? And if we relax to topological embeddings/isomorphisms? > Counter-examples? > G. Rodrigues For topological embeddings, I have a feeling that the CBS theorem is true because I remember hearing that all Banach spaces are topologically equivalent to Hilbert space. === Subject: Re: CBS for Banach spaces >> Hi all, >> Is Cantor-Bernstein-Schroeder true for Banach spaces? IOW let A and B >> be Banach spaces. A <= B iff there is an *isometric embedding* A->B. >> Is it true that if A<=B and B<=A then A and B are isometrically >> isomorphic? And if we relax to topological embeddings/isomorphisms? >> Counter-examples? >> G. Rodrigues >For topological embeddings, I have a feeling that the CBS theorem is >true because I remember hearing that all Banach spaces are topologically >equivalent to Hilbert space. They're all homeomorphic, as topological spaces without linear structure, but I don't *think* they're all linearly homeomorphic. It isn't clear to me whether GR means topological embeddings/ isomorphisms to preserve linear structure or not. Lee Rudolph === Subject: Re: CBS for Banach spaces > Hi all, > > Is Cantor-Bernstein-Schroeder true for Banach spaces? IOW let A and B > be Banach spaces. A <= B iff there is an *isometric embedding* A->B. > Is it true that if A<=B and B<=A then A and B are isometrically > isomorphic? And if we relax to topological embeddings/isomorphisms? > Counter-examples? > > G. Rodrigues >>For topological embeddings, I have a feeling that the CBS theorem is >>true because I remember hearing that all Banach spaces are topologically >>equivalent to Hilbert space. >They're all homeomorphic, as topological spaces without linear >structure, but I don't *think* they're all linearly homeomorphic. >It isn't clear to me whether GR means topological embeddings/ >isomorphisms to preserve linear structure or not. By topological isomorphism I mean a linear homeomorphism. By topological embedding I mean an injective continuous (bounded) linear map. Should have added the word linear in the question. G. Rodrigues === Subject: Re: CBS for Banach spaces >>Hi all, >> >>Is Cantor-Bernstein-Schroeder true for Banach spaces? IOW let A and B >>be Banach spaces. A <= B iff there is an *isometric embedding* A->B. >>Is it true that if A<=B and B<=A then A and B are isometrically >>isomorphic? And if we relax to topological embeddings/isomorphisms? >>Counter-examples? >> >>G. Rodrigues >For topological embeddings, I have a feeling that the CBS theorem is >true because I remember hearing that all Banach spaces are topologically >equivalent to Hilbert space. >>They're all homeomorphic, as topological spaces without linear >>structure, but I don't *think* they're all linearly homeomorphic. >>It isn't clear to me whether GR means topological embeddings/ >>isomorphisms to preserve linear structure or not. If you are preserving the linear structure then Banach spaces are definitely not topologically isomorphic. For example, the sequence spaces l_p and l_q are not isomorphic for p not equal to q. While this is true, it does take quite some thinking to come up with a counterexample, and the way I know of comes down to studying to what extent the n-vector parallelogram law fails as n->infinity (so called type and cotype). Actually, the isomporphic structure of Banach spaces is what consumes most of the researchers in this area**. It is a difficult subject, and rather rich, but unfortunately is filled with counterexamples to almost every conceivable conjecture. ** Actually my impression is that recently people are into studying Lipshitz maps between Banach spaces. > By topological isomorphism I mean a linear homeomorphism. By > topological embedding I mean an injective continuous (bounded) linear > map. Should have added the word linear in the question. > G. Rodrigues Then my other post applies, and if you want the isomorphic counterexample, you will need to study the counterexample of Gowers and Maurey. Definitely not straightforward stuff. Stephen === Subject: Re: CBS for Banach spaces > Hi all, > Is Cantor-Bernstein-Schroeder true for Banach spaces? IOW let A and B > be Banach spaces. A <= B iff there is an *isometric embedding* A->B. > Is it true that if A<=B and B<=A then A and B are isometrically > isomorphic? And if we relax to topological embeddings/isomorphisms? > Counter-examples? > G. Rodrigues The question for linear isomorphisms is interesting and difficult. The CSB is true if A is linearly isomorphic to A+A (the direct sum of A with itself), and similarly for B. I think this is due to Pelczinski, and that the short proof can be found, for example, in the book by Joe Diestel on Banach spaces. However if there is no such condition A linearly isomorphic to A+A, the answer is negative. This is related to the counterexample of Gowers and Maurey, and is definitely difficult and deep mathematics. Stephen === Subject: Re: CBS for Banach spaces >> Hi all, >> Is Cantor-Bernstein-Schroeder true for Banach spaces? IOW let A and B >> be Banach spaces. A <= B iff there is an *isometric embedding* A->B. >> Is it true that if A<=B and B<=A then A and B are isometrically >> isomorphic? And if we relax to topological embeddings/isomorphisms? >> Counter-examples? >> G. Rodrigues > The question for linear isomorphisms is interesting and difficult. The > CSB is true if A is linearly isomorphic to A+A (the direct sum of A with > itself), and similarly for B. I think this is due to Pelczinski, and > that the short proof can be found, for example, in the book by Joe > Diestel on Banach spaces. > However if there is no such condition A linearly isomorphic to A+A, > the answer is negative. This is related to the counterexample of Gowers > and Maurey, and is definitely difficult and deep mathematics. > Stephen OK, I got this wrong. Both results cited above are concerned with the following version of CBS for Banach spaces. If A and B are Banach spaces such that A embeds complementedly into B and vice versa, then is A isomorphic to B? We say that A embeds complementedly into B is B is (linearly and topologically) isomorphic to A+C (here + means direct sum). THe counterexample when we don't have the complementedly might be L_1 (i.e. L_1(0,1)) and L_1+l_2, since l_2 embeds into L_1 via sums of independent gaussian random variables. Presumably L_1+l_2 is not isomorphic to L_1 - perhaps this follows because perhaps L_1 has no complmented subspaces isomorphic to l_2, but I am not expert enough to say for sure. The Pelczinski argument is rather nice. So A=B+C, B=A+D and A=A+A and B=B+B. A=B+C=B+B+C=A+D+B+C=A+D+A=A+A+D=A+D=B. === Subject: Re: CBS for Banach spaces > Is Cantor-Bernstein-Schroeder true for Banach spaces? IOW let A and B > be Banach spaces. A <= B iff there is an *isometric embedding* A->B. > Is it true that if A<=B and B<=A then A and B are isometrically > isomorphic? And if we relax to topological embeddings/isomorphisms? > Counter-examples? > G. Rodrigues For topological spaces CBS does not hold. For a counterexample take the real line R and R* = R{0}. jhn === Subject: Re: CBS for Banach spaces >>Is Cantor-Bernstein-Schroeder true for Banach spaces? IOW let A and B >>be Banach spaces. A <= B iff there is an *isometric embedding* A->B. >>Is it true that if A<=B and B<=A then A and B are isometrically >>isomorphic? And if we relax to topological embeddings/isomorphisms? >>Counter-examples? > For topological spaces CBS does not hold. > For a counterexample take the real line R and R* = R{0}. I think that the OP was not writing about topological embeddings of topological spaces, but about topological embeddings of Banach spaces. Jose Carlos Santos === Subject: Re: .99999... still=/= 1 Isn't the real way: 10x = 9.999... x = .9999... 10x - x = 9x = 9 x = 1 This is the traditional way, at least. Poly-poly man === Subject: Re: .99999... still=/= 1 > Isn't the real way: > 10x = 9.999... > x = .9999... > 10x - x = 9x = 9 > x = 1 Many steps have been left out. This is a non-rigorous non-proof as it stands. Bob Kolker === Subject: .99999... still=/= 1 Okay, multiply that by a reeaaly big number. You would get numbers that are a few off being EQUAL! I know this goes against what I said before, but they cant be equal!! === Subject: Re: .99999... still=/= 1 - explanation ?! >Isn't the real way: >10x = 9.999... >x = .9999... >10x - x = 9x = 9 >x = 1 >This is the traditional way, at least. >Poly-poly man Absolutely correct. It is standard high school and college mathematics. In the same way one proves in general that 1 + r + rr + rrr + .... = 1 / (1 - r) provided the series is absolutely convergent, i.e. provided |r| < 1 . Ordinary arithmetic extends to absolutely convergent infinite series. I would like to repeat a posting of several months ago about the ongoing smoldering peat-moor fire on the subjects 0.999999... = 1, 0.999999 =/= 1 and the like. It may be an explanation on why 0.999999... baffles people time and again! As long as I am surfing the world-wide web and the newsgroups for mathematical stuff I have been intrigued by the phenomenon Is 0.999999.... = 1?. I got the impression that it is a recurring phenomenon. It seems to coincide more or less with the start of the education season. In my opinion 0.999999..... is the most elusive representation of 1, even more so than 1 = exp(2.pi.i). Let me explain. 0.9999... is a fabricated number. It cannot be obtained in any way as the outcome of a long division carried out in the usual manner. As far as I know nobody before noticed this. This may be the reason why it pops up time and again in newsgroups and similar forums. But you can perform long division in a different way as follows: Consider long division A/B as a process of exhaustion in the style of Archimedes, i.e. take away from the dividend A as many times of B as possible. If nothing is left then you are done; otherwise proceed with taking away from the remainder as many parts B/10 as possible, etc. Now look at A/B = 1/1, but consider A as 10 * 0.1 instead of 1 * 1, and take away nine parts B/10 = 0.1 instead of all ten parts. Write down 0.9 in the quotient field to record that you took away nine parts of size 0.1 Shift down a factor of 10 and treat the remainder like you treated the original dividend previously. The quotient becomes 0.99 and the new remainder is 0.01; etc. Only two things really matter in the process of long division: (1) maintaining the relation A = Qn * B + Rn where Qn and Rn are the quotient and the remainder at the n-th stage of the process; (2) getting Rn eventually equal to zero, or at least getting Rn arbitrarily close to zero. I hope that it is clear from the above that 0.9999... has a sensible meaning and can be equal only to unity. I have no illusion that this note will spoil the repetitive character of the phenomenon 0.999999...... = 1?. === Subject: Re: .99999... still=/= 1 This might have been said before, but why not just say duhhhh...... 1 1 1 - + - + - = 1 3 3 3 1 - = .33333... 3 === Subject: Re: .99999... still=/= 1 >This might have been said before, but why not just say duhhhh...... >1 1 1 >- + - + - = 1 >3 3 3 > - = .33333... Because, duh --> duh --> duh --> goes to duh 1/3 = 1/3 1/3 =/= .333... 1/3 ~ .333..., because you can't precisely go back to 1/3 from .333... . This is my theory. It's called, Mathematical Entropy. There is a mathematical loss in the process of division from 1/3 to .333... . If you look into reality. Entropy is a fact of life. But has it ever been discovered mathematically within the numbers themselves? No. I think I discovered this. Mathematical Entropy (Discovery by Smart1234) Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 > (Reference AOL dictionary) > Main Entry: real number > Function: noun > : one of the numbers that have no imaginary parts and comprise the > rationals and the irrationals. >>Dictionary definitions describe how a term is used. >>Mathematical definitions stipulate what a term means. >>The above definition does not stipulate what real number means, >>but merely describes how the term is used. >>Dedekind is credited with giving the first mathematical definition >>of the real numbers. He (essentially) defined a real number to be >>a set S of rational numbers such that >>1) S is neither empty nor all the rationals, >>2) each element of S is less than any element not in S, and >>3) there is no greatest element of S. >>There is a canonical mapping from the rational numbers to the >>real numbers: the real number corresponding to the rational >>number q is set of rational numbers less than q. >>Similarly, a string such as 3.14... is defined to represent >>this real number: the union of the set of rational numbers >>less than 3 and the set of rational numbers less than 3.1 and >>the set of rational numbers less than 3.14 and ... >>According to these definitions: >>* the real number denoted 1 = the set of rational numbers >>less than (the rational number) 1, and >>* the real number denoted 0.99999... = the union from n=1 to >>infinity of the set of rational numbers less than 1 - 10^-n. >>Therefore the statement 0.99999... != 1 *means* that the two >>sets described above are not identical. >>If you want to argue that 0.99999... != 1, you have to show that >>these sets are different. For example, you could exhibit a >>rational number that belongs to one, but not the other. >>Or, you could just reject everything I'm saying. Why should you >>accept Dedekind's definition of real numbers? It's weird. Your >>idea seems better to you. It expresses the true nature of real >>numbers. Etc. >>But you can't have it both ways. You can't argue that what you >>mean by real number is equivalent to what Dedekind meant (and >>hence equivalent to what all mathematicians mean), and yet argue >>that what 0.99999... != 1 means is not equivalent to what I've >>said above. >>Unfortunately, it takes a certain amount of mathematical maturity >>to appreciate when a concept is well-defined, or what constitutes >>a proof. The fact that you would proffer the above dictionary >>definition of real numbers in support of your arguments indicates >>that you don't have this maturity yet. >>Here's an exercise for you: show that the two sets marked with >>* above are, in fact, identical. It's never too late to learn >>something (assuming you're not Jms Hrrs). >Reference ( AOL dictionary) >Main Entry: irrational number >Function: noun >: a number that can be expressed as an infinite decimal with no set of >consecutive digits repeating itself indefinitely and that cannot be expressed >as the quotient of two integers >And again, >Main Entry: real number >Function: noun >: one of the numbers that have no imaginary parts and comprise the rationals >and the irrationals. > I'm trying to keep things as simple as possible. So the AOL dictionary is >sufficient. >.999... isn't an irrational number because, quoting from what an irrational >number can not be, ....of consecutive digits repeating itself indefinitely, >.999... isn't a real number. The number 1 is a real number. > A real number can't equal something that isn't a real number. > So from another point of view, >.999... =/= 1 For even an irrational number to be expressed as a real rational number, you have to be able to type in all the digits to the right of a decimal number in a fraction form. Try 10 significant digits of .999... . 9999999999/10000000000 We seem to be able to make .999... almost look like a real number here but now try .999... . 9999999 --> oo ------------ 10000000 --> oo You just can't do it. .999... isn't a real number. It's in the class of surreal and hyperreal numbers. You may say but you can make it converge to a real number, but a number that isn't real, can't equal a real number. Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 I think people should also realize that, not only does .999... =/= 1, but any series, which includes real numbers, with ... added to the right of a decimal number does not precisely equal that number. Like for example, sqrt(2) =/= 1.41421... sqrt(2) ~ 1.41421... where ~ means approximately equal to. The number of significant figures used determines the level of accuracy or degree of error, etc... . This is proven in reality. So it must be true in math. . Can a bird = a cat ? no In fact, can bird#1 = bird#2? No They may have similarities. But every creature is unique, including people. But what about this? dummy#1 =/= dummy#2 There could be an exception to the rule here. ( hhehehehe) Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 Let's look at .999... = 1 or .333... = 1/3, with respect to entropy. Let's start with, 1/3 now perform the division. 1/3 = .333... Now try to get back precisely to 1/3 from .333... . 3 * .333... = .999... You can't. Mathematical Entropy, ( a word coined after Smart1234), occurs with math itself. In reality it is proven that entropy exists. So it must also be true that way in math, for math to be correct. Reality and Math MUST be equivalent. If they are not, something must be incorrect. But if keep 1/3 in it's original form, then 3 * 1/3 = 1 Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 Another perspective of .999... and 1, with respect to time moving toward 1. Can .999... reach 1 in time. It has been shown that there appears to be a space separating .999... | | 1. But how much time would it take for .999... to reach 1. In reality how long would a computer program have to run to go from .999... to 1? Let's see. f(t) = t^1-1/10^t d f(t) = 1 + 10^-t LOG(10) If we spend oo time reaching 1, then: 1 + 10^-oo = 1 But if we start at 1 it doesn't take any time at all to reach 1. f(t) = t^1 d f(t) = 1 Let's take a closer look at this: d f(t) = 1 + 10^-t LOG(10) at t = 1 = 1 + .1 at t = 2 = 1 + .01 at t = oo -1 = 1 + .000000...1 It appears we have to add extra energy or extra numbers, for .999... to reach 1 then at oo = 1 So .999... still=/= 1, unless a person can create or add extra energy to restore .999... to 1. or restore, .333... back to 1/3. So Mathematical Entropy can be reversed with Created Energy. So what can restore life back to a dying person? Extra created life energy. Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 --> Mathematical Entropy --> ... > Another perspective of .999... and 1, with respect to time moving toward > Can .999... reach 1 in time. It has been shown that there appears to be a >space separating .999... | | 1. > But how much time would it take for .999... to reach 1. In reality how long >would a computer program have to run to go from .999... to 1? Let's see. >f(t) = t^1-1/10^t >d f(t) = 1 + 10^-t LOG(10) > If we spend oo time reaching 1, then: >1 + 10^-oo = 1 >But if we start at 1 it doesn't take any time at all to reach 1. >f(t) = t^1 >d f(t) = 1 >Let's take a closer look at this: > d f(t) = 1 + 10^-t LOG(10) Correction: Even in this form spending eternal time, you are still only approaching 1 from .999... . BUT, you can't get any closer to 1 than eternal time moving toward 1. The only way to get to 1 is to be 1 from the start. ( Spiritual view) You are 1. There is no one else like you. Others can't be you. They can only approach you. >at t = 1 > = 1 + .1 >at t = 2 > = 1 + .01 >at t = oo -1 > = 1 + .000000...1 > It appears we have to add extra energy or extra numbers, for .999... to >reach 1 >then at oo > = 1 > So .999... still=/= 1, unless a person can create or add extra energy to >restore .999... to 1. or restore, .333... back to 1/3. > So Mathematical Entropy can be reversed with Created Energy. > So what can restore life back to a dying person? Extra created life energy. Mathematical Entropy can be very closely reversed by an on going process of creation, or added energy to a system, to help maintain the balance. Can perpetual motion be maintained? Mathematical Entropy seems to appear to preven this. But, with eternal time, the motion can be perpetual. The upper mean life span of a proton is >10^30 years. This doesn't mean that the proton will not continue to be relatively perpetual in time. Notice this is the upper limit. This limit can go from >10^30 > 10^oo, if the balance is maintained perfectly. There can be no loss in the movement. The Smart Model or ( The Creation Model) has what appears to be perpetual motion in it's universal unified structure. If there is even one iota of unbalance, this could change the perpetual state of the universe by, ( Non-standard analysis) n-->oo - 1 9/10^n --> 90/10^oo This shows that entropy would still exist from just 1 digit away from infinity. How can this balance remain which makes universal perpetual motion? All people and being must agree to exist as 1 in their own world, without disturbing anyone else. As so as one tries to go again this balance, death are gradual death appears to occur. Entropy is a type of death. A star dies, when the entropy state of the star overcomes it. But through a new creation process, a new star can be born to replace it. This is another way to maintain the perpetual state movement of the universe. We do observe this in reality. But The Smart Model goes even further. Eventually the life/death cycle can end, leaving only eternal life of stars and people. The Smart Model has already observed in it's theories that massive stars can cause fusion states that are set in such a way they the star will never die or burn out. As the universe gets larger, growing in eternal time, TRUE continuous perpetual motion will finally be reached. ( Spiritual View) There will no longer be death and suffering, for human life. The life of stars will continue eternally. Paradise and Heaven can finally be reached forever. The Creation Model, was in the beginning, is now, and ever shall be. People can one day be creators too, like THE CREATOR, and make their own universe, and live happily ever after. --------------------------------------------------------- A Note: Mathematical Entropy (Discovery by Smart1234) Universal Perpetual Motion ( Discovery by Smart 1234) Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 > > reference LINK : Math definition for above quote of irrational number. >>I asked you to define an unreal number, not an irrational number. The use of the word unreal was to imply, that .999... isn't a real number. >>Bob Kolker > Oh you try to change the subject. You fail to admit your mistake about the >math definition of an irrational number? Think about it then. Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 > >>could > reach the speed of light and cause .999... = 1, which would make, >>This has nothing to do with dividing by zero. Besides there is only a >>finite amount of energy in the entire physical cosmos. So the upperbound >>Bob Kolker > Mathematics can lead a person to fairy tale land. It's important to try >your >best to see what science shows with experimental evidence, THEN math can be >applied to it. We can see in physical reality that .999... can't = 1 >because >it can't reach it. This is proven in reality. > I noticed you snipped the part about the computer program never reaching 1 >from .999... , but anyway we can see in reality, >1) the tooth fairy doesn't exist >2) the fairy godmother doesn't exist >and >3) .999... = 1 > Math trickery and math illusions was used in the development of the >Periodic Table of Elements, too. They made believe that electron orbitals >existed and then made a math story of how it could actually work. But reality >is beginning to show us with real atomic images that electrons don't show >orbitals but intelligence logic structures. The Smart Model predicted this >about 10 years before they knew it. > I have shown you repeatedly ..., that everything even in math, and in >physical reality shows ust that, >.999... =/= 1 > If you want to believe .999... = 1, it's up to you, but it doesn't. > You may ask how can light reach >3.0 X 10^8 m/sec when matter can't. This is because photons start at a >unified >state or oneness, of this amount of energy. It doens't start with .999... and >then reaches 1. It is 1, that is 1 with itself at that energy state, to >start >with. > Can someone else be you? No, because you are 1. You are you. Others may try >to reach you .999... ---> 1 you, but you will always be unique, and only you. >An exact clone of you can never be made, because .999... can't reach 1. You >can >make close clones of something ( .999...), but not the exact clone, 1. No one has refuted this showing further proof .999... =/= 1 in reality. A perfect clone can't be made. If it could, .999... = 1. Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 > > You may ask how can light reach > 3.0 X 10^8 m/sec when matter can't >>do photons move at light speed (in vacuo), they cannot move at any other >>speed. > So, .999... can't apply to photons. But can apply to mass. >>energy will take it to light speed. There is only a finite amount of >>energy in the kosmos so it is impossible for any massive body to move at >>light speed. >>Bob Kolker So, mass in reality can reach the speed of light, if it did, .999... would have to equal 1. No one has refuted that reality shows us that, .999... =/= 1 Further proof write a computer program with .999... and see if it reaches 1. So far some one tried on another post and this hasn't been refuted. So again reality shows us that, .999... =/= 1 If it's false in reality, it must be false in math. And don't give me this bull that a derivate goes to the limits of infinity so it can be true in reality. A computer program can be write using various methods to calculate derivatives of functions. So the derivative in proven in reality, so it must be true in math. Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 >>In sci.math, S. Enterprize Company >> >>if there is a difference between 0.999... and 1, then what is that >>difference? >> >>is the difference 0.000...(infinity)...1 ? because thats not possible >> >>x = 0.999... >> >>10x = 9.999... >>- x = 0.999... >>--------------------- >>9x = 9 > Nope, > 10 x = 9 > x = .9 >>If you're going to refute it at least do it properly. >>10x = 9.999... >> x = .999... >>10x - x = 8.999... >> >>9x/9 = 9/9 >> >>x = 1, x=0.999..., 1=0.999.... >> > 9/9 = 1 not .999... > If 9/9 = .999... > then 8/8 = .999... >>And it does, in base 11. :-) >>[.sigsnip] >>-- >>#191, ewill3@earthlink.net >>It's still legal to go .sigless. > You use equations to equate real numbers, not surreal or hyperreal numbers. >These must be evaluated independently. > I can place i in an equation and make it real, but it isn't real alone. >Your style of proof: > x = i > a = x^2 > a = -1 > So i is a real number. No one has refuted this, so it must be correct. Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 > > It's not rational or irrational. >>Contradiction. It violates the law of the excluded middle. >>Bob Kolker > What law is that? > .999... is in a different class of numbers all it's own. >Is this pi or a real number? >3.14159999999999999999... No one has refuted this so it must be correct. Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 >> >> >> > What is { | } ? = 0 >> >>You are confalting surreals with hyperreals. In short, you do not know >>what you are talking about. >> >>Bob Kolker > > > A Surreal Number can have these similar two forms, > > 1) Superreal > or > 2) Hyperreal. > > http://en.wikipedia.org/wiki/Surreal_number >>Learn to read. Both the hyperreals and the surreals cosntitute ordered >>non-archimedean fields. They are not the same. They are not constructed >>in the same way. By the way, do you know what an ultri-filter and an >>ultra-product are? >>Bob Kolker >Hyperreal Number >--------------------------- > Hyperreal numbers are an extension of the real numbers to include certain >classes of infinite and infinitesimal numbers. A hyperreal number x is said >be finite iff |x| < n for some integer n. x is said to be infinitesimal iff >|x| >< 1/n for all integers n. >Surreal Number >------------------------ > The most natural collection of numbers which includes both the real >numbers >and the infinite ordinal numbers of Georg Cantor. They were invented by John >H. Conway in 1969. Every real number is surrounded by surreals, which are >closer to it than any real number. Knuth (1974) describes the surreal numbers >in a work of fiction. >The surreal numbers are written using the notation {a|b}, where , { | } = 0. >{ 0| } is the simplest number greater than 0, { | 1} = 2 is the simplest >number >greater than 1, etc. Similarly, { | 1} = -1 is the simplest number less than >0, etc. However, 2 can also be represented by { 1 | 3}, { 3/2 | 4}, { 1| >omega >} , etc. >Surreal Number - another quote about surreal number. > [...] surreals are algebraically similiar to superreal numbers and >hyperreal numbers. > When I stated Surreal/Hyperreal Numbers I was referring to infinitesimal >numbers that are less than integers n. where, |x| < 1/n. > In this category, > a = .0000...(999...) > b = .000....1 > a < b > .000... (.999...) < .000...1 > { a | b } represents a space in this case { | } that separates a from b. >This >space is what I am calling something that isn't a rational or irrational >number. It is something that can only be shown as 0 and THEN the next number >appears. I also proposed that this space could be represented as time >dependent >or a funtion of time. This time is relative. The more time you spend there >moving toward the next number the closer you get to the next number. > YOU need to learn to read. I had to not only show you the LINK but I had to >type it out so others would see YOU don't know what you're talking about. > And I already told you what an ultra-filter is by an example of people like >you. An ultra-filter is needed to keep the noise out so you can see the true >signal. Ultra-filters are used in engineering. >http://mathworld.wolfram.com/Ultrafilter.html >In signal processing, a filter is a function or procedure which removes >unwanted parts of a signal. The concept of filtering and filter functions is >particularly useful in engineering. One particularly elegant method of >filtering Fourier transforms a signal into frequency space, performs the >filtering operation there, then transforms back into the original space >(Press >et al. 1992). Since no one has refuted this we can say, .999... < 1 So, .999... =/= 1 Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 >In sci.math, S. Enterprize Company > >In sci.math, robert j. kolker > >: >> >> >> >> > What is { | } ? = 0 >> >> You are confalting surreals with hyperreals. In short, you do not know >> what you are talking about. >> >> Bob Kolker >> > >How does Stirling's factorial approximation even *get* into a >discussion about .999... = 1? > >My brain hurts. > >-- >#191, ewill3@earthlink.net -- insert random painkiller here >It's still legal to go .sigless. > >> >> The Gamma Function and the Stirling Function are similar functions >> used in factorials. >As I recall, the one is an approximation of the other. >How factorials get into this, I don't know; the series >under discussion is a geometric series. If one uses >factorials one might get Euler's number, e: >e = 1/0! + 1/1! + 1/2! + ... + 1/n! + ... >and the related function, >exp(x) = e^x = 1/0! + x/1! + x^2/2! + ... + x^n/n! + ... >The gamma function can be defined as >Gamma(z) = integral(t = 0 to +oo) (t^(z-1) * e^(-t) dt) >and Gamma(n) = (n-1)! for integer n > 0. >Stirling's approximation has >ln n! =~ n * ln n - n; >presumably there are better approximations available, >e.g. Well's: >n! =~ n^n * e^(-n) * sqrt(2 * pi * n) =~ sqrt(2*pi) * n^(n+0.5) * e^(-n) . >http://mathworld.wolfram.com/GammaFunction.html >http://mathworld.wolfram.com/StirlingsApproximation.html >> When you do a multi-dimensional analysis of the nth term >Multi-dimensional analysis on a constant series? >s_n = 9 * 10^(-n). S_n = sum(i=1,n) s_n = 1 - 10^(-n). >One has at most one dimension -- namely, the term index. Where's >the other dimensions? >> of the series for .999..., to see what occurrs infinitesimally >> between .999... and 1, the solutions show, gamma functions as >> part of the solutions with, >> >> lim --> DIM oo >> 9/10^n --> >> >> At DIM oo >> >> The surreal/hyperreal space shows something that is too complex >> to even show on this NG. But it is basicaly something like this, >> >> 9 * 1^oo * gamma ( 1 + 9/10^oo) >> ------------------------------------------------- >> 10^10^oo >Assuming you meant >G = lim(n -> +oo) (9 * 10^(-n) * Gamma(1 - 9/10^(-n)) / (10^10^(-n))) >(where *did* all that come from?!) >where G is primarily for my own convenience, that reduces to >G = lim(n -> +oo) (9/10 * 10^(-10^(-n)-n) * Gamma(1 - 9/10^(-n))) = 0. >Not horribly interesting. >> >> What I did was use the Stirling Function which is similar to the gamma >> function to observe what happens with .999... factorial as compared to 1 >> factorial. >Oh, so you want to replace >G = lim(n -> +oo) (9 * 10^(-n) * Gamma(1 - 9/10^(-n)) / (10^10^(-n))) >with >G' = lim(n -> +oo) (9 * 10^(-n) * exp((1 - 9/10^(-n)) * log(1 - 9/10^(-n)) > - (1 - 9/10^(-n))) / (10^10^(-n))) ? >Suit yourself. >G' = lim(n -> +oo) (9 * 10^(-n) * exp((1 - 9/10^(-n)) * log(1 - 9/10^(-n)) > - (1 - 9/10^(-n))) / (10^10^(-n))) > = lim(n -> +oo) (9/10 * 10^(10^(-n)-n) * exp((1 - 9/10^(-n)) > * log(1 - 9/10^(-n)) - (1 - 9/10^(-n)))) > = 0 again. >> >> I used MathCAD Profession to show the results. What occurs is >> (.999...)! --> 0 whereas 1! --> 1 >You do know why they call it Stirling's Approximation, I hope. >BTW, exp(1 * ln 1 - 1) = 1/e. That's not even close to Gamma(1) = 0! = 1. >[rest snipped; it gets more ridiculous from there] > Yes, you do get more ridiculous from there, because I show that (.999...)! = > and 1! = 1 > And I even told you to check it on your own calculator. .999999.... --> 0 > when you plug it in the factorial function, not 1. Then type in 1! in the > factorial function and you get 1. > I even used the factorial function in expanded form on MathCAD using the > lim (.999...)! = 0 > n-->oo > This proves by the factorial function, > .999... =/= 1 > There are even other references that clearly show that, > .999... < 1 > So, > .999... =/= 1 >-- >#191, ewill3@earthlink.net >It's still legal to go .sigless. > Smart's Alt. Physics News Group > http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 > S. Enterprize (Science Journal) > http://smart1234.s-enterprize.com/ I started reading this thread as I was waiting for something to print off. I started skipping around when I found ignoramus and subhuman entering the messages. This is one of my favorite topics but I have found it is difficult to change someone's mind once they have decided .999999...and 1 are not equal. Since I have not read through ALL the posts I am sure some of my arguments have already been presented. 1. .9999... = .9 + .09 + .009 + .0009 +... and this is an infinite geometric series with first term .9 and common ratio .1. By a well-known theorem on infinite geometric series, this series converges and the sum is .9/(1 - .1) = .9/.9 = 1. 2. Let x = .999999... Then 10x = 9.9999..... Subtract these two equations to get 9x = 9 which gives x = 1. (This one might be a little shaky since it requires the distributive law to apply to infinite sums.) 3. 1/3 = .3333..... Multiply both sides by 3 to get 1 = .999999.... 4. Lemma: If the average (mean) of two numbers equals one of the numbers, then the two numbers are equal. The proof is left to the reader. Then find the mean of 1 and .9999999. Refer to the lemma. 5. For people who think 1 and .99999... are not equal, I am sure all of them believe 1 is the larger of the two. Produce a number which is between those two numbers. If you can't, doesn't that make them equal? I have seen lots of loose talk dealing with limits and sequences of partial sums and the like. It all goes back to definitions. Change the definitions and you might change the results. The definitions in the books I have read and learned from and taught from would all lead me to conclude that 1 and .9......are equal Robert A. Meyer Omaha North High School Omaha, Nebraska === Subject: Re: .99999... still=/= 1 >>In sci.math, S. Enterprize Company >> >>In sci.math, robert j. kolker >> >>: >>> >>> >>> >>> >> What is { | } ? = 0 >>> >>> You are confalting surreals with hyperreals. In short, you do >not know >>> what you are talking about. >>> >>> Bob Kolker >>> >> >>How does Stirling's factorial approximation even *get* into a >>discussion about .999... = 1? >> >>My brain hurts. >> >>-- >>#191, ewill3@earthlink.net -- insert random painkiller here >>It's still legal to go .sigless. >> >>> >>> The Gamma Function and the Stirling Function are similar >functions >>> used in factorials. >> >>As I recall, the one is an approximation of the other. >>How factorials get into this, I don't know; the series >>under discussion is a geometric series. If one uses >>factorials one might get Euler's number, e: >> >>e = 1/0! + 1/1! + 1/2! + ... + 1/n! + ... >> >>and the related function, >> >>exp(x) = e^x = 1/0! + x/1! + x^2/2! + ... + x^n/n! + ... >> >>The gamma function can be defined as >> >>Gamma(z) = integral(t = 0 to +oo) (t^(z-1) * e^(-t) dt) >> >>and Gamma(n) = (n-1)! for integer n > 0. >> >>Stirling's approximation has >> >>ln n! =~ n * ln n - n; >> >>presumably there are better approximations available, >>e.g. Well's: >> >>n! =~ n^n * e^(-n) * sqrt(2 * pi * n) =~ sqrt(2*pi) * n^(n+0.5) * >e^(-n) . >> >>http://mathworld.wolfram.com/GammaFunction.html >>http://mathworld.wolfram.com/StirlingsApproximation.html >> >>> When you do a multi-dimensional analysis of the nth term >> >>Multi-dimensional analysis on a constant series? >> >>s_n = 9 * 10^(-n). S_n = sum(i=1,n) s_n = 1 - 10^(-n). >> >>One has at most one dimension -- namely, the term index. Where's >>the other dimensions? >> >>> of the series for .999..., to see what occurrs infinitesimally >>> between .999... and 1, the solutions show, gamma functions as >>> part of the solutions with, >>> >>> lim --> DIM oo >>> 9/10^n --> >>> >>> At DIM oo >>> >>> The surreal/hyperreal space shows something that is too complex >>> to even show on this NG. But it is basicaly something like this, >>> >>> 9 * 1^oo * gamma ( 1 + 9/10^oo) >>> ------------------------------------------------- >>> 10^10^oo >> >>Assuming you meant >> >>G = lim(n -> +oo) (9 * 10^(-n) * Gamma(1 - 9/10^(-n)) / >(10^10^(-n))) >> >>(where *did* all that come from?!) >> >>where G is primarily for my own convenience, that reduces to >> >>G = lim(n -> +oo) (9/10 * 10^(-10^(-n)-n) * Gamma(1 - 9/10^(-n))) = >> >>Not horribly interesting. >> >>> >>> What I did was use the Stirling Function which is similar to the >gamma >>> function to observe what happens with .999... factorial as >compared to 1 >>> factorial. >> >>Oh, so you want to replace >> >>G = lim(n -> +oo) (9 * 10^(-n) * Gamma(1 - 9/10^(-n)) / >(10^10^(-n))) >> >>with >> >>G' = lim(n -> +oo) (9 * 10^(-n) * exp((1 - 9/10^(-n)) * log(1 - >9/10^(-n)) >> - (1 - 9/10^(-n))) / (10^10^(-n))) ? >> >>Suit yourself. >> >>G' = lim(n -> +oo) (9 * 10^(-n) * exp((1 - 9/10^(-n)) * log(1 - >9/10^(-n)) >> - (1 - 9/10^(-n))) / (10^10^(-n))) >> = lim(n -> +oo) (9/10 * 10^(10^(-n)-n) * exp((1 - 9/10^(-n)) >> * log(1 - 9/10^(-n)) - (1 - 9/10^(-n)))) >> = 0 again. >> >> >>> >>> I used MathCAD Profession to show the results. What occurs is >>> (.999...)! --> 0 whereas 1! --> 1 >> >>You do know why they call it Stirling's Approximation, I hope. >> >>BTW, exp(1 * ln 1 - 1) = 1/e. That's not even close to Gamma(1) = >0! = 1. >> >>[rest snipped; it gets more ridiculous from there] >> Yes, you do get more ridiculous from there, because I show that >(.999...)! = >> 0 >> and 1! = 1 >> And I even told you to check it on your own calculator. .999999.... >--> 0 >> when you plug it in the factorial function, not 1. Then type in 1! in >the >> factorial function and you get 1. >> I even used the factorial function in expanded form on MathCAD >using the >> lim (.999...)! = 0 >> n-->oo >> This proves by the factorial function, >> .999... =/= 1 >> There are even other references that clearly show that, >> .999... < 1 >> So, >> .999... =/= 1 >> . >> >>-- >>#191, ewill3@earthlink.net >>It's still legal to go .sigless. >> Smart's Alt. Physics News Group >> http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 >> S. Enterprize (Science Journal) >> http://smart1234.s-enterprize.com/ >I started reading this thread as I was waiting for something to print >off. I started skipping around when I found ignoramus and subhuman >entering the messages. This is one of my favorite topics but I have >found it is difficult to change someone's mind once they have decided >.999999...and 1 are not equal. Since I have not read through ALL the >posts I am sure some of my arguments have already been presented. >1. .9999... = .9 + .09 + .009 + .0009 +... and this is an infinite >geometric series with first term .9 and common ratio .1. By a >well-known theorem on infinite geometric series, this series converges >and the sum is .9/(1 - .1) = .9/.9 = 1. Convergence doesn't mean equality. The total sum .999... isn't .9/(1 - .1). .8 / ( 1 - .2 ) = .8/.8 = 1 Does this mean .8 = 1 ? No. >2. Let x = .999999... Then 10x = 9.9999..... Subtract these two >equations to get 9x = 9 which gives x = 1. (This one might be a little >shaky since it requires the distributive law to apply to infinite >sums.) And it doesn't apply to equality of the infinite sums. >3. 1/3 = .3333..... Multiply both sides by 3 to get 1 = .999999.... Nope, you can divide 1/3 and get .333..., but the reverse doesn't return precisely back. He even show it as .999... . .999... =/= 1 >4. Lemma: If the average (mean) of two numbers equals one of the >numbers, then the two numbers are equal. The proof is left to the >reader. >Then find the mean of 1 and .9999999. Refer to the lemma. Nope, m = .999... = x1 x2 = 1 The average mean isn't 1. (.999... + 1)/2 = (1.999...)/2 >5. For people who think 1 and .99999... are not equal, I am sure all >of them believe 1 is the larger of the two. Produce a number which is >between those two numbers. If you can't, doesn't that make them equal? No, it makes it another class of numbers like surreal and hyprereal.. { 1 | 10 } 1 < 5 < 10 Does this mean 1 = 10? no 1< 10 >I have seen lots of loose talk dealing with limits and sequences of >partial sums and the like. It all goes back to definitions. Change >the definitions and you might change the results. The definitions in >the books I have read and learned from and taught from would all lead >me to conclude that 1 and .9......are equal Which is incorrect. That is why the debate is here. In reality, .999... is never reaches 1. Proof write a computer program and see if it does. If it is false in reality. It must be false in math. >Robert A. Meyer >Omaha North High School >Omaha, Nebraska Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 In sci.math, robb566@hotmail.com >>In sci.math, S. Enterprize Company >> >>In sci.math, robert j. kolker >> >>: >>> >>> >>> >>> >> What is { | } ? = 0 >>> >>> You are confalting surreals with hyperreals. In short, you do > not know >>> what you are talking about. >>> >>> Bob Kolker >>> >> >>How does Stirling's factorial approximation even *get* into a >>discussion about .999... = 1? >> >>My brain hurts. >> >>-- >>#191, ewill3@earthlink.net -- insert random painkiller here >>It's still legal to go .sigless. >> >>> >>> The Gamma Function and the Stirling Function are similar > functions >>> used in factorials. >> >>As I recall, the one is an approximation of the other. >>How factorials get into this, I don't know; the series >>under discussion is a geometric series. If one uses >>factorials one might get Euler's number, e: >> >>e = 1/0! + 1/1! + 1/2! + ... + 1/n! + ... >> >>and the related function, >> >>exp(x) = e^x = 1/0! + x/1! + x^2/2! + ... + x^n/n! + ... >> >>The gamma function can be defined as >> >>Gamma(z) = integral(t = 0 to +oo) (t^(z-1) * e^(-t) dt) >> >>and Gamma(n) = (n-1)! for integer n > 0. >> >>Stirling's approximation has >> >>ln n! =~ n * ln n - n; >> >>presumably there are better approximations available, >>e.g. Well's: >> >>n! =~ n^n * e^(-n) * sqrt(2 * pi * n) =~ sqrt(2*pi) * n^(n+0.5) * > e^(-n) . >> >>http://mathworld.wolfram.com/GammaFunction.html >>http://mathworld.wolfram.com/StirlingsApproximation.html >> >>> When you do a multi-dimensional analysis of the nth term >> >>Multi-dimensional analysis on a constant series? >> >>s_n = 9 * 10^(-n). S_n = sum(i=1,n) s_n = 1 - 10^(-n). >> >>One has at most one dimension -- namely, the term index. Where's >>the other dimensions? >> >>> of the series for .999..., to see what occurrs infinitesimally >>> between .999... and 1, the solutions show, gamma functions as >>> part of the solutions with, >>> >>> lim --> DIM oo >>> 9/10^n --> >>> >>> At DIM oo >>> >>> The surreal/hyperreal space shows something that is too complex >>> to even show on this NG. But it is basicaly something like this, >>> >>> 9 * 1^oo * gamma ( 1 + 9/10^oo) >>> ------------------------------------------------- >>> 10^10^oo >> >>Assuming you meant >> >>G = lim(n -> +oo) (9 * 10^(-n) * Gamma(1 - 9/10^(-n)) / > (10^10^(-n))) >> >>(where *did* all that come from?!) >> >>where G is primarily for my own convenience, that reduces to >> >>G = lim(n -> +oo) (9/10 * 10^(-10^(-n)-n) * Gamma(1 - 9/10^(-n))) = > 0. >> >>Not horribly interesting. >> >>> >>> What I did was use the Stirling Function which is similar to the > gamma >>> function to observe what happens with .999... factorial as > compared to 1 >>> factorial. >> >>Oh, so you want to replace >> >>G = lim(n -> +oo) (9 * 10^(-n) * Gamma(1 - 9/10^(-n)) / > (10^10^(-n))) >> >>with >> >>G' = lim(n -> +oo) (9 * 10^(-n) * exp((1 - 9/10^(-n)) * log(1 - > 9/10^(-n)) >> - (1 - 9/10^(-n))) / (10^10^(-n))) ? >> >>Suit yourself. >> >>G' = lim(n -> +oo) (9 * 10^(-n) * exp((1 - 9/10^(-n)) * log(1 - > 9/10^(-n)) >> - (1 - 9/10^(-n))) / (10^10^(-n))) >> = lim(n -> +oo) (9/10 * 10^(10^(-n)-n) * exp((1 - 9/10^(-n)) >> * log(1 - 9/10^(-n)) - (1 - 9/10^(-n)))) >> = 0 again. >> >> >>> >>> I used MathCAD Profession to show the results. What occurs is >>> (.999...)! --> 0 whereas 1! --> 1 >> >>You do know why they call it Stirling's Approximation, I hope. >> >>BTW, exp(1 * ln 1 - 1) = 1/e. That's not even close to Gamma(1) = > 0! = 1. >> >>[rest snipped; it gets more ridiculous from there] >> Yes, you do get more ridiculous from there, because I show that > (.999...)! = >> 0 >> and 1! = 1 >> And I even told you to check it on your own calculator. .999999.... > --> 0 >> when you plug it in the factorial function, not 1. Then type in 1! in > the >> factorial function and you get 1. >> I even used the factorial function in expanded form on MathCAD > using the >> lim (.999...)! = 0 >> n-->oo >> This proves by the factorial function, >> .999... =/= 1 >> There are even other references that clearly show that, >> .999... < 1 >> So, >> .999... =/= 1 >> . >> >>-- >>#191, ewill3@earthlink.net >>It's still legal to go .sigless. >> Smart's Alt. Physics News Group >> http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 >> S. Enterprize (Science Journal) >> http://smart1234.s-enterprize.com/ > I started reading this thread as I was waiting for something to print > off. Welcome to the Zoo. :-) > I started skipping around when I found ignoramus and subhuman > entering the messages. This is one of my favorite topics but I have > found it is difficult to change someone's mind once they have decided > .999999...and 1 are not equal. Since I have not read through ALL the > posts I am sure some of my arguments have already been presented. > 1. .9999... = .9 + .09 + .009 + .0009 +... and this is an infinite > geometric series with first term .9 and common ratio .1. By a > well-known theorem on infinite geometric series, this series converges > and the sum is .9/(1 - .1) = .9/.9 = 1. A good argument though it might need some backup, mostly because the formula a/(1-r) only works if the common ratio r is such that -1 < r < 1. Otherwise it's straightforward enough. > 2. Let x = .999999... Then 10x = 9.9999..... Subtract these two > equations to get 9x = 9 which gives x = 1. Infinite borrow problem rears its head here; this has been argued before. 10x-x can equal either 9.000... or 8.999... . This means one's back at Square 1. > (This one might be a little shaky since it requires the > distributive law to apply to infinite sums.) > 3. 1/3 = .3333..... Multiply both sides by 3 to get 1 = .999999.... Assuming the distributive law does in fact make sense for the infinite sum 3 * (.3 + .03 + .003 + ...). This is not trivial, though since the series .3 + .03 + .003 + ... is absolutely convergent it turns out to be true. One can, of course, do it the long way using limits. > 4. Lemma: If the average (mean) of two numbers equals one of the > numbers, then the two numbers are equal. The proof is left to the > reader. > Then find the mean of 1 and .9999999. Refer to the lemma. Interesting approach. Lessee. Let m = (r1 + r2) / 2, the arithmetic mean of two numbers. case 1: m = r1. Then r1 = (r1 + r2) / 2. 2*r1 = r1 + r2. r1 = r2. case 2: m = r2. Essentially similar to case 1. Nice little lemma. I for one don't see why it shouldn't hold up under nonstandard analysis. Mind you, S.E. is showing signs of Gary Denkeism [*], and he may claim that the mean of 1 and .999... = .999...5. This way, of course, lies madness. > 5. For people who think 1 and .99999... are not equal, I am sure all > of them believe 1 is the larger of the two. Produce a number which is > between those two numbers. If you can't, doesn't that make them equal? Actually, producing a number between 1 and .999... is fairly easy, assuming they're unequal (my favorite is (.999... + 9) / 10). The problem is that any such number must have the same decimal expansion as .999... . Is .999... = 1, or is it a collection of numbers in an equivalence class, all of which are such that 1 - 1/n < .999... < 1 for any positive integer n? Either way, things get slightly screwy. > I have seen lots of loose talk dealing with limits and sequences of > partial sums and the like. It all goes back to definitions. Change > the definitions and you might change the results. The definitions in > the books I have read and learned from and taught from would all lead > me to conclude that 1 and .9......are equal There is that; the definitions for standard analysis require that 1 = .999... , especially if one wants to get into calculus (limits). Although I lack the machinery and/or knowledge to verify it, I'm told that, even under nonstandard analysis' assumptions, the infinite series .9 + .09 + .009 + ... still equals 1. > Robert A. Meyer > Omaha North High School > Omaha, Nebraska [*] A very weird sort who claims, among other things, that .999... != 1, that (.999...)^2 = .999...998...001, and other such stuff. He also claims 1.000...1 or 0.000...1 is infinity. While some of this can be inferred from finite expansions (e.g., .999999^2 = 0.999998000001), infinite expansions get one into transfinite ordinals ('omega', which looks a bit like a lowercase w) and the ellipses in such expressions cease to be useful. -- #191, ewill3@earthlink.net It's still legal to go .sigless. === Subject: Re: .99999... still=/= 1 No one refuted that, (.999...)! = 0 (1)! = 1 0 < 1 So I guess this is one for the Gipper. And it shows us that, .999... =/= 1 Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 In sci.math, S. Enterprize Company > No one refuted that, > (.999...)! = 0 > (1)! = 1 > 0 < 1 > So I guess this is one for the Gipper. > And it shows us that, > .999... =/= 1 You need to fix your calculator. n! has domain W, range a subset of N. What you really want is Gamma(1.999...). Gamma(k) = (k - 1)! if k is a positive integer. Experimentation suggests that Gamma(1 - k) =~ 1 - .5772156649... * k for very small but positive k. This means of course that Gamma(1.999...) = 0.999... again, which means we're back to square one again. [.sigsnip] -- #191, ewill3@earthlink.net It's still legal to go .sigless. === Subject: Re: .99999... still=/= 1 >In sci.math, S. Enterprize Company > >> No one refuted that, >> (.999...)! = 0 >> (1)! = 1 >> 0 < 1 >> So I guess this is one for the Gipper. >> And it shows us that, >> .999... =/= 1 >You need to fix your calculator. n! has domain W, range a subset of N. I also used MathCAD using factorial equations and they all show that .999... factorial = 0. If .999... really equaled 1, the factorial function would have given 1 when .999... is plugged in. And again, you really should trust scientific calcualtors more. Mine is accurate up to 32 significant digits. It's simple. Plug in, (.9999---32digits) into the factorial function and you get 0. I can't help it if you done even trust your own calculator. >What you really want is Gamma(1.999...). Gamma(k) = (k - 1)! if >k is a positive integer. >Experimentation suggests that Gamma(1 - k) =~ 1 - .5772156649... * k >for very small but positive k. This means of course that >Gamma(1.999...) = 0.999... again, which means we're back to >square one again. That's right too. So it never reaches 1. The gamma function is also a factorial function. If you use a certain number of significant digits on a calculator, .999... it reaches 0 not 1. If .999... = 1 the gamma function would not lead you back to square 1. I leads you to the proof that .999... =/= 1. I used the Stirling Factorial approximation of a factorial with MathCAD with .999..., it leads to 0, just as my scientific calculator does. So in either case, .999... still=/= 1 >[.sigsnip] >-- >#191, ewill3@earthlink.net >It's still legal to go .sigless. Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 > There is that; the definitions for standard analysis require that > 1 = .999... , especially if one wants to get into calculus (limits). > Although I lack the machinery and/or knowledge to verify it, > I'm told that, even under nonstandard analysis' assumptions, > the infinite series .9 + .09 + .009 + ... still equals 1. Google Bob Kolker === Subject: Re: .99999... still=/= 1 In sci.math, robert j. kolker : >> There is that; the definitions for standard analysis require that >> 1 = .999... , especially if one wants to get into calculus (limits). >> Although I lack the machinery and/or knowledge to verify it, >> I'm told that, even under nonstandard analysis' assumptions, >> the infinite series .9 + .09 + .009 + ... still equals 1. > Google http://mathworld.wolfram.com/TransferPrinciple.html http://mathforum.org/dr.math/faq/analysis_hyperreals.html Interesting. A bit over my head. > Bob Kolker -- #191, ewill3@earthlink.net It's still legal to go .sigless. === Subject: Re: .99999... still=/= 1 >In sci.math, robert j. kolker > >: > > There is that; the definitions for standard analysis require that > 1 = .999... , especially if one wants to get into calculus (limits). > > Although I lack the machinery and/or knowledge to verify it, > I'm told that, even under nonstandard analysis' assumptions, > the infinite series .9 + .09 + .009 + ... still equals 1. >> Google >http://mathworld.wolfram.com/TransferPrinciple.html >http://mathforum.org/dr.math/faq/analysis_hyperreals.html >Interesting. A bit over my head. >> Bob Kolker >-- >#191, ewill3@earthlink.net >It's still legal to go .sigless. I developed a new term in math called, Mathematical Entropy, which shows that in cases where .999... is involved, ... or even the division of integers, there is a loss where ... is again involved. And this leads to this. You can get from, 1/3 --> to .333... BUT, you can't get precisely back to that number. There is a loss in the division itself too. Try going back, watch: 3 * .333... = .999... This is Mathematical Entropy. But, if you keep 1/3 in it's current form without the division then multiply it then, 3 * 1/3 = 1 Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 > http://mathforum.org/dr.math/faq/analysis_hyperreals.html This guy is very readable. You don't need a PhD in math to read this and it covers the main points. Perfect for someone who wants to know about hyperreals but does not want to get into the gory details. You will notice that this never, ever, ever refers to surreals. SEnterprise is blowing shit out his rectum. Bob Kolker === Subject: Re: .99999... still=/= 1 >> http://mathforum.org/dr.math/faq/analysis_hyperreals.html >This guy is very readable. You don't need a PhD in math to read this and >it covers the main points. Perfect for someone who wants to know about >hyperreals but does not want to get into the gory details. >You will notice that this never, ever, ever refers to surreals. >SEnterprise is blowing shit out his rectum. Usually people that can't admit a loss in a debate, they usually resort to name calling. Some even go so far as to use f words. >Bob Kolker Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 In sci.math, robert j. kolker : >> http://mathforum.org/dr.math/faq/analysis_hyperreals.html > This guy is very readable. You don't need a PhD in math to read this and > it covers the main points. Perfect for someone who wants to know about > hyperreals but does not want to get into the gory details. > You will notice that this never, ever, ever refers to surreals. > SEnterprise is blowing shit out his rectum. > Bob Kolker Agreed, it's a good intro. Not that S.E. cares, though hopefully a lurker or two or a dozen might. :-) I should point out that http://mathworld.wolfram.com/SurrealNumber.html does define the surreals using a notation {a|b}, where {|} = 0, {0|} = the simplest number greater than 0 (namely, 1), {|0} is the simplest number less than 0 (-1), and 2 = {1|} = {1|3} = {3/2|4} = {1|w}. Unfortunately {a|b} isn't explicitly defined, and the concept of simplicity isn't explained, either. Also, every real number is surrounded by a number of surreals, which are closer to it than every real number. Not unreasonable, but not horribly useful either (but then, neither are the reals, really; every FPP on the planet uses a multiple of a power of 2 :-) ). -- #191, ewill3@earthlink.net It's still legal to go .sigless. === Subject: Re: .99999... still=/= 1 |I should point out that | |http://mathworld.wolfram.com/SurrealNumber.html | |does define the surreals using a notation {a|b}, where |{|} = 0, {0|} = the simplest number greater than 0 |(namely, 1), {|0} is the simplest number less than 0 |(-1), and 2 = {1|} = {1|3} = {3/2|4} = {1|w}. | |Unfortunately {a|b} isn't explicitly defined, and the |concept of simplicity isn't explained, either. I believe simplicity amounts low rank, where we define the rank of a number as the smallest ordinal greater than the ranks of the numbers in its left and right sides. Thus {|}=0 has rank 0, {{|}|}=1 has rank 1 and so on. Each surreal corresponds to a function from an ordinal to {up, down}. The ordering on them is that the first place where they disagree, the one with the up is greater, and if one ends before the other one does, the longer one is greater if its next term is up and lesser if its next term is down. Simplicity is shortness. Finite sequences correspond to dyadic rationals, m/2^n. The sequence of n ups is +n and the sequence of n downs is -n. The complexity of dyadic rationals between two integers is in order of the size of the denominator. So up-up is 2, up-up-down is 3/2, up-up-down-up is 7/4. To get the reals, take all finite sequences plus ordinary infinite sequences that have infinitely many ups and downs in them. One can read off the binary expansion from the sequence. Then the sequences up-up-up-... and down-down-down-... correspond to omega and -omega. Ones that have only finitely many ups or finitely many downs are dyadic rationals plus or minus infinitesimals. The surreals obtained by sequences of ups and downs based on larger ordinals are the more exotic surreals you hear about. This may all sound a bit arbitrary, but Conway developed it out of his game theory. He considered games where the winner is decided by the loser not having any more moves. The notation {L|R} represents the game where if it's left's turn, the legal moves are L, while if it's right's turn, the legal moves are R. Then he defines the sum of two games as being the game where on each turn, a player can make a move in either game. Some better-behaved games count as numbers. What counts as a number and when one game counts as <= another are defined together by induction. The sequence of ups and downs can be thought of as corresponding to a game where each player is allowed to truncate the sequence at one of the positions, but left has to truncate it at an up and right at a down. A sequence of n ups gives left n free moves, while a sequence of n downs gives right n free moves. Having two sequences up-down is equivalent in a certain sense to having just one sequence that is up, so it functions like 1/2. Left can get a free move by eliminating one of the sequences entirely if right takes the down off of the other one. That takes one move from each of them, leaving left with a free move. Or if left eliminates one of them, right can take the top off the other one, limiting left to just one free move. 2^n games of the form up-down-down-...-down with n downs is equivalent in a sense to just one extra turn for left. Left and right can take turns eliminating one of these games and taking one of the downs off the end respectively. They are left with 2^{n-1} games with one fewer down on each. Then repeat this. When they are done, they are left with just one up which is the spare move that left gets. This illustrates how a single one of those games, up-down-...-down, counts like 1/2^n. If I make a game {L|R} where the elements of L and R are games based on these ordinal sequences, and the elements of L are less than the elements of R, this should be equivalent in a sense to a single game which is the simplest that lies between L and R. I guess I should've defined the sense of equivalence, but it doesn't seem so hard to see. If s is a sequence (possibly indexed by an infinite ordinal), L={s+down+t1}, and R={s+up+t2}, {L|R} is similar to s. If it's left's turn, right can respond by truncating s+down+t1 down to just s, and conversely if it's right's turn, left can respond by truncating s+up+t2 to just s; neither player has to use up a move to do this. The relevance to 0.999... is somewhat weak. I think the temptation would be to hope(?) that it makes sense to think of an infinite binary expansions ending in 111... as corresponding to a surreal number represented with an infinite sequence of ups at the end of it. This idea is ugly in a few ways. For one thing, it allows us to represent only some of the surreals representable with an ordinary infinite (i.e. indexed by the natural numbers) sequence of ups and downs. Moreover, that set of surreals is not itself very nice; it's not closed under addition for example. Keith Ramsay === Subject: Re: .99999... still=/= 1 > Moreover, that set of surreals is not itself very nice; it's > not closed under addition for example. Bob Kolker === Subject: Re: .99999... still=/= 1 >> Moreover, that set of surreals is not itself very nice; it's >> not closed under addition for example. > Bob Kolker I think the surreals described in this thread are not the Conway surreals, since the Conway surreals are a field but are not a set. That is, they satisfy all the field axioms except for not being a set. -- Dave Seaman Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling. === Subject: Re: .99999... still=/= 1 Knuth and Conway have a little book, in stort form about the surreals, that you can read; the main idea is that of Dedikind's cut, I believe. . --The Pinochet Plan for Social Security! http://larouchepub.com === Subject: Re: .99999... still=/= 1 > Knuth and Conway have a little book, in stort form -Surreal Numbers- by D.E.Knuth. > about the surreals, that you can read; > the main idea is that of Dedikind's cut, > I believe. That is correct. bob Kolker === Subject: Re: .99999... still=/= 1 >In sci.math, robert j. kolker > >: > http://mathforum.org/dr.math/faq/analysis_hyperreals.html >> This guy is very readable. You don't need a PhD in math to read this and >> it covers the main points. Perfect for someone who wants to know about >> hyperreals but does not want to get into the gory details. >> You will notice that this never, ever, ever refers to surreals. >> SEnterprise is blowing shit out his rectum. >> Bob Kolker >Agreed, it's a good intro. Not that S.E. cares, though >hopefully a lurker or two or a dozen might. :-) >I should point out that >http://mathworld.wolfram.com/SurrealNumber.html >does define the surreals using a notation {a|b}, where >{|} = 0, {0|} = the simplest number greater than 0 >(namely, 1), {|0} is the simplest number less than 0 >(-1), and 2 = {1|} = {1|3} = {3/2|4} = {1|w}. >Unfortunately {a|b} isn't explicitly defined, and the >concept of simplicity isn't explained, either. >Also, every real number is surrounded by a number of surreals, >which are closer to it than every real number. Not >unreasonable, but not horribly useful either (but then, >neither are the reals, really; every FPP on the planet >uses a multiple of a power of 2 :-) ). Oh so indirectly you imply that I'm right, then use name calling on a post before this. Which is it? Are you confused? >-- >#191, ewill3@earthlink.net >It's still legal to go .sigless. Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Prime? Is 1 prime or composite? What about 0? What do you think? Poly-poly man === Subject: Re: Prime? > Is 1 prime or composite? > What about 0? > What do you think? By convention 1 is not a prime. That is a matter of definition. 0 is divisible by any number other than 0 so it cannot be a prime. Bob Kolker === Subject: Re: Prime? >> Is 1 prime or composite? >> What about 0? >> What do you think? >By convention 1 is not a prime. That is a matter of definition. This is not definition; 1 is a unit. Multiplication or division by a unit does not change primality. >0 is divisible by any number other than 0 so it cannot be a prime. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: Prime? >> Is 1 prime or composite? >> What about 0? >> What do you think? >By convention 1 is not a prime. That is a matter of definition. > This is not definition; 1 is a unit. > Multiplication or > division by a unit does not change primality. Lehmer called 1 a prime. If primality were to be defined to not exclude units, then obviously all units are prime, and thence multiplication or division by a unit would still not change primality. So your argument becomes void. Phil -- The gun is good. The penis is evil... Go forth and kill. === Subject: Re: Prime? 1 is only one factor; the factor of 1 is 1. To say that 1 = 1 x 1 is redundant. Unlimited factorizations of 1 can be made, all using nothing other than 1. Any other integer can be factored until each resulting FINAL factor in the set of factors be factorable as P x 1. Each final resulting P would be prime, according to the definition of prime number. Does this make it easier to understand how 1 is accepted as NOT being prime? The number, 1, is probably also NOT composite. It is both NOT composite, and NOT prime. G C === Subject: Re: Prime? >> Is 1 prime or composite? >> What about 0? >> What do you think? > By convention 1 is not a prime. That is a matter of definition. >> This is not definition; 1 is a unit. >> Multiplication or >> division by a unit does not change primality. > Lehmer called 1 a prime. If primality were to be defined to not > exclude units, then obviously all units are prime, and thence > multiplication or division by a unit would still not change > primality. So your argument becomes void. > Phil Poor old Lehmer! Ultimately, one has to have a natural number divisible _uniquely_ by the (usual definition of) primes. If unity (one) be prime, then (rather obviously) /every/ natural number is divisible by one - and not only that: any number of times one wishes. The _only_ definition of prime which results in _unique_ factorization is this: Let N be a natural number. N is prime if _and only if_ it has two /distinct factors/: unity and itself (/i.e./ N). If unity be allowed as a prime, unique factorization breaks down. Sorry if this idea seems *too* obvious. Nevertheless, what I have just suggested amounts to the only consistent definition of primes. Given the time, I will _merely_ add: Merry Christmas and a Happy New Year! John johnDOTmorrisonATtescoDOTnet -- Why do they sterilize the needle for lethal injections? - Mark Ayliffe === Subject: Re: Prime? > Lehmer called 1 a prime. > Poor old Lehmer! Ultimately, one has to have a natural number divisible > _uniquely_ by the (usual definition of) primes. If unity (one) be prime, > then (rather obviously) /every/ natural number is divisible by one - and not > only that: any number of times one wishes. > The _only_ definition of prime which results in _unique_ factorization > is this: > Let N be a natural number. N is prime if _and only if_ it has two /distinct > factors/: unity and itself (/i.e./ N). If unity be allowed as a prime, > unique factorization breaks down. What makes you think that one would be permitted to use an alternative definition of prime without being also able to alter the definition of unique factorisation? Does your definition of unique factorisation not already make explicit reference to the special nature of units? > Sorry if this idea seems *too* obvious. Nevertheless, what I have just > suggested amounts to the only consistent definition of primes. No, the one which requires vastly the fewest inclusions of special cases elsewhere. I believe that makes it the most sensible one to use. > Given the time, I will _merely_ add: Merry Christmas and a Happy New Year! Likewise. Phil -- The gun is good. The penis is evil... Go forth and kill. === Subject: Re: Prime? > Lehmer called 1 a prime. ... > The _only_ definition of prime which results in _unique_ factorization > is this: > > Let N be a natural number. N is prime if _and only if_ it has two /distinct > factors/: unity and itself (/i.e./ N). If unity be allowed as a prime, > unique factorization breaks down. > What makes you think that one would be permitted to use an alternative > definition of prime without being also able to alter the definition of > unique factorisation? Yup, indeed. And when you go to other rings you *have* to consider alternative definitions. In most rings unique factorisation is generally defined upto multiplication by units. If we do that also with the natural numbers, there is no immediate reason not to call 1 a prime. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: Prime? > > Lehmer called 1 a prime. > ... > > The _only_ definition of prime which results in _unique_ factorization > > is this: > > > > Let N be a natural number. N is prime if _and only if_ it has two /distinct > > factors/: unity and itself (/i.e./ N). If unity be allowed as a prime, > > unique factorization breaks down. > > > > What makes you think that one would be permitted to use an alternative > > definition of prime without being also able to alter the definition of > > unique factorisation? > Yup, indeed. And when you go to other rings you *have* to consider > alternative definitions. In most rings unique factorisation is generally > defined upto multiplication by units. If we do that also with the natural > numbers, there is no immediate reason not to call 1 a prime. If you want to go to other rings, the usual definition of prime comes from a prime ideal. So it would be reasonable to define an element r of a ring R to be prime if the ideal is a prime ideal, in which case units don't qualify. This of course is equivalent to the usual definition for a natural number n, since is a prime ideal if and only if n is prime. === Subject: Re: Prime? >> > Lehmer called 1 a prime. >> ... >> > The _only_ definition of prime which results in _unique_ factorization >> > is this: >> > >> > Let N be a natural number. N is prime if _and only if_ it has two /distinct >> > factors/: unity and itself (/i.e./ N). If unity be allowed as a prime, >> > unique factorization breaks down. >> > >> > What makes you think that one would be permitted to use an alternative >> > definition of prime without being also able to alter the definition of >> > unique factorisation? >> Yup, indeed. And when you go to other rings you *have* to consider >> alternative definitions. In most rings unique factorisation is generally >> defined upto multiplication by units. If we do that also with the natural >> numbers, there is no immediate reason not to call 1 a prime. >If you want to go to other rings, the usual definition of prime comes >from a prime ideal. So it would be reasonable to define an element r of >a ring R to be prime if the ideal is a prime ideal, in which case >units don't qualify. This of course is equivalent to the usual >definition for a natural number n, since is a prime ideal if and >only if n is prime. is a prime ideal in which ring? Presumably the integers. I am not sure whether you regard 0 as a natural number or not, but according to that definition, 0 is a prime in the ring of integers. Derek Holt. === Subject: Re: Prime? ... >> > What makes you think that one would be permitted to use an alternative >> > definition of prime without being also able to alter the definition >> > of >> > unique factorisation? >> >> Yup, indeed. And when you go to other rings you *have* to consider >> alternative definitions. In most rings unique factorisation is generally >> defined upto multiplication by units. If we do that also with the natural >> numbers, there is no immediate reason not to call 1 a prime. > >If you want to go to other rings, the usual definition of prime comes >from a prime ideal. (I was talking about other definitions of unique factorisation. But, whatever.) That may be true, but the usual way it is stated is: a is prime when, if a | bc, a | b or a | c, and that one does not disallow units, with that formulation you have (again) to explicitly disallow units. And again, I feel that the only reason to disallow units is to simplify some statements. But unique factorisation is *not* simplified, because in its definition you have still to allow for units. And for *that* definition of unique factorisation it does not matter whether units are considered prime or not. > So it would be reasonable to define an element r of >a ring R to be prime if the ideal is a prime ideal, in which case >units don't qualify. This of course is equivalent to the usual >definition for a natural number n, since is a prime ideal if and >only if n is prime. > is a prime ideal in which ring? Presumably the integers. > I am not sure whether you regard 0 as a natural number or not, > but according to that definition, 0 is a prime in the ring of integers. Yes, also with that definition something special has to be done (like excluding zero elements). -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: Prime? |0 is divisible by any number other than 0 so it cannot be a prime. There are some authors (e.g. Hardy and Wright) who use a definition of divisible that makes 0 not divisible by 0, and there are others (e.g. Harvey Cohn) who use a definition of divisible that makes 0 divisible by 0. My impression was that the latter convention was gaining in popularity, but I didn't do a thorough survey so I could be wrong. In either case, 0 is not considered prime. Keith Ramsay === Subject: Re: Prime? > |0 is divisible by any number other than 0 so it cannot be a prime. > There are some authors (e.g. Hardy and Wright) who use a > definition of divisible that makes 0 not divisible by 0, and there > are others (e.g. Harvey Cohn) who use a definition of divisible > that makes 0 divisible by 0. My impression was that the latter > convention was gaining in popularity, but I didn't do a thorough > survey so I could be wrong. I think your impression is quite well founded. > In either case, 0 is not considered prime. Prefacing the definition with within the multiplicative group is a good way of not getting any unwanted properties attatched to the 0. Phil -- The gun is good. The penis is evil... Go forth and kill. === Subject: Re: Prime? <87r7lfa2q5.fsf@nonospaz.fatphil.org> So what definition are you using for prime and composite anyway? === Subject: Re: Prime? > Is 1 prime or composite? Neither. > What about 0? The same answer applies. Jose Carlos Santos === Subject: Re: prove that sqtr of 2 is irrational by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBOGvwL28718; >hi can u guys help me prove that the sqrt of 2 is irrational? Homework, eh? Google it. === Subject: Re: Why (or not) use single letter variable names? <41c87811$12$fuzhry+tra$mr2ice@news.patriot.net> <41ca2855$10$fuzhry+tra$mr2ice@news.patriot.net> at 12:34 PM, hrubin@odds.stat.purdue.edu (Herman Rubin) said: >If you can recognize the letters, you could read >mathematics written with them as symbols, even if you >did not know any of the names. Of course, but I can read more quickly when I do recognize the symbols. >English, French, Spanish, Latin, and German are written in >essentially the same orthography. People using these languages will >not pronounce the names of the letters the same. But if I can read a paper written in one of those languages, then I can read and pronounce the names of letters in the same language. -- Shmuel (Seymour J.) Metz, SysProg and JOAT 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 === Subject: Re: Why (or not) use single letter variable names? > at 12:34 PM, hrubin@odds.stat.purdue.edu (Herman Rubin) said: >>If you can recognize the letters, you could read >>mathematics written with them as symbols, even if you >>did not know any of the names. >Of course, but I can read more quickly when I do recognize the >symbols. >>English, French, Spanish, Latin, and German are written in >>essentially the same orthography. People using these languages will >>not pronounce the names of the letters the same. >But if I can read a paper written in one of those languages, then I >can read and pronounce the names of letters in the same language. Not necessarily. I have read papers in many foreign languages, but I do not know the names of the letters in all those languages. I have read mathematical papers in all the languages I have listed, and at best I know the names of some of the letters outside of English. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: Why (or not) use single letter variable names? <41c87811$12$fuzhry+tra$mr2ice@news.patriot.net> <41ca2855$10$fuzhry+tra$mr2ice@news.patriot.net> >> If you can recognize the letters, you could read >> mathematics written with them as symbols, even if you >> did not know any of the names. I could do this with >> Russian letters, and I do not know their names. >and >> As I said, I do not need to name them. I would not >> have any problem with using Russian letters for >> symbols, but I would have a much greater problem >> if the TeX representations for them were used. >The question of which characters ought to be used for creating variable >identifiers has been a Unicode issue for some time and a Unicode >technical document treating this issue has been several times updated. >Oddities appear, such as which do not correspond between uppercase and >lower case, which mean in a computer language which is >case-insensitive, _¤_ in lowercase should match with _SS_ in >uppercase which means also that _¤_ in lowercase must match with _ss_ >in lowercase: variables foo¤, FOOSS, and fooss (and FoOsS and so >forth) should be treated as identical. >The current technical annex covering this appears at >http://www.unicode.org/reports/tr31/tr31-3.html . It reads in part: ><< The formal syntax provided here is intended to capture the general >intent that an identifier consists of a string of characters that >begins with a letter or an ideograph, and then includes any number of >letters, ideographs, digits, or underscores. Each programming language >standard has its own identifier syntax; different programming languages >have different conventions for the use of certain characters from the >ASCII range ($, @, #, _) in identifiers. To extend such a syntax to >cover the full behavior of a Unicode implementation, implementers need >only combine these specific rules with the syntax provided here. >> >Using full Unicode letters and ideographs in c and similar languages >could be used to make such languages even more difficult to readm, even >for programmers who recognize non-Latin letters and ideographs, as >letter character U+01C0 LATIN LETER DENTAL CLICK is identical in >appearance to the ASCII | symbol and U+01C3 LATIN LETTER RETROFLEX >CLICK is identical in appearance to the ASCII ! symbol. Also many >uppercase Greek and Cyrillic characters are identical in appearance to >particular Latin characters and to each other. The occasional confusion >now between 1 and l (one and el) in reading code would be greatly >extended. For those of us whose jobs it was to do operating system development, we were able to learn a new computer language by reading code or scanning (and I do mean scanning extremely fast) the lanugage's manual; none of those Dummy books. For those of us who were getting paid to produce code, we were expected to learn a new lanugage in less than three days. Learning how to use a new operating system in a couple of hours. We called all of this pre-learning ramping up. Now, in reading code cold, there is a heirarchy of things a pro looks for and learns. If a variable name is indistinguishable from a language keyword, the programmer has serious problems. One the math guys just pointed this out in his post (I think it was David). It doesn't matter what the glyph is as long as I can mentally assign a meaning to it and that meaning stays consistent throughout the exercise. /BAH Subtract a hundred and four for e-mail. === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem <14ras09md0bvs1r3grod1q6d948ecjsjhu@4ax.com> > Note the phrase We let N be the first-order system whose > axioms are.... That's quite explicit: he's defining a > set of axioms. > Also note the sentence Thus, the provable formulas of N are > nothing more than the axioms of N. If this were a definition > of provable then that Thus would make no sense - the word > Thus means that what he's saying here _follows_ _from_ the > definition he's just given. It can't follow from that if > provable has not yet been defined - the only way it can > follow from the previous part of the paragraph is if we > already know what provable means. We already know what provable means because Smullyan just defined it to be truth in the first phrase. So your points are that (1) he isn't defining the theorems, he's defining the axioms and rules, and (2) someone else is defining the theorems. I see. So, instead of saying, Smullyan defines provability to be truth., we should instead say, Smullyan defines provability to be truth with the help of coauthors. Is that better? Actually, (A) the first-order system whose axioms are all the correct formulas does not imply (B) the provable formulas of N are nothing more than the axioms of N. B is equivalent to (B') The derivation rules applied to the axioms produce only axioms. B is a relation between the derivation rules and the axioms. It can be true or false, even when A is true, because A doesn't say anything about the derivation rules. A is about the axioms and B is about the relationship between the derivation rules and the axioms. Regardless of what A says, B can be true or false depending on the derivation rules. A => B here only because Smullyan is also (must be) assuming that (B') the derivation rules produce nothing outside of the axioms. B (thus) is dependent on this fact. In fact, given assumption B', B is merely equivalent to this assumption and statement A plays no role in the truth of B at all. > You know this really is hilarious: Before you posted that > quote people were explaining to you that no, he's not > defining provability to be the same as truth How could they refer to what Smullyan is defining before I posted his definition? (speaking of hilarious) 1. Is provability the same as truth in system N? (Answer: Yes.) 2. Who defined System N? (Answer: None other than Raymond Smullyan himself.) > people > who'd never read the book were explaining that, basing > their assertions solely on the fact that Smullyan > knows what he's talking about! Well, actually, of course it's based on that plus the assumption (belief) that defining provability to be truth is foolish. I agree with the logic: if it were foolish then Smullyan would not likely be doing it. The mistake is that this second premise is not true. It is not at all foolish, and as we can see, Smullyan in fact does use a system in which provability is defined to be truth. (As) If that is not enough, consider another instance of someone defining a system in which provability equals truth: 1. Assume that unprovability is expressible. (There is a wff that says Wff number x is not provable.) 2. Define provability to be truth. <== [ you called ignorant ] 3. Then the provable sentences are the true sentences. 4. Thus expressible equals representable. 5. And so unprovability is representable. 6. But simple diagonalization shows that unprovability is not representable. 7. Thus if unprovability is expressible, then provability does not coincide with truth. 8. Thus there is a sentence that is true and unprovable, or false and provable. 9. If the system is sound, then no sentence is false and provable. 10. Thus, if unprovability is expressible and the system is sound, then there is a sentence that is true and unprovable. This of course is a high-level proof of Godel's 1st. Incompleteness Theorem (based on soundness.) > Now you post that quote, > thinking it shows you're right. But if you read it > you see it shows just the opposite. Darn!! > Yes, you have to read it carefully, paying attention > to exactly what's written. Logic is like that. The only relationship between what you're saying and Logic is that in all of the references that I see, Logic contradicts what you're saying (see details above.) C-B > ************************ > David C. Ullrich === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem >> Note the phrase We let N be the first-order system whose >> axioms are.... That's quite explicit: he's defining a >> set of axioms. >> Also note the sentence Thus, the provable formulas of N are >> nothing more than the axioms of N. If this were a definition >> of provable then that Thus would make no sense - the word >> Thus means that what he's saying here _follows_ _from_ the >> definition he's just given. It can't follow from that if >> provable has not yet been defined - the only way it can >> follow from the previous part of the paragraph is if we >> already know what provable means. >We already know what provable means because Smullyan just defined it to >be truth in the first phrase. >So your points are that (1) he isn't defining the theorems, he's >defining the axioms and rules, and (2) someone else is defining the >theorems. I see. So, instead of saying, Smullyan defines >provability to be truth., we should instead say, Smullyan defines >provability to be truth with the help of coauthors. Is that better? >Actually, (A) [N is] the first-order system whose axioms are all the >correct formulas does not imply (B) the provable formulas of N are >nothing more than the axioms of N. I just realized that it could be you actually don't see why A implies B. If so then that would explain much of your confusion. The fact that A implies B is very simple: Suppose that P is a formula provable in N. The Soundness Theorem says that P is true in every model of the axioms of N, that is, in every structure in which all the axioms of N are true. In particular, P is true in the standard structure consisting of the positive integers - that is, the Soundness Theorem shows that P is what Smullyan is calling correct, and hence P is indeed one of the axioms for N. QED. >B is equivalent to (B') The >derivation rules applied to the axioms produce only axioms. B is a >relation between the derivation rules and the axioms. It can be true >or false, even when A is true, because A doesn't say anything about >the derivation rules. >A is about the axioms and B is about the relationship between the >derivation rules and the axioms. Regardless of what A says, B can be >true or false depending on the derivation rules. A => B here only >because Smullyan is also (must be) assuming that (B') the derivation >rules produce nothing outside of the axioms. B (thus) is >dependent on this fact. In fact, given assumption B', B is merely >equivalent to this assumption and statement A plays no role in the >truth of B at all. >> You know this really is hilarious: Before you posted that >> quote people were explaining to you that no, he's not >> defining provability to be the same as truth >How could they refer to what Smullyan is defining before I posted his >definition? (speaking of hilarious) >1. Is provability the same as truth in system N? (Answer: Yes.) >2. Who defined System N? (Answer: None other than Raymond Smullyan >himself.) >> people >> who'd never read the book were explaining that, basing >> their assertions solely on the fact that Smullyan >> knows what he's talking about! >Well, actually, of course it's based on that plus the assumption >(belief) that defining provability to be truth is foolish. I agree >with the logic: if it were foolish then Smullyan would not likely be >doing it. The mistake is that this second premise is not true. It is >not at all foolish, and as we can see, Smullyan in fact does use a >system in which provability is defined to be truth. >(As) If that is not enough, consider another instance of someone >defining a system in which provability equals truth: >1. Assume that unprovability is expressible. (There is a wff that says >Wff number x is not provable.) >2. Define provability to be truth. <== [ you called ignorant ] >3. Then the provable sentences are the true sentences. >4. Thus expressible equals representable. >5. And so unprovability is representable. >6. But simple diagonalization shows that unprovability is not >representable. >7. Thus if unprovability is expressible, then provability does not >coincide with truth. >8. Thus there is a sentence that is true and unprovable, or false and >provable. >9. If the system is sound, then no sentence is false and provable. >10. Thus, if unprovability is expressible and the system is sound, then >there is a sentence that is true and unprovable. >This of course is a high-level proof of Godel's 1st. Incompleteness >Theorem (based on soundness.) >> Now you post that quote, >> thinking it shows you're right. But if you read it >> you see it shows just the opposite. >Darn!! >> Yes, you have to read it carefully, paying attention >> to exactly what's written. Logic is like that. >The only relationship between what you're saying and Logic is that in >all of the references that I see, Logic contradicts what you're >saying (see details above.) >C-B >> ************************ >> David C. Ullrich ************************ David C. Ullrich === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem Charlie-Boo says... >We already know what provable means because Smullyan just defined it to >be truth in the first phrase. No, he didn't. The quote that you give from Smullyan does not say that at all. He says thus the provable sentences and the true sentences coincide for his system. Thus implies that he is drawing a *conclusion* rather than making a definition. It *follows* from the *usual* definition of provable that for a complete theory, the true sentences and the provable sentences coincide. >So, instead of saying, Smullyan defines >provability to be truth., we should instead say, Smullyan defines >provability to be truth with the help of coauthors. Is that better? It's better to say that Smullyan defines the axioms of his system to be all true sentences. Therefore, it follows from the usual definition of provable that the provable sentences and the true sentences coincide for his system. At no point is Smullyan defining provability in terms of truth. >Actually, (A) the first-order system whose axioms are all the >correct formulas does not imply (B) the provable formulas of N are >nothing more than the axioms of N. Yes, it does. >A is about the axioms and B is about the relationship between the >derivation rules and the axioms. Regardless of what A says, B can be >true or false depending on the derivation rules. The derivation rules are fixed by the fact that we are dealing with first-order logic. (Or rather, I should say that the logical consequence relation is fixed by the fact that we are dealing with first-order logic.) >A => B here only because Smullyan is also (must be) assuming that >(B') the derivation rules produce nothing outside of the axioms.' That's not an assumption, that is an easily proved *conclusion*. >In fact, given assumption B', B is merely >equivalent to this assumption and statement A plays no role in the >truth of B at all. Well, that's completely wrong, but I think that has already been pointed out before. -- Daryl McCullough Ithaca, NY === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem Discussion, linux) >>Actually, (A) the first-order system whose axioms are all the >>correct formulas does not imply (B) the provable formulas of N are >>nothing more than the axioms of N. > Yes, it does. That is, it does *since* the rules of inference are sound. I don't know if the big brane of Charlie-Boo is alluding to this missing step, but maybe so. Or maybe not. -- But remember, as long as one human being follows the rules of mathematics, then mathematics as a human discipline survives. Right now I'm that one human being, so mathematics survives. -- James S. Harris === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem >Actually, (A) the first-order system whose axioms are all the >correct formulas does not imply (B) the provable formulas of N are >nothing more than the axioms of N. >> Yes, it does. >That is, it does *since* the rules of inference are sound. I don't >know if the big brane of Charlie-Boo is alluding to this missing >step, but maybe so. >Or maybe not. I had a thought just now - maybe it's not that he's alluding to this missing step, maybe he actually doesn't see it! That would explain a lot, replacing a sort of willful obstinate ignorance with simple incompetence. For his benefit: Suppose that S is a structure, A is the set of all statements true in S, and T is the set of all logical consequences of the axioms in A. Then T = A. Proof: A is a subset of T by definition. To show that T is a subset of A, assume that P is an element of T. Now the Soundness Theorem shows that P is true in every model of A. In particular P is true in S, and hence P is an element of A. QED. (Glossary: A _structure_ is what's often called a model on sci.logic: A set together with relations on that set. A model of a set of sentences A is a structure in which every element of A is true.) ************************ David C. Ullrich === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem >> Note the phrase We let N be the first-order system whose >> axioms are.... That's quite explicit: he's defining a >> set of axioms. >> Also note the sentence Thus, the provable formulas of N are >> nothing more than the axioms of N. If this were a definition >> of provable then that Thus would make no sense - the word >> Thus means that what he's saying here _follows_ _from_ the >> definition he's just given. It can't follow from that if >> provable has not yet been defined - the only way it can >> follow from the previous part of the paragraph is if we >> already know what provable means. >We already know what provable means because Smullyan just defined it to >be truth in the first phrase. There's really no point in continuing this until you answer Daryl's question: >>No, he's not. Look, suppose that all the coins in my pocket are >>pennies. Does that many that penny has been redefined to mean >>the same thing as coin? ************************ David C. Ullrich === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem <14ras09md0bvs1r3grod1q6d948ecjsjhu@4ax.com> > There's really no point in continuing this until you answer > Daryl's question: Regardless of your statements (absurd or otherwise)? >>Look, suppose that all the coins in my pocket are >>pennies. Does that many that penny has been redefined to mean >>the same thing as coin? Formal systems are defined. Coins are minted and exchanged for goods and services. 1. Is provability the same as truth in system N? (Answer: Yes.) 2. Who defined System N? (Answer: None other than Raymond Smullyan himself.) Now those are some relevant questions. You have given no technical objection, only a dictum that it shouldn't be done. C-B Smullyan does it and Godel does it. So is it a good idea? Apparently not. Why? Because C-B does it! > ************************ > David C. Ullrich === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem Charlie-Boo says... >1. Is provability the same as truth in system N? (Answer: Yes.) >2. Who defined System N? (Answer: None other than Raymond Smullyan >himself.) >Now those are some relevant questions. No, they aren't relevant. The issue was whether Smullyan *defined* provability to be the same as truth. He didn't. That's a *consequence* of his choice of axioms. -- Daryl McCullough Ithaca, NY === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem Discussion, linux) > Charlie-Boo says... >>1. Is provability the same as truth in system N? (Answer: Yes.) >>2. Who defined System N? (Answer: None other than Raymond Smullyan >>himself.) >>Now those are some relevant questions. > No, they aren't relevant. The issue was whether Smullyan *defined* > provability to be the same as truth. He didn't. That's a *consequence* > of his choice of axioms. Have you ever noticed that on Usenet, the problem isn't so much people that beat dead horses into the ground, but the people that want to be the dead horse? Charlie seems intent on being wrong in as many words as he can. -- Jesse F. Hughes Basically there are two angry groups. I am a harsh force of one. Against me is a society of mathematicians. So far it's been a draw. -- JSH gives another display of keen insight. === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem <14ras09md0bvs1r3grod1q6d948ecjsjhu@4ax.com> >>[...] >> Hint: although it's hard to see what you're _trying_ to prove, >> what you _are_ proving is clear to everyone but you. >Off-the cuff (afterthought), unsubstantiated (only the claim is given), >all-encompassing (everyone). > Giggle. It's not the sort of assertion that's susceptible to > mathematical proof. Thought you might be interested because > it's true nonetheless (as we well know, truth and provability > are different things...) Yes! Not only is it unsubstantiated, but it never will be substantiated. Isn't that actually even worse? I mean, do you really think it makes sense (especially as part of a scientific discussion) to make assertions that you will never substantiate? C-B > ************************ > David C. Ullrich === Subject: Re: Lemma Bersayt's >Anybody know something about lemma Bersayt's??? I suspect this is a transliteration to English of a transliteration to Russian of a name in some other language, and it's rather hard to say what the original would be. Maybe Burnside's lemma? It might help if you said what area of mathematics this is from. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: Make quick cash $$$$$$$$$$$$$ fast so what does $$$$$$$$$$$$ ... converge to? === Subject: Re: Make quick cash $$$$$$$$$$$$$ fast > so what does $$$$$$$$$$$$ ... converge to? By a miracle of modern marketing, the series is: 1 + 2 + 4 + 8 + ... + $lots more$!!1! + ... . Now, let x = 1 + 2 + 4 + ... , then 2x = 2 + 4 + 8 + ... 2x+1 = 1 + 2 + 4 + 8 + ... = x. Now we have 2x+1 = x, which we can easily solve for x = -1. Yep, that's pretty much spot on. - Tim === Subject: Re: Make quick cash $$$$$$$$$$$$$ fast nice! === Subject: Re: Make quick cash $$$$$$$$$$$$$ fast [the usual Ponzi crap] To my mind, the only thing more dumb than posting a pyramid scheme to a mathematics NG where readers will see through it immediately, is posting it to one of the net-abuse NGs (especially news.admin.net-abuse.email) where people will not only see through it (having already seen approaching aleph-sub-null of the things) but are likely to report it -- and to know where to report it! === Subject: Re: Make quick cash $$$$$$$$$$$$$ fast > Well GUESS WHAT!!... within 7 days, I started getting money in > the mail! I was shocked! I figured it would end soon, but the money > just kept coming in. In my first week, I made about $25.00. By the end > of the second week I had made a total of over $1,000.00! In the third > week I had over $10,000.00 and it's still growing. This is now my > fourth week and I have made a total of just over $42,000.00 Yes, I can just picture this poor sucker drowning in 42,000 ENVELOPES! Happy Christmas Richard === Subject: Re: Make quick cash $$$$$$$$$$$$$ fast This is total crap. This procedure leads to an exponentially increasing sequence. And it is sorta 6^n. It will very soon (probably in 20 to 30 mails) become much more than the current population of the world. Such a stupid mail to sci.math! === Subject: Re: Nested roots >> Then, f(x)^2 = x + f(x+1) (1) >> The equation f(x)^2=f(x+1) has got a simple solution f(x)=A^(2^x) , >> So if p(x) is a polynomial we may perhaps try approximate (1) >> with f1(x)=A^(2^x)+p(x)*A^(-2^x) . >> and compute p(x)... >This should be taken as the beginning of a series. With A^(-2^x) = w >I get >f(x) = 1/w + 1/2*x*w + (-1/8*x^2+1/4*x+1/4)*w^3 >+ (-1/8*x^2-1/8*x+1/16*x^3)*w^5 >+ (5/32+3/32*x^3-1/16*x-5/128*x^4)*w^7 + ... >It looks like there will be a formal series solution >f(x) = sum_{j=0}^infinity p_j(x)*w^(2*j-1) >where each p_j is a polynomial of degree j. >Of course this is only formal, and I don't know about convergence >(though my guess is that for A > 1 the series will converge for >every x). Slightly more generally: if w is a solution of w(x)^2 = w(x+1) and f(x) = sum_{j=0}^infinity p_j(x)*w^(2*j-1) with p_0 = 1 and p_1 = x/2, the equation f(x)^2 = x + f(x+1) becomes the system of equations sum_{j=0}^{n+1} p_j(x) p_{n+1-j}(x) = p_n(x+1) for n from 1 to infinity. This is satisfied if p_{n+1}(x) = 1/2 * (p_n(x+1) - sum_{j=1}^n p_j(x) p_{n+1-j}(x)) By induction, each p_j is a polynomial of degree <= j. The leading coefficient is the coefficient of x^j in the Taylor series of sqrt(1+x). The coefficient of x^(j-1) (for j > 1) is the coefficient of x^(j-1) in the Taylor series of -1/(2*sqrt(1+x)). I don't know about the other coefficients. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada