rr6 complained when I moved this to pseudo and gave him an infraction for posting bullshit in the main forum. I said I'd give examples of how he's talking numerological incoherent tosh so.... No, it isn't infinite nor does it have any property unique to it. It is irrational and transcendental, which is the case for most numbers, the set of algebraic numbers has measure zero within the Reals. Except that you don't cube pi when you consider 3 dimensional volume forms, you cube the length scale. For example, the 'area' for a 1-sphere is \(2\pi r\) and a 2-sphere is \(4 \pi r^{2}\) while for a 2-ball it is \(\pi r^{2}\) and a 3-ball it is \(\frac{4}{3}\pi r^{3}\). The general forms are here. So? Give me a number less than 100 and I'm sure there is some part of the human body which has that many pieces to it, your factoid is utterly vapid. So? Once again, give me any number below 100 and I can find a geometric construct with that many pieces to it. Why the icosahedron? Why not the cube? Of course, the cube doesn't have 31 of something obvious so you went and found something which DID have 31 of something and declare it some important fact. This is numerology, plain and simple. You're misusing terminology. You don't mean 'infinite', you mean 'non-terminating decimal expansion'. All irrational numbers have such a property, so what. You're the troll. You have so little knowledge of mathematics you think what you say is impressive or even worth the electrons it takes to transmit across the internet. No, as I just illustrated that third power is NOT the third power of pi but rather the length scale in question. And then only in particularly pleasant geometric constructs. Wow, talk about projecting. I gave you warnings for posts like this, which are so blatently bullshit but which you are so enamoured with that you had to whine to me multiple times via PM. Right back at you. Nothing in your posts or threads are of any scientific merit. If people wanted random facts about integers they can use Wikipedia. Seriously, I cannot believe you think what you say is worthwhile. Have you ever read a textbook or scientific article? Pure numerology. The quantities you use all have units so if we worked in kilograms and not \(MeV/c^{2}\) they would all be different. The mass of the proton in kilograms is \(1.67 \times 10^{-27}\). That's much much less than 1, so it is not a whole multiple of 11. Of how about if we worked in 'natural units', ie Planck units, the mass of the proton is about \(7.5 \times 10^{-20}\) Planck masses. Still not divisible by 11. In fact in kilograms NONE of the elementary particle properties are even close to 1, never mind integers between 10 and 1000. That's the classic mistake made by hacks doing numerology, they are so ignorant of how science works that they do not realise that quantities which has units do not have 'fundamental' values, they depend on the choice of units. The only meaningful quantities in fundamental physics are dimensionless, such as the fine structure constant \(\alpha \approx \frac{1}{137}\), which is that value in any units system because the scalings cancel one another out. Hence if you're stupid enough to try numerology at least do it on dimensionless quantities. Of course then there's a second mistake hacks make all the time which is they fail to realise coupling constants undergo energy scale renormalisation flows so \(\alpha \approx \frac{1}{128}\) at the electroweak scale. Anyway, I'm sure all of this rationality and reality is making your head hurt so suffice to say you've shown you are 'pity', despite calling others that, that you're a 'troll', despite calling others that and that you're grossly ignorant of even the basic qualitative concepts in science. I completely stand by my decision to move this thread to the fringe section. It and everything else you post is without scientific merit and has no place within the main maths/physics forum. If you post a thread in there which in any way resembles this kind of BS you'll be banned for a period of time, as you have been warned. And seeing as you're obviously incapable of evaluating the scientific merit of your own delusional nonsense I'll make it even clearer; until such time as you have demonstrated in the fringe section you're coherent and not a numerology peddling hack said restriction amounts to you not being allowed to post any thread in the main forum.
"non=terminiating decimal" = infinite dude. A Alpha, you really think that Pi or its powers are not "infinite"? http://en.wikipedia.org/wiki/Pi .."Since π is irrational, it has an infinite number of digits in its decimal representation, and it does not end with an infinitely repeating pattern of digits".. If Pi is not infinite then tell my what is the last/final number on the irrational side of the decimal point? The last/final number is limited only to the calculator being used. Even if some don't want to consider an infinite aspect of Pi or its powers, that is irrelevant to almost of all of my post and given statements. So if you or some one else wants to correct me on any comment then do so. Slapping others in the face mentally is not the correct way to behave in any forum and especially for a moderator. imno So, I've never said it wasnt irrational or trancendental and again, for almost everything I've posted "infinite" is irrelevant. Go back and read Alaphas, I stated many times that I was trying to STOP people from considering infinities of Pi. Yeah you ignore those aspects of my posts don't you? Huh? I cubed Pi and now your trying to say I "dont" cube Pi. Alpha, you need to hit the books again dude. Take any number to the third power and that is cubing-- and Fuller can show you how it is also gives same volume count with tetrahedroning but that is an aside for another thread ---. Huh? Alpha I may have flunked 9th grade math by I do know that Pi^3 is a cubing or tetrahedroning of Pi and I've done it and know one has stated any time until now that I or you or somebody does "don't cube Pi" yet I have done it. Please tell me in simple language why the resultant for Pi^3 is in anyway not a valid resultant. Now I say that "you don't" follow simple logic of powering irrespective of whether the number is Pi or not. Huh? What has the question got to do with the Pi^3 that I gave? Absolutely nothing Alapha. You need to address my comments as stated, not as your project some other facts that are not related to my comments as stated. And if you ever really have sincere heart, then you would ask questions to see begin with to see if anything Ive offerred follows any kind of rational logical sense. You do not because for whatever reasons--- like the other troll around here ---have already written me off. So, if and when you want to understand why any of the rational logic for my believing there is an association beyond just a number between Pi^3 and our 31 left-righ skew spinal nerves, I will be happy to explain. Tho I believe I have stated some or most of that info in one or more emails in those regards. Read them address them as stated but you need to see a more wholistic relationship that is occurring and how that may relate to more cosmic/cosmological pattern that is occurring and specifically withing the context of gravitational spacetime. Do you really want to know why? My guess is that it was already given in this thread. Did you read my emails in sequence to attempt to follow any of the rational logic that connects teh dots of my given comments? Dude, I don't think you've really given any sincere considerartion of why not the cube and yes the icosa(20)hedron. It has to do with great/equlaltorial circle planes. My guess is that they are in this thread already and you did not read them, did not read them with any sincere heart to actually have a chance to connect the dots and actually see a pattern of associations between the primary seven axis sets ergo 31( left and right skew ) great/equaltorial circle planes( GrCP's ), 25( GrCP ), 56 GrCP's, 73 grCp's and 87 GrCp's and all the numerics of quantum, cosmological, and biological that I try offer as underlying set of connections that we do yet understand. If you only look at three dots, on a page that consists of a 100 dots, then Alpha, you will not ever be able to follow any rational logic that connects all of the dots into more coherent whole picture. Again, most of the trolls have not and do not ask questions first. They shoot first and do mental head slaps and maybe occasionally one of them will ask a question some 5 - 15 emails later, after the posters head has been mentally slapped by a tag team of shoot-from the hip trolls. Sincerely dude. Your incorrect Alapha, as most of what I stated is facts. You can continue to deny the facts I've given. I will give you that pi MAY not be considered an infinite number by some--- certainly some fi not many do --- but really that is just a matter of where someone chooses to STOP and I give reasons as to why I STOP where I do and again just as physicists did years ago when they kept getting infinite results, the had to STOP somewhere and I believe that their STOPPING of infinite values was called 'renormalization'. And infinite is irrelevant to all most of all of my comments. Your the first one to ever tell me that Pi or its powers is not infinite, so how much do you want to mentally slap-me-in-the-head for something that is mostly irrelevant to everything I've posted and tried to get others to stay away from going off into infinities? Sincerely Alpaha, I dont' know why you or the other trolls want to keep head slapping me, when for the most part all Ive stated is facts? If you want to ignore that truth of mostly facts, then your being a troll. imho. I think it is probably a group of well known trolls complaing to you, when they themselves, have not attempted to have rational logical disscusion with me, for the most part and again, your the first one to state that Pi or its powers are not infinite. Tho again, that is mostly a moot point. Ok fine. I don't mind being corrected when I'm in error. For most part my comments are not in error or if they are it is mostly inconsequential to conveying the basics and connecting the dots on page/scenario that I'm laying out for others to consider. Not head slap. Again, show me where anyone has stated to me in any reply post that it is better or more correct to state "non-terminating decimal expansion". I will argue non-terminating is not any differrent from stateing "infinite' but thats ok. Isnt it? Isnt that what any forum is about, to state what we belive is correct and disscuss rationally and logical our pros and cons? I would love to be in on the thread that actually argues that your "non-terminating" comment is infinite. Because I dont have your level of education i'm a troll? Are you being a snob now Alapha. Maybe your just pretending to be troll by ignoring all the facts of my posts, to avoid having to admit your a snob? Please Register or Log in to view the hidden image! Just kidding, kinda of. Again, I think there is few or alot of your type around here who basically can't stand my level of education--- yet you cant really that much invalid statements by me ---ergo piss on this dude, head slap hime until he leaves etc.... Well, so many of you are wasted about wasted band width, so I'e tell you Alapha, I see more head slapping by trolls--- especially directed at me ---and that is really the waste of bandwidth. So much more can be gained if they stopped being snobby and trolly and begin to do even a 100th of what you have done in these semi-sincere reply to me. HuH? Pleas explain simple language Alapha why following two are not both correct and why if you think the first one is correct, why the 2nd one is incorrect. Please use simple language and I trust you will give us rationally logic explanation that us commonfolk can grasp. I flunked math in 9th grade so that was the last of my formal education. Please keep that in mind. 2.4^3 = 13.824 Pi^3 = 31 00 62....... I have posted mostly facts dude. You need to stop ignoring the facts and address my specific comments as stated, not as you project them to be. Incorrect Alapha and this just your troll if not also snobbery side speaking. I have posted mostly facts from mathematics and science and you ignore almost all of the fact and focus above on "infinite" as being an error by me, and then you state it should be stated as "non-terminating decimal" etc... C,mon dude, for most people I would ask if your on or off your medication if you really belive that "non-terminating decimal " whatever is not exactly the same meaning as infinite if not 99% of being the same meaning. Take note, I replied to your private message before reading this post by you. Here you've made quasi-sincere attempt to actually give a fair trial on two points, trying to use rational logic; 1) tho perhaps "infinite" is perhaps correct is irrelevant for the most part as i explained above, 2) your rational logic to distingush "infinite" from "non-terminating decimal" whatever I find laughble from someone with so much education, and again, please direct me to the thread that argues the pros and cons of your rationale. Please continue to try to be fair Alaha, as I know your a moderator and it must get frustrating dealing with people who are not posting facts as I have done repeately from various sciences along with links when I have them or asked to show them. In my regards, I can give you a list of trolls--- in my regards -- that do more waste band width than I do with the many facts and intellectual explaoration of our cosmos via various sciences. Your chose, have some more moral integrity and trust me when I say, the trolls are trolls becuase they have little moral integrity-- in my regards ---and are not fair. Its that simple. . Well actually it is more complicated but..... Huh? I don't see my original text so i'm not sure what your concern is. If this was the most recent posts of mine, then they are not meant be super accruate--- their approximations --- or have any significant meanings. The most recent was just laying in bed exploring what numbers led to what and 511, .511 and the quark masses was just passing time Alapha. Don't have a cow over the last couple of posts dude. Please Register or Log in to view the hidden image! Huh? I cant makes head nor tails of what it is your going about above. There is a lot of meaningless symbols "tex" in brackets...makes it all screwey. Again, I have posted valid facts for the most part. Deny that and ignore it is just being a troll. Yeah you stand by it because you ignore 99% of the facts I state. Your troll Alapha. You think facts are delusional. Your deluding your self by denying the facts of my statements. Lets see now, how many invalid statements by me have your and all of or your trollbuddies actually found? Huh? How many Alapha? Oh yeah you say Pi is not an "infinite" rather it is a "non-terminating deciemal" whatever. Dude, that is irrational illogical to thing that pi is not infinite and then state that. Your and troll buddies who ignores the facts of my posts. The trolls are the true waste of bandwidth. imho Please come back and talk to me when you have something more valid than Pi is not infinite, it is "non-terminating decimal" whatever.....Please Register or Log in to view the hidden image! r6
Thanks for showing you either didn't read or didn't understand what I and Wikipedia said. I explicitly said that you shouldn't say "infinite" but "non-terminating". I even mentioned irrational numbers and that's exactly what your quote of Wikipedia mentions! Pi is not infinite in the sense of "Larger than any Real", since clearly 3 < pi < 4. The decimal (base 10 or otherwise) expansion of an irrational number is always non-terminating (as well as non-repeating) and thus has no 'last digit'. I corrected your terminology, you complain and then use as your evidence a Wikipedia quote which backs up what I have said to you. Funny, you're the one who needs to read what I said. Okay, it is now clear you are not actually able to read my posts, either because English isn't your first language (perhaps?), you're not paying attention or you're being deliberately obtuse. I clearly explained in what context I was talking about, that 3 dimensional volumes are not related to the cube of pi but rather the cube of the length scale, with the pi factors being dictated by a different thing. You seriously think I said not to cube pi? I said it has nothing to do with volume, which is what you were claiming, in amongst all your numerology, as well as in another thread. You then go on to hammer further on this straw man caused by your inability or unwillingness to read. Since the majority of your post is then just more hammering in that I'll point out another example of your clear lack of understanding of something you talk about a lot, namely this infinite/non-terminating property of pi. As both I and Wikipedia has said, the 'infinite' aspect of pi is in regards to its decimal expansion. What you've just said is that pi may or may not be 'infinite' in this regard, some people view it one way, some another. No, pi is proven to be irrational, it was done centuries ago. Since then it has also been proven to be transcendental. Here is the proof pi is irrational and therefore it's decimal expansion never terminates. If you work with a truncated decimal expansion you aren't working with pi, you're working with an approximation. In school they often use 22/7 for a fraction or 3.142 as a decimal. Both of these are not pi. That isn't a matter for debate or opinion, it is a mathematical fact. You claim to work with mathematical facts and you clearly like to mess around with pi a lot and you obviously like to go around and around with the infinite/non-terminating thing but despite all of your interest and 'facts' you show, again, you are ignorant of even the most basic of mathematical concepts. Of course I'm giving you the benefit of the doubt and assuming you don't interpret Wikipedia's ""Since π is irrational, it has an infinite number of digits in its decimal representation, and it does not end with an infinitely repeating pattern of digits" to mean that pi's value is infinite, ie it is bigger than 10, bigger than 100, bigger than 100000000000000000000000 etc. I have seen hacks who think that if something has a non-terminating decimal expansion then it is of infinitely large value, ie greater than any Real you can name. Just to check, you do accept that 3<pi and pi<4, right? This possible confusion is why I made the clarification in my response, as I have seen people much less batshit than you make that mistake. I could reply to the rest of your post but it goes around in circles, illustrating you didn't understand what I said, plus I have some actual mathematics to do. Unlike you deluding yourself for 15 years you're doing mathematics I have to actually demonstrate the validity of my results.
Pi and Its Powers Reveiwed And I thanked you for your clarification previously in regards to "infinite" "non-terminating" but I still disagree that "non-terminating" is not exactly the same meaning as infinite. Again direct me to the thread where this is being argued pros and cons. It is silly for you or anyone to think that those two sets of words/phrases do mean/infer/imply/suggest the exact same meaning. As for Pi being "irrational", I repeat I've never stated that Pi is not irrational ergo I've never argued that Pi or its powers are not irrational. Micro-infinity Alpaha, micro-infinite. C,mon dude, you know what your stating above is really no differrent than invoking a never ending--- infinite --- subivision of a linear numerical/interger set between any two numbers, which include your givens above of 3 and 4 where Pi begins and ends, only because we say to STOP or the calculator has limited capacity. You appear to being playing some kind of hide and seek of the infinite associations with Pi and or its powers Alapha. Many people, scientific, mathematical or not, refer to the infinite assosciation with Pi and/or its powers. We could say that, if our finite Universe is the a caculator accounting for every discrete quantum of action of all fermions and bosons, then we still arrive at a finite value, onbly because our finite Universe, as calculator, is finite/limited. Sorry Alpha, you and someguy want to go off into base-ten and I cant go there. I have enough to recall and learn about whatever base we commonly use now. What is is duo-decimal ergo 12? Yeah english use 12 and most of the world uses metric and that is base ten is my guess. I dunno. Too confusing to me for to go off on various bases. I have tried to read and reply to your posts to me Alapha. I think when I go into this reply window I only sometimes not getting my original quotes, that your replying to, so kind of hard for me to reference what exactly your above or similar situations are in going on about. Such is the way communication via text, forums, internet etc...appreciate your at least attempting to have rationally logical disscussion with me tho. Such is far and few between around here. Mostly shoot-from-the-hip and never ask questions or rarely, after they've head slapped- a few times. No I didnt say that. Your mistaken. Yeah I think you said "we dont cube pi' but I not only have I posted it and your the first person to even question the validity of such a process. What I did is a valid process to best of my knowledge. So Alpha, if and when you can explain to me in a simple way, that Pi^n is not a valid process than please do so. You have not to date done such and please forgive me if you did and I'm not clear on your specific rational for not powering Pi. I stand by the validity of my cubing/tetrahedroning of Pi. What it means exactly is still debatble. Thx for any attempt by you to clarify what Pi^3 or Pi^4th power may mean to you, and/or if it is invalid to do any powering of Pi then make it clear why it is invalid. I repeat again, I have read your posts and replied to best of my ability. Powering pi is valid operation and you try to make statements that I'm incorrect and can't or "don't" do that from the get go. Now here above you seem to be trying to change your tune and actually allowing for some kind of validity in my powering of Pi. I'm sorry Alpha, but I think you were in error with inferrences regarding Pi powering and jsut trying to cover your error by stating "I did not read". I bet you say that to alot of others. I think I'm pretty clear what you inferred in regards to validity of powering Pi the first time around. I stated that to you early on dude. Limited only by the calculator. Maybe that was the ongoing conversation you having with me privately. It is too confusing to do both. Pi is associated with infinity and you know it. I think your a bit of snob and trying to pull intellectual senority over me. Well you know what i say to that dont you-- no what you say to that dude ---its better than being head-slapped by a troll....ROFL.
You really should not discuss Cantor's actual infinity with me. In ZFC, there is an infinite set of all decimal digits of pi. Let that set be X. All decimal digits of Pi are all in this set.
You're just making up terminology now. Please define 'micro-infinity'. You prove how little mathematics you know. Pi can be expressed in all kinds of ways using algebraic formulae, it isn't dependent on calculators. For example \(pi = 4 \arctan(1)\) or \(\cos(\frac{\pi}{2}) = 0\) or \(\pi = 4 \sum_{n=1}^{\infty}(-1)^{n+1)\frac{1}{2n+1}\). There is a very long list on Wikipedia and it is by no means exhaustive. If you use a calculator to compute some of the terms of pi then you're working with an approximation. If you don't have infinitely many terms in your decimal expansion then you don't have pi, you have a different number. However this doesn't mean pi is infinite in the sense of 4<pi. It is a not uncommon mistake made by non-mathematicians in thinking that if you add together infinitely many things you must get an infinite value. All irrational numbers are expressed in decimals using infinitely many terms and there's plenty of irrational numbers greater than 3 but less than 4, pi being one of them. The fact you think if we added together all the relevant terms we'd get an infinite value for pi illustrates you don't know the most fundamental concepts in mathematics, that of a convergent series. It underpins pretty much all of mathematics because it is how to DEFINE the set of Real numbers. Want a simple example? Let's consider \(\sqrt{2}\). It is defined as the positive solution to \(x^{2} = 2\). Now obviously we have \(1 < 2 < 4\) and so \(1 < x^{2} < 4\). I claim that \(1 < \sqrt{2} < 2\). Square each term and using the fact they are all positive we get \(1^{2} < (\sqrt{2})^{2} < 4\) but as just seen we know that by its definition \(1 < x^{2} < 4\) so indeed \(1 < \sqrt{2} < 2\). Want another way of looking at it? Let's go back to pi. A series which converges to pi is just ever extended decimal approximations, ie 3.1, 3.14, 3.141, 3.1415,... etc. Now this limits to pi. Clearly the '1' after the decimal place will not change as we progress and so it is clear each and every term in this sequence is less than 3.2, since they all start with 3.1.... They are also all obviously larger than 3. Hence 3 < pi < 3.2. Want another way? Let's consider the definition of pi, it satisfies for a circle : diameter*pi = circumference. Every circle satisfies this, circumference/diameter is always pi, for all circles. Now if pi were really of infinite value, ie larger than any Real, it would mean that diameter*pi is also infinite. And that's equal to the circumference of the circle. So if pi is infinite in value it means every circle has infinite size, both in terms of its circumference since the perimeter is \(\pi D\) and in terms of its area, \(\pi (\frac{D}{2})^{2}\). Circles do not have infinite size, pi is not infinite in value. The fact it can be expressed as a sum of infinitely many non-zero numbers doesn't mean it is infinite, EVERY number can be expressed like that. These are concepts taught in school. Geometric progression, for example, is taught to 16/17 year olds. Well done, you know less than a high school student in something you claim to have spent 15 years on. Go you. No, I am not 'appearing' to do anything, I actually am being precise and consistent and correct with my usage of terminology. And many people think the Earth is 6000 years old and humans lived with dinosaurs, "argument by popularity" is a logical fallacy. What matters is truth and fact. Pi is a number with finite value, 3 < pi < 4. It is also expressable as an infinite term decimal expansion, as any number can be, it just happens it must be given its irrationality. You've gotten your terminology wrong, you've made some up and you've shown you don't understand the most basic of concepts within mathematics. You don't like being told that so you whine. You also make stuff up, as I'll get to in a moment. The question is whether you do it deliberately or whether you're just stupid. Metric/Imperial measurement systems are entirely separate from the base our standard arithmetic use. Speaking as a person from England I can assure you we use base 10, ie 10 = ten rather than 10 = twelve, as base 12 arithmetic would imply. Imperial measurements where 16 ounces make a pound and 14 pounds make a stone still represent the numbers using base 10, you're once again confused about the relevancy. Oh and I'd point out that the UK has now largely followed Europe in shifting to a metric system, with imperial units concurrently used for legacy issues. It is the US which still has to adopt the metric system in a complete official capacity. And now on to the bit about you lying.... I didn't say "we don't cube pi", I explained how the expression for volume is not done by cubing pi. The expression for volume of a sphere is \(\frac{4}{3}\pi r^{3}\), we cube the length scale. Of course you can put into a calculator pi^3 and see what it gets, just as you can cube any number you want to. The fact you think I said cubing a number "is not a valid process" shows the astonishing stupidity of your mindset. Seriously? You think I said no one is to cube pi?! That it isn't a valid process?! I clearly explained in my post what I was referring to. Here is the post. I'll even quote the line for you, "Except that you don't cube pi when you consider 3 dimensional volume forms, you cube the length scale. For example, the 'area' for a 1-sphere is \(2\pi r\) and a 2-sphere is \(4 \pi r^{2}\) while for a 2-ball it is \(\pi r^{2}\) and a 3-ball it is \(\frac{4}{3}\pi r^{3}\). The general forms are here. ". Plain and simple and yet you couldn't understand that. I'm sorry you're too thick to understand basic English and formulae taught to 12 year olds, I really am but that is your problem. Misrepresenting me, claiming I said things I haven't said, doesn't change that though. Likewise with your ignorance of mathematics, of even basic concepts like what pi actually is. You've spent 15 years doing mathematics in some capacity? It is, honestly, cringing to think of such a complete waste of time and effort as 15 years. No wonder you whine so much when people call you crazy, you're obviously in denial about yourself. You obviously cannot read. Seriously, I say one thing and you read another. Is English your first language? Seriously, I'm wondering what the explanation for your terrible reading skills might be. The fact I've now explained several times how you're misrepresenting me and how you're factually wrong speaks for itself. Clearly your self denial is what is hindering you. If you were a little more in touch with reality you might actually learn something. Talk? How can I have a conversation with you when you're unable to even comprehend what I said? Again and again you claim I said cubing pi wasn't a valid process, despite me correcting you several times. If you cannot read and process English discussion is impossible. Oh good, another person who cannot form a coherent mathematical thought or statement. chinglu, until such time as you can form a coherent mathematical statement and engage in discussion beyond incoherent assumptions please kept yourself to yourself. Now I'm sure there's a bucket of sand somewhere you have to eat so run along.
I just want to understand. Are you claiming there is no infinite set in ZFC containing all digits of PI?
No one believes this, because you ignore hyperlinks or posts presented to you. A set which contains (nothing but) all the (decimal) digits of \(\pi\) is \(D_{\tiny 10}= \left{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 \right}\). It is not an infinite set. Note that this set has no particular relation to \(\pi\). A set which contains all the natural number (non-negative integers) is \(\mathbb{N}_0 = \left{ 0, 1, 2, 3, \dots \right}\). It is an inifinite set but one without particular relation to \(\pi\). However, \(D_{\tiny 10} \subset \mathbb{N}_0\) so \(\mathbb{N}_0\) is trivially an infinite set that contains all non-negative integers and thus the ten digits of pi. Likewise \(\mathbb{Z}\) and \(\mathbb{R}\), which goes to expose just how flawed your "challenge" is. The following set exponentiation gives all possible mappings from \(\mathbb{N}_0\) to \(D_{\tiny 10}\): \(F = D_{\tiny 10}^{\mathbb{N}_0} = \left{ m | m: \mathbb{N}_0 \to D_{\tiny 10} \right}\). One of these is uniquely special: \( \exists ! f_{\pi} \in F \quad \pi = \sum_{k \in \mathbb{N}_0} f_{\pi}(k) 10^{-k}\) So there is a function or sequence of digits and this function or sequence can be modeled as an infinite set in ZFC in various ways. But if you can't even distinguish correctly between a set and a function or sequence, your question makes no sense. Because there is more than one way to model the function \(f_{\pi}\) as a set there is no set which uniquely models the sequence or function \(f_{\pi}\) and thus your "X" is not defined well enough to be specified in ZFC.
Highly Educated at PLahying Dumb Micro is towards zero--- and eternally short of ever arriving at zero, < 3 or any number and greater than 0, or, towards infinitely smaller scales of subdivision between any a set of two numbers. Do I really need to get dictionary definition of infinity for someone with your educational background. Your playing dumb, again. Your playing dumb and both accounts above. You know very well the concept/scenario of infinite subdivision between 0 and 1 or etc....2 as i have mentioned previously to you in this thread or the private posts. To confusing doing both. And you also know very well that macro is eternally going away from zero ergo eternally addition. Go play dumb with others trolls who like such mind games. Again, you like to make arguments with yourself as tho to insinuate I've stated otherwise. The number of decimals of Pi is dependent on a calculator and that is all I've done and posted here and you want to play dumb mind games that in no way detract from the validity of given facts. Come back and talk to me when you have something rationally logical that invalidates my given comments as stated starting with the first post in this thread. You have not to date done that yet you claimed or inferred/suggested/implie etc....that pretty much everything I've stated is "BS". Nothing you have stated invalidates my given facts and you cant handle the facts of my comments as stated. Duhh, thats what I've done with the powering. Go back and read my comments in posts, as stated. Ok so all of my given facts or approximations of infinite Pi. The rational side of Pi or its powerings never change and the irrational the first numbers change less and less as go refine Pi to greater decimal places towards macro-infinite set of irrational decimals. And again, If I started out in this thread by stating Pi is infinite when it is not, then it is insignifcant error on my part, since you and many others keep associating infinity--- "non-terminating" --- with Pi. So again, direct me to the thread that argues that "non-terminating" is not the same as infinite. You typed "4<Pi" and makes no sense you must be in error I think you meant Pi < 4. Irrelevant the intentions of this thread. There you go again, like so many others, who associate "infinitely" with Pi. Huh? I don't recall making any such claims. Alapha you do as much misrepresenting of others text as anyone else dude. Or do you think you never error, intentionally or otherwise? Duh, your telling us that 3 < the Pi is not new news to anyone Alpha. I think you spend a fair amount of time arguing with yourself, or is that what they call putting in place and strawman, and arguing with it. It is very clear by your own statements--- and many other humans on Earth ---that Pi can and does have an association to infinite. Yes a curved circle and and a Euclidean triangle are both 2D, and finite, but Pi is also associated with an infinite set of angles of a the most purely abstract conceptualization of a circle i.e. the most highly refined circle is an infinite set of angles that define such abstractly pure circle. This latter above also means that the no such circle exists in reality as it is mathematical concept only. If you can't understand that, then you need to consider the alternate cases for 2D triangle; Riemman( 2D convex ) > 180 > degrees i..e the sum of the angles is great than 180 degrees, and, ..take note here again Alpha the arrows also direct us in the direction of macro-infinity.... Lobvskian( 2D concave ) < 180 < i.e. the sum of the angles is less than 180 degrees. ...Take note here again Alaha the arrows also signify in the direction of micro-infinity... Ok so diameter is equal to circumference and I think what your saying is that, if the diameter is finite then the circle is finite and if that is the case then Pi is truncate at mimumum at the rational #3. If we want a more refined circle then we truncate 3.1 or is it 3.000000000000000009 or something in that direction which is toward the direction of 3.1. Here my math skills begin to disintegrate. A purely abstract 2D circle enclosure has infinite number of angles. The minimal set of angles for a 2D enclosure is 3 and is called a triangle. You have not yet invalidated any of given facts as stated. Pi has an association with infinite. That it is not a an infinite number does yet make sense to me, but that is insignificant to my given facts as stated and that you have not invalidated in any way. If anything you've mostly convoluted the issue for those readers who do not have your eductational background to follow of your mind games with terminologies. Ex "non-terminating" is more correct than saying infinite. That makes no sense to me and imagine not to most common people have some grasp of those words. Direct me to the thread that argues that "non-terminating decimal expansion" does not equate as Barring your errors, then again, when you have something to offer that invalidates my comments as stated then please share. I've yet to see you do that and certainly with a simple terminologie or math that those with out your educational background can begin to make sense of. My given powerings of Pi is simple fact that anyone can do with a calculator adn not the repeated "BS" you attacked me with. Sad lack of integrity on your partPlease Register or Log in to view the hidden image! Irrelevant strawman analogyg Alpaha, as you and many others associate Pi with infinity. You have offerred nothing to invalidate my Powerings of Pi. Come back and share when you have something that addresses my specific comments so as to validate your "BS" attacks of my Pi powerings as stated. I did inferred both in my opening statement of this thread and yove attacked me with "BS" like comments aftewords. You were in error then and still in error, in regards to my comments as stated, not to mention mostly facts of my comments. Your "BS" and other type comments were unwarranted. When you can address the specific comment by me that is in errot with relatively simple, rational counter-argument I will read, and make my best attempts to understand, where appropriate to the my intentions of this thread, as stated. Ok, so the Brits and U.S. both use base ten. Again, your going of the my educational background ergo I can see no relevance to my given facts of comments as stated. Yea! The more the merry. imho I put in quotes what was the best I could recall of what you stated and how it appear to be intended. P^3 = 31.00 62 7 is valid, fact, and is XYZ powering procedure/process/methodolgy etc...to best of my knowledge and you've offered nothing that shows my assessment is invalid or does not refer to 3D space, in some way or another. I asked you what does, if anything does the process mean to you. So once again, what does the Pi^3 process/method mean to you, if anything? 31 great/equaltorial circles enclose a 3D space and I believe this is a cosmically mathematical relationship occurring here that crosses over into or manifests in our reality aka occupied space called Universe Pi^3 is XYZ process with assessing some relationship associated with 3D. Cubing also equates tetrahedroning and there differrent shapes. Yeah, and you you like to play dumb. You doto know what I mean, and that most of my comments are facts or referencing facts. I dont have your comments from them, sorry I put what i thought was teh closes approximation of what you stated in quotes. You did use the word the word "don't" and again I thought you said cube whatever. Go back and look for your self if you havent deleted it. It is irrelevant to the Pi^3 is valid process and I have done, and anyone can do, so your "BS" comments were unwarranted. What isn't a valid process? I do not see my comment your addressing in this window. Ok fine Alpaha length^cubing or tetrahedroning. I've stated what I belive P^3 means to me and given other facts I believe are interrelated mathematically cosmically whole conceptual set, and I believe those have relationship to our reality and gave rational logical reasoning explanations for my conclusions. I understand what I get when I do a powering of Pi, now you can keep throwing out all kinds of partially tangent and/or irrelevancies strawmans aside and keep your "BS" remarks to yourself for a what my calculator states, and all of the other mathematical facts I've stated. Fairenough Alpaha, but that shoe goe/flies/fitss both ways and quite often happens in forums or any communication that relies so much on our typing in our thoughts to convey concepts. Hey dude, I never claimed to be and expert on Pi or any mathematics. I'm just stating some facts, seeing possible cosmic associatsions both matehetmatically in our occupied space reality we call Universe. Yeah, as a hobby in evenings after work. My first significant geometric findings--- early 90's ---was of the quasi/semi-orderly pattern of prime numbers expressed geometrically. I sent my findings to three science-like magazines and then 6 months later I get a letter from a well known--- a that time -- mathematician with return address of OXford University England/Britan. Wow! was I suprised. He told me that he ahd never seen this geometric pattern before and that the algebraic forumlae for expressing it had been known for some 200 years already. So still, I felt pretty good for discovering myself just using pencil and paper. I lost my free web service via my ISP 6 months back so all of graphics explaining that pattern and others on the net, no longer there. Please Register or Log in to view the hidden image! Well you like to degrade me and you don't really know much about me, my circumstances for last 15 years etc..... What I know is, that you "BS" remarks were unkind, unwarranted as is all of your other derogatory remarks from you first post to me. When you actually have something that invalidates the my statements of facts and processes I have presented then please share. I've yet to seen anything of any significance, to invalidate my comments as stated and certainly not anything that is simple and clear for teh less educated to understand. Come back and talk to me when you have something valid that directly addresses and invalidates the the facts and intentions of this thread and my posts. r6 You obviously cannot read. Seriously, I say one thing and you read another. Is English your first language? Seriously, I'm wondering what the explanation for your terrible reading skills might be. The fact I've now explained several times how you're misrepresenting me and how you're factually wrong speaks for itself. Clearly your self denial is what is hindering you. If you were a little more in touch with reality you might actually learn something. Talk? How can I have a conversation with you when you're unable to even comprehend what I said? Again and again you claim I said cubing pi wasn't a valid process, despite me correcting you several times. If you cannot read and process English discussion is impossible. Oh good, another person who cannot form a coherent mathematical thought or statement. chinglu, until such time as you can form a coherent mathematical statement and engage in discussion beyond incoherent assumptions please kept yourself to yourself. Now I'm sure there's a bucket of sand somewhere you have to eat so run along.[/QUOTE]
Revising and Reclarifiying Previous Reply( We do power Pi ) Hi Alphas, I realized later how tired I was in my last reply to you ergo not thinking clearly. Micro = >IN< Macro = <OUT> If you still need help understanding the word infinite either singularly or in conjunction with either of these two above, I'm here to assist you. It should be simple for someone with educational level, tho maybe that has become a hinderance for you. I dunno. My last formal mathematics educations was in 9th grade and I nearly flunked out. You will have to allow yourself to be more tolerant of those who do not have your educational level. imho Again, I'm sorry if that is what has happen during this back n forth complex of texted ideas. I think that is quite often occurrence for all parties involved beyond just myself and you. The basic feeling of your intentions is to degrade me and not address the facts I posted as facts. More degrading text that is uncalled for and uneccesary. Pi^3 is a valid process/method/procedure and has what I've done with my calculator from day one of the seeing the possible connection of 31.00 62 7 to 3D 31 great/equaltorial circle planes of the icosahedron. You made some comments that implied via words like we "don't" cube Pi etc......and I've made clear that I 'do' powering of Pi irrespective of what "we" your or others may not do. Get yourself a calculator Alapha that has Pi symbol on it and x^3 or x^y symbol on it and you too can cube/tetrahedron Pi. So if want to do as you suggested somewhere in one of your replies to me, that assign a value to the XYZ edges/lines of such cube, the what 'we' are doing with a calculator is giving the truncated Pi value to each XYZ edge/line i.e. my given 31.00 62 7 becomes the 3D volumetric number of cubes or tetrahedra. That is fine and dandy by me, and never really considered that fact as being relevant to my considerations of the 3D 31 great/equlatorial circles of the icosahedron. If there is someway of equating the cubic or tetradral volume to an spherical defined by 31 GrCP's, then I'm not aware of it. Actually it do so, might be akin to Archimedes squaring of the 2D circle or was circling of the 2D square? :--) So has anyone ever cubed or tetahedroned the sphere, or is it sphericalized the cube? I'm sure some human has attempted it and gotten approximations, just as Alpha likes to make clear, any truncation Pi is less accurate than infinite/non-termination of the irrational side decimal expansion, approximation of circles diameter to circumerference relationship. I'm just a simpleton oberving the facts of my cosmic explorations, and speculating on possible underlying order of Universe, and primarily via gravitational spactimes relationship to all other ferminonic matter, and bosoninc forces or any combination thereof. I'm not afraid to be naive and my not having higher degrees of education assist in ability to be naive and open to possibilties. imho None of what I've offered is in anyway likened to classical/standard/pure numerology as Alpha and others have suggested/inferred/implied. And I was in error to say I have never ever added the sequential integers of number together. I did do that once years ago, and confirmed to myself that was irrational, illogical process/approach to understanding a true nature of our Universe. Recently tho someone did reply to my some of my most recent playful pondering explorations of Pi^4 / 4 = 24. 35 22 7... where I had pointed out that the .35 was rationally divisible 7 and others should by now know my thoughts on the signficance of #7. So anyway this dude does a sort of reverse numerology thingie on me i.e. he asked me to notice that the 22 / 7 = 3.14 28 57 14 28 571428571428571428571..... Well yeah I was enamorued by the the reference back to Pi( 3.14 ) but I was quick to point out to the person that they were doing a reverse numerology process i.e. instead of adding integers from left to right he was dividing. r6
No, no you don't and that is your problem. And rr6, if you're unfamiliar with and unable to use terminology and coherently form sentences that isn't my problem. Feel free to continue whining in this pseudoscience forum, it's the most you'll ever achieve when it comes to mathematics.
Micro-infinite and macro-infinite are relatively simple concepts to grasp. imho Again, I was only mentioning that the irrational side .35 was evenly rational by 7 and he was pointing out that 22 / 7 creates are recursive/repeating set of integers. So irrespective of how this appears as just numerologically interesting coincidence, the facts of their existence and operational mathematics as stated. Again, it is further confirmation of #7 having a STOP like function i.e. no need to go further into inrrational infinity. Again this is simple, not complex, obvious facts so trolls need not apply. r6
I notice that you have your own definition for terms so I imagine your made up defintion for a troll is someone with greater than a highschool education that points out that you are posting ignorant gibberish.
Non-terminating Decimal = Infinite Non-terminating decimal = infinite decimal. Duhh! Fine structure constant/alpha = 0.00 73 i.e. rounding off of 0.00 72 99 87 primary circles - 14( redundant ) = 73, non-redundant, primary great circles. Pi^3( 3D ) = 31 . 00 62 7 where 7 falls in the 7th integer place/position when considering both sides of the decimal point i.e. both rational and irrational sides. Pi^4( 4D ) = 97.40 90 9 and / by 4 = 24.35 22 7 97 / 31 = 3.12 90 rounded off to 3.13 is almost Pi( 3.14 ) just a little less. So in review, we have 7 axis sets i.e. 3, 4, 6, 12 of the VE and 6, 10 15 of icosahedron which totals to 56 primary sets, when not considering left and right skew sets of the icosahedrons 31 GrCP's. 56 / 7 = 8 8 shares common 4 axi of tetrahedron, 4 axi of octahedron, 4 axi of icosahedron, 4 axis of cube, 4 axi of VE/cubo-octahedron--- here they actually define the VE/cubo-octahedron. So 4 is very common but so is 12 and 12-7 = 5. 12 surface angles of tet. 12 chords of octahedron 12 chords of cube 12 nodal vertexial events of the VE 12 nodal vetexial events of the icosahedron 12 faces of the pentagonal dodecahedron 12 faces of the rhombic dodecahedron What I'm coming to realize, is that there is the diametric axis association as mentioned above, but the each great circle also is a central axis of toroidal tube/ring/torus/tori. So 87 or 73 or 56 great circles is actually great toroidal tubes. A equaltorial/great circle is central axis of a great toroidal tube ex a texticonic symbol/simple may be as follows; O or as ( ( ( ) ) ) where blue is outer, green is central axis and red inner. http://en.wikipedia.org/wiki/Torus A great toroidal tube has four kinds of great circle associated with it; 3) outer great circle on surface of great toroidal tube, 2) great circle as central--inside the tube---axis, 1) inner great circle on surface of toroidal tube. The central axis can be likened the spinal chord of a biological with nervous system. ..think nematode/worm..... The great circles are associated with three aspects of a polyhedron; 3) the vertexes/nodes/crossings/intersections/joints/knucles/points---*--- ...these have the greatest/longest diameter---diameter is two radii--- 2) the chords/edges/trajectorys/vectors/relationships/struts---____----- ..these have next longest diameter/two radii... 1) the faces/surfaces/openings/planes/hedra--- /\ ---- ..these have the shortest diameter/two radii.... The toroidal tube has three differrent diameter associations. 3) outer diameter (-------) 2) inside central diameter (-----), 1) inner diameter(---) Proton, neutron ergo hadrons are associated with 6 great circle tubes of the duo-tet-cube, imho; OO--OO--OO http://www.rwgrayprojects.com/synerg...igs/f5511.html The electron is also associated with 3 great circle tubes, that are double valenced as 6 GrCTubes as the contracted octahedron, imho; (O)--(O)--(O) http://www.rwgrayprojects.com/synerg...igs/f6008.html When constructing a octahedron from great circle or polygonal paper planes it takes 6 paper planes to do it. r6
4 GrCP - Pi Associations Since the torus has four differrent great circles it has 4 differrent Pi ratios. Interesting that the Vector Equilibrium is defined by 4 cGrCp's and the torus has 4 differrent GrCP's. SPACE (( SPACE )) SPACE = torus/tori/toroidal ex a doughnut(( )) SPACE (*.*( SPACE )*.*) SPACE = torus with tubular content/body i.e. content/body between the inner and outer surface of tube. Volume = 2 × π2 × R × r2 Surface Area = 4 × π2 × R × r Ive tried for years to make correlation between spherical VE and the torus but sphere and torus are not topoogically equilvalent, so it is difficult find a synonomic/same connection. Actually been a few years since I looked into this. r6
Pi^3 31.00 62 7 66-----Pi^3---ergo 3D ie XYZ or abc ...icosa(20)hedron has 12 vertexes.. ...icosa(20)hedron has 30 edges. ..66 / 3 = 22... 24.35 22 7 27----(Pi^4) / 4----abc + time ..cubo-octahedron/Vector equilirbium has 12 vertexes... ..cubo-octahedron has 24 edges/chords... ...27 = 3^3.... 3.14 15 92 65 35----Pi----a ..14 = 7 + 7.... ...icosahedron has potential for 15 golden rectangles 9.86 96 04 40----Pi^2----ab 97.40 90 91 03 40 02--Pi^4----abcd ...a zero in almost every dual numerical set... --hyperdimension begins with 'd' i.e the volumetric diagonal of the abc/XYZ cube..... ...hyperdimension = cells or polyhedral within polyhedra ex cube withing cube with 8 diagonal 'd's' connceting inner cube to outer cube http://en.wikipedia.org/wiki/Hypercube
