Bignose

It's just another of math's undefined terms, like 0/0 or infinity/infinity. In general these have no meaning, though sometimes they can point out where problems are.

Any chance that any of my (in my opinion) valid points will be addressed? Why aren't the zones affected by the wobble in the Earth's rotation and the instability of rotating fluid flows?

Cap'n, don't overlook some of your local large state colleges. I've attended or been friends with people who've attended 6 different state/public schools, and while none of them have the giant reputations that MIT or CalTech or Cambridge have, they still have very excellent programs, and very excellent professors. * Good questions to ask those kinds of schools would be to find a course catalog (probably online) and ask the administrators in the physics and math programs how often the advanced classes have been taught. I.e. if most of the advanced physics or math classes have been taught once every two years, then there is a good group of faculty there. If there haven't been taught in a long time, then there probably is no one knowledgeable enough to teach them or no interest from the students, and the program may not be good at the higher levels. Really, apart from "bragging rights" the name of the school on the diploma isn't that big of a deal. Even in the academic world, the quality of your work (research) means many times more than the name of the school you are stationed at. * I wanted to interject a comment at that point, but it didn't flow with the rest of the paragraph, so I'll add it here: Depending on the kind of experience you want, going to a "big-name" school can be downright awful. I had a friend who did go to MIT. And while they overall enjoyed the experience, he told me quite some horror stories about faculty availability. Things like, if you wanted a half-hour meeting with a professor to talk about the subject material you are covering in class, you'd have to get with the secretary and schedule something 3, 4, or even 6 weeks in advance! Now, today, all professors are busy. The average professor sits on something on the order of 10 different committees now (i.e. school committees, that doesn't count thesis/research committees). But, the average professor at a larger state school isn't anywhere near as harried as the average professor at MIT or CalTech. All my friends and I who attended state schools noted that while there were some individuals in the departments who were that busy, most of the faculty members were happy to have open-door polices, and invited students to come in and talk at length about the class material, or even just talk about the subjects in general. I would confidently count several professors in my department as friends. They weren't super-close friends or anything like that, be we had good discussion on what I wanted to do as a career, the experiences the professor had had in industry and academia, etc. My friend that went to MIT pretty much confirmed that such a thing would be impossible there. So, again, every individual's experience will vary, but I am more of a laid-back casual person, and I don't think that I would be very happy as a student at such as place as MIT. But, that is just me. Some people crave and thrive in such an environment, so, it really comes down to how well do you know yourself.

No other real-world fluid does this because of turbulence. Real fluids are never perfectly symmetrical. Why should this be the case with the Earth? Rotating fluids aren't inherently stable. They form bands, called Taylor vortices. Look in this picture: http://www.kgroesner.de/forschung/experiment/taylor2.gif This picture is done with cylinders, but the same thing can be seen with a rotating sphere. See Bartels, "Taylor vortices between two concentric rotating spheres", Journal of Fluid Mechanics, 1982. Besides, the earth itself isn't perfectly symmetrical, in shape or in rotation. The earth is shaped like a sphere with a fat tummy, even if you ignore things like mountains and valleys. And the rotation has a wobble in it: http://en.wikipedia.org/wiki/Chandler_wobble Shouldn't these "graveyards" move in accordance to the wobble? Shouldn't these "graveyards" move in accordance to the instability of the rotating flow?

As Stephen Colbert would say, why let a little thing like facts get in the way of the truthiness you feel in your heart?

This is a more difficult question that you may realize, because one can become a very accomplished mathematician in one aspect of math without even knowing the basics of the other aspects. I.e. one can become and expert at discrete probability and statistics without ever taking a calculus class. One can become an expert on solving differential equations and proving existence and uniqueness of those solutions without necessarily knowing anything about abstract algebra. There are many experts of discrete mathematics who are very weak in continuous mathematics. So, it isn't as simple as there being any one order to take math. That said, there is a natural progression and it is probably worth knowing the basics of a lot of different branches to see what part of the tree you want to go up. You'll probably want to take calculus, a good probability and statistics class, and some discrete mathematics and build from there.

Ok, so what? The point is that the series I gave follows exactly what the OP wants. You can take any [math]a_0[/math] you want, it is will still halve the number every step in the series. It performs exactly what the OP wanted.

[math]a_n = \frac{1}{2}a_{n-1}[/math]

I didn't read the whole thing, but this leapt out as dead wrong. Power is the time derivative of Work [math]P=\frac{\partial W}{\partial t}[/math] And Work is the integral of the force times distance [math]W=\int \mathbf{F}\cdot d\mathbf{l}[/math] And force is mass times acceleration [math]\mathbf{F}=m\mathbf{a}[/math] So, the relationship between power, P, and acceleration, a is: [math] P = \frac{\partial}{\partial t} \int m \mathbf{a} \cdot d \mathbf{l} [/math] Power definitely isn't the product of mass and acceleration. Maybe you meant work, but it certainly isn't power.

Atheist has it spot on. Put some numbers in there to show it to be wrong. Let a^5 = 7 and let b^5 = 10 8*7*5 + 10*7*5 = 280 + 350 = 630 = 18*7*5 Not 18*(7*7)*(5*5) = 22050

Not necessarily. What is the expansion is governed by a function proportional to [math]r^{2.5}[/math]? Or something like [math]r^3 + e^{0.001r}[/math]. You only get linear functions as the result of one or multiple differentiations if the function is a polynomial with integer exponents. There are many, many other functions out there.

Remember that taking the derivative for polynomial functions will decrease the exponent by a full unit. In this case something is to the power -3/2, after taking the derivative it will have to be the the power -5/2. If you didn't get something to the -5/2 power, then you made a mistake. Use the product rule and the chain rule and you should get the result the book printed.

Shouldn't your thesis adviser know how to get something published in your field? It basically is you submit your work to a journal that published papers on the topic that your paper is on. All the journals have the rules for submitting papers to them on their webpages or in their hard copies of the journals (i.e. there may be certain ways to cite papers, or a certain format, or a certain electronic format (MS Word vs. TeX) or a certain minumum or maximum length). Then, it gets refereed, and it is either accepted (usually with some minor or major revisions) or rejected. Like I said, your thesis adviser should have some good ideas about what journals are a good fit for your work. At the very least, you should have some good ideas because you should know what journals you read the most papers from for your own work.

Ok, I'll request them. Peer reviewed sources as much as possible, please.

No traveler, the point is that it is impossible to say what is moving and what isn't. Consider a universe where there are two balls, one red and one blue. The distance between the two balls is increasing at 1 m/s. Which one is moving? It is impossible to say because it differs depending on the reference frame. I.e. if we choose a coordinate system that keeps the red ball at (0,0), it appears that the blue ball is moving. If we choose a coordinate system that keeps the blue ball at (0,0) is appears that the red ball is moving. If we choose a coordinate system that keeps (0,0) right between both balls, then it appears that both are moving. Which one is "correct"? The answer is that they all are, from their point of view. There is no such thing as a preferred reference frame -- the laws of physics work equally well in ant reference frame. And, it is also impossible to tell which scenario is true (red ball moving, blue ball moving, or both moving). Because we can choose a frame that makes each of the scenarios true. So, in effect, any object can have a velocity of zero, if you choose a coordinate system to follow that object. The definition of velocity is intricately linked to the definition of coordinate system. If the object doesn't change coordinates -- say by using a coordinate system that keeps the object at (0,0) (or any other fixed point), then the object has no velocity. The big thing is that coordinate systems are an invention of mankind, and are primarily chosen to make the math easier. Nature doesn't know if you picked a coordinate system to follow one object or another, or it you picked Cartesian, cylindrical or spherical coordinates, not does Nature care. Because there are no coordinate systems in Nature, any and all different ones are equally valid. And indistinguishable.

All the unit conversions are done in the same way, whether the unit is in the numerator or denominator. For example, I would do this unit conversion like: [math]\frac{1}{cm} \cdot \frac{1 cm}{10^7 nm} = \frac{1}{10^7 nm}[/math] where the cm in the numerator and denominator cancel each other out. Note that since 1 cm = 10^7 nm, that the [math]\frac{1 cm}{10^7 nm}[/math] is equal to multiplying the term by 1.

Don, this is getting beyond silly. You are ascribing meaning to using Arabic numerals. A number is no more or less valid if it is written in a different way. By your logic, Roman numerals are less valid because they would take more than 1 symbol to write. II isn't good because it takes two symbols to write. But, 2 is okay because it takes one. Neverthemind that II and 2 represent the same thing. Those Roman numerals that only take one symbol to write must be really, special, eh? V, X, L, M, C, D. Those are the good ones, right? It's a good thing that we don't commonly spell out the numbers. Because two is clearly inferior to 2. As is zwei, dos, deux, twee, due, etc. etc. All those require more than one character to write out. It doesn't matter what you use to represent a number. So long as that number is clearly defined. I can write x = 2 = 1+1 = 3-1 = [math]{\sqrt{2}}^2[/math] = 14/7 = 1.99999999999 repeating = [math]-e^{i\pi} - i^2[/math] = II = zwei = [math]\int_0^2 y dy[/math] = any of an infinite other number of ways to result in 2. They all have the same value. Just naming something x and saying nothing else confers no meaning whatsoever on x. And, yes, Don. Sometimes the entire universe is indeed represented by one symbol. When mathematicians deal with a very specific problem on a specified domain, a symbol that is often used to represent that domain is [math]\Omega[/math]. And, in regarding that problem, the is the entire universe to that problem. So, yes, the entire universe is often represented by a single character. You will see this notation often when integrating over the entire domain. Something like [math]\int_{\Omega} \rho(\mathbf{r})d\mathbf{r}[/math] is common when integrating a density [math]\rho[/math] over a domain, for example. ============= While I think that Don was very dishonest about his intentions and very self-aggrandizing at the beginning of this thread, there could be some value to the work. It may have implications about the Beal Conjecture. I do think that Don needs to start a new thread specifically about the Beal Conjecture and talk about his possible results there. He does seem to miss the point that just because a variable only takes 1 character to write out doesn't confer on it with any special meaning whatsoever. If you want to limit a variable to certain values, you state that as part of the description. Period.

Right, I made a small mistake there. But, nevertheless, irrational and transcendental bases do exist and are used. The value of 7 in a base [math]\pi[/math] system would probably be an irrational number. It doesn't really matter if you think it is meaningful or not, it nevertheless can be done. And that's my point. We can choose any base so that any number can be written with just one digit. Just the fact that it can be done defeats your logic that just a symbol x must represent a single digit (base 10) integer. Because any number, rational, irrational, positive or negative, can be represented by one character. It doesn't have to necessarily make sense to you or to anyone, it can be done.

Don, I hate to seem like I am beating a dead horse here, but there are other examples where I can show your logic wrong. Consider a number in base [math]\pi[/math]. In such a base [math]\pi_{10} = 1_{\pi}[/math] where the subscript denotes the base. That only requires one symbol, "1", if you are working in base [math]\pi[/math]. (And, yes, there has been a base [math]\pi[/math] proposed, see Bergman, G. "A Number System with an Irrational Base." Math. Mag. 31, 98-110, 1957/58. as one example) There have also been transcendental bases proposed, even negative number bases. If you are going to include that in your considerations, then again, I think that every single number can be written in "1 character". So, once again, every single number is a good as any other, real, rational, irrational, etc. The bigger point is that you understand the need to state upfront the restrictions on the variables, don't you? Otherwise, pretty much everyone assumes that any variable can take on any value: integer, negative, real, or complex.

Let's look at results the equations of fluid mechanics give us: If the fluid is at rest, and gravity is in the negative z direction, the Navier-Stokes equations (actually the full conservation of momentum equations, N-S is specifically for Newtonian fluids only) becomes [math]\frac{\partial p}{\partial z}= - \rho g [/math] where [math]p[/math] is pressure in Pa [math]\rho[/math] is density in kg/m^3 and [math]g[/math] is the acceleration due to gravity Now, for an incompressible fluid, like water, the density is constant, so the integration of the equations above is easy: [math]p = \rho g h + p_0[/math] where p is the pressure at a height, h, from the height the reference pressure, p_0 was taken from. Now, with a compressible fluid, like air, density is not constant. If we use the simplest relationship between a gas's temperature, pressure, and density, the ideal gas law, this is: [math]\rho = \frac{p}{RT}[/math] where R is the gas constant and T is the temperature Putting that equation in for density and integrating the above equation yields: [math]p_2 = p_1 \exp[-\frac{g(z_2-z_1)}{RT_0}][/math] So, you can easily see how the pressure goes down exponentially, even assuming the acceleration due to gravity is constant. Pressure and number of molecules are basically the same thing as pressure is caused by the impact of the the molecules running into things.

Utterly ridiculous. X is a variable. In fact, in mathematics, it isn't even formally correct to just leave X hanging out there by itself. You should write something like [math]X \in \mathbb{Z}^{+}[/math] where [math]\mathbb{Z}^{+}[/math] would represent the non-negative integers. There are other symbols used other than Z, but the point is to define what the variable is limited to. In general, the assumption is if there is a variable without explicit limits on what it's domain is, it is completely open. I.e. [math] X \in \mathbb{C} [/math] where [math]\mathbb{C}[/math] is the set of complex numbers. Negative, positive, zero, imaginary, and reals are all in play. A big part of mathematics is being as explicitly clear about what your symbols mean as possible. Just because you interpret a symbol one way doesn't mean that everyone else is going to interpret it that same way. Read any mathematics journal article (if you are planning on trying to publish your work, you should read a lot of them to get a feel for how it is going to be expected to be written, anyway), and they will state up front exact what every variable means, and what its values are limited to. Even many of the engineering and physics journals have a table at the begining or end of the article listing what every variable means (and as such explicitly or implicitly what their values are limited to. I.e. if an equation is written for total kinetic energy, k, it is going to be a positive real). Had you stated this limitation up front, it would have saved much, much consternation. =========== Your logic "told that it represents a number" is kind of illogical to me anyway. Why is 10/3 not as good of a number as 10? Both are "numbers". Aren't [math]\sqrt{2}, \pi, 14.101001000100001..., \frac{17}{13} [/math] numbers, too? Furthermore, your logic also limits X to just 0,1,2,3,4,5,6,7,8, and 9. Because anything else would require "more than one symbol" to write it out. 10 requires two symbols. I just sure hope you don't ever work in binary, because, then you'll only be limited 0 and 1! But, [math]\pi[/math] or [math]e[/math] or [math]\phi[/math] are numbers that only require one symbol to write out -- are they supposed to be included too? [math]\frac{6}{2}[/math] is a number, too. It happens to be equal to 3, but it requires more than one symbol to write out. You probably didn't want to exclude it from consideration, did you? The only time I've ever seen a variable be limited to the number of characters it takes to write something out is on those "letter" math puzzles: somthing like M A T H + F U N ---------- C O O L and the trick is to figure out what digit each letter stands for. That doesn't mean that there isn't math out there like that, I just have never personally encountered a variable interpreted in that way before. ==== Just be more forthright about your intentions up front, and everyone will be happy. I actually don't know anything about "co-primes" and "cohesive terms" and what not, but know a lot of applied math (i.e. solving differential equations, integro-differential equations, statistics & stochastic calculus, etc., stuff as it applies to physics and engineering). I don't know a whole lot about the more fundamental stuff. But, when someone shows up telling us that canceling is wrong and saying nothing else, it is going to rub people (i.e me) the wrong way. Had you stated up front that your variables were all going to be limited to non-negative integers, well, then I think that the reception you would have gotten would have been a lot friendlier.

To take a slightly different tack this this conversation, most people know a lot more calculus than they ever thought. I.e. we intuitively know how long it takes a dropped ball to fall to the ground or similarly at what angle and how hard to throw a ball to make sure it gets to another person or place; anyone who's driven a car for even a short amount of time knows how hard to press the brake pedal so the car stops in front of the stoplight or the car in front of you; we know concepts like what goes in must come out (conservation of mass) that are formerly written in terms of differential equations or as surface & volume integrals. Certainly, it is pretty uncommon to find a person who can express these concepts in mathematics, but a lot of people know them.

This is NOT what this thread started talking about. (The word "integer" doesn't even appear until the 32rd post!!!) You asked if your equation was true, and called it "the most important equation ever". No talk about co-primes or limits on the exponents. Only talk about why canceling of terms is wrong (which it isn't). Check the first few pages of this thread. NOW, this stuff about coprimes and whatnot. If that is what you wanted to talk about, why didn't you just state it up front? Why the deception? What was the point of asking about one thing then turning it into a discussion of something else, when that something else is obviously what you wanted to talk about in the first place? Also, you never did "show" why canceling is wrong. Maybe you've showed that indeed when the common factors are divided out, one of the exponents has to be 1 or 2 (when limited to non negative integers). But that doesn't make canceling wrong. They are almost totally two different topics. I really feel like you've wasted a lot of people's time here, because you weren't upfront about your intentions. You never said anywhere at the beginning that your variables in you equation was limited to non-negative integers. Had you done so, it may have saved a lot of trouble. How were we supposed to know that? Just read you mind? You have to state these restrictions. And what your main point is -- we did ask you what your point was several times. All you've really done now is 1) people probably aren't going to want to discuss your work in this thread because it is so filled with things that you really didn't want to discuss in the 1st place and 2) if you should start another thread, people are going to wonder if the first post in that will actually be about what you want to talk about. Don, this forum is a good place for discussions like about whether your proof is complete or not. But, you have to be upfront and honest about your intentions. This end around nonsense just annoys people. And, whether intentional or not, as was mentioned above, your tone comes of very condescending and arrogant. If you want to discuss your proof, then I suggest you start a new thread -- with a less grandiose and arrogant and more on-topic title -- and discuss the idea there.

But jerry, you didn't show any interest in my banana slinky theory or mooeypoo's pink elephant theory. Turnabout is fair play, both of these have played by the exact same rules you applied. If you want people to take you seriously, abide by the rules of this forum and abide by the principle of science, and you'll get a much warmer reception. Otherwise, sorry to be so blunt, but I doubt you'll be missed. It won't be too long before another person just like you comes along, anyway.

Now taking all bets. How much longer until this thread gets closed? I'm giving 3 to 1 odds that about one more day ought to do it... I mean, jerry himself says that there is no evidence, so there isn't much point in discussing it is there?