uncool

One way to do it is to simply note that it is always e^(-1/x^2)*(a0 + a1/x^2 + ... + an/x^n) for some finite n (you can actually find what n is). In that case, there clearly is only 1 x at which this is discontinuous. Another way is to try to use extend that function to the entire complex plane. If you can create what is known as a holomorphic function over the entire plane, then the function over the real line must be infinitely continuous. =Uncool-

There are ways, but they're not very nice. These include the dictionary ordering - check the first coordinate, and use it if the two are not equal. If not, go to the second coordinate, etc. =Uncool-

Alright; it basically goes like this: Assume you have a polynomial such that for all n >= 0 (n is an integer), f(n) is prime. Then f(0) is prime. Let it be called p. Then f(a*p) must be divisible by p, as polynomials are preserved modulo a prime. Therefore, f(a*p) must be p for all a, as the only prime that p divides is itself. However, a polynomial can only be a value infinitely many times if it is constant. Therefore, any polynomial that is always prime is constant - and therefore trivial. =Uncool-

A few things: First, to insane_alien: he said d must be odd, which gives the formula 14d - 11. Now, to Amod: There are an infinite number of exceptions to this formula. Any d divisible by 11 will create a number divisible by 11, so the formula doesn't work. However, there is a theorem called Dirischlet's theorem that says that an infinite number of outputs from your formula will be prime. Another thing to Amod: It is known that there are an infinite number of primes. In fact, it's been known for over 2000 years (by Euclid) that any finite list of primes is incomplete. Here's the proof: Assume there are a finite number of primes. Let them be in the set S. Then take the product of all the elements of S, and add 1. Let this number be A. A must have a prime divisor. However, this prime divisor cannot be in S - so there is a prime number not on the list, so the list is incomplete. This means that the number of primes must be infinite. Now, as a note: there is also a simple proof that any polynomial cannot always generate prime numbers. Do you want it? =Uncool-

True, as the only force that changes the direction of the Earth is a mass-independent force - gravity. =Uncool-

Usually, the definition of infinity actually doesn't define infinity itself - it defines limits to infinity, instead. However, in some non-standard structures, there's a definition of infinity - it's just an extra point on the extended real line. Or it's a point in the projective real line. Or perhaps it's the compactification of a topological space... =Uncool-

das - you do realize that a specific find of where the line is wrong will boost your case so much that seriously, you would get a Fields medal for finding such a line. A proof that Godel's theorem is wrong would get you huge acclaim in the math world. =Uncool-

So long as a series of axioms aren't self-contradictory, they can't automatically be considered wrong. The reason we don't say Godel was wrong is the same reason as the reason we don't say Ramsey was wrong. Once again, find the contradiction in the proof - find the line where the proof goes wrong - and people will believe you. Not before, not after. =Uncool-

das...find an explicit statement and proof of Godel's theorem, and then find where it is wrong. I dare you. Find the exact spot where it is wrong. =Uncool-

Godel was simply proving what you say Poincare and Russel said. He is referring to them in order to say you can't have all of them - that is the entirety of his paradox. You have actually accepted his paradox by accepting the fact that you cannot use self-referential statements. =Uncool-

Essentially Godel's theorem says you can't have unlimited scope in having statements talk about themselves. To put it a bit more rigorously, Assume a system in which a statement is always allowed to refer to its own truth value or provability value. Then, if the system is consistent, there is a statement that cannot be proven. Where do you disagree? =Uncool-

Some information for you: Experiment 1 has already been done - and it's been found that special relativity correctly predicts the outcome. Ditto Experiment 2. Now, you have not shown any self-inconsistency in relativity, nor have you done any experiments that you have shown to show it wrong. However, there are extremely many experiments that show relativity to be correct. The burden of proof is on you. Prove the self-inconsistency or show an experiment. =Uncool-

That doesn't really mess with the laws, more with the constants assumed. Though you could interpret it as messing with the laws by replacing m with m0*(Lorentz factor)*a. =Uncool-

Linky no worky. =Uncool-

Pssst. That's median. Grrr. [uncool]

Oy vey...you're just trying to confuse people because they haven't included the "equal and opposite force" of the falling objects on the "ground-like" object. Therefore, your ideas of proving Einstein wrong are completely irrelevant. Incidentally, you actually are getting incorrect answers. When m1 and m2 are released at the same time in the same place, then the force of each on the Earth is added - so the attraction of the Earth to the objects is the same, and the attraction of the objects to the earth (in terms of acceleration) is the same. Therefore, the earth would meet both objects at the same time. =Uncool-

2 is sometimes defined as 1+1, and sometimes as the successor of 1. The two must be proven equivalent. Otherwise, I don't think I understand your question... =Uncool-

Not always; in an axiomatic definition of the integers, you can prove that; it is defined in that case as the least integer greater than 1. =Uncool-

It is ridiculously easy to find the difference between the two poles - just have another magnet in the meter. Or, make an electric pulse through the field and look at which way it turns. I personally think it's more likely to be the magnet. The idea that people have been using is this: If you switch EVERY magnet's north and south poles, and you switch left with right, then you will get effectively the same universe as you did before. =Uncool-

Actually, sterilization is necessary, but not having had kids is not necessary. That is in the rules. =Uncool-

Can you state the "central limit theorem" for the mode in mathematical terms? =Uncool-

This is just asking "what is 2007 in base 9, with symbols 1,2,3,4,5,6,8,9,0?" Answer: [hide]2680[/hide] =Uncool-

Do you mean that there are an infinite number of one of them, or rather, that the number of planets which are either occupied or unoccupied is infinite? Because one of them could be finite... =Uncool-

...What you wrote doesn't even make any sense... =Uncool-

Thank you very much. I'm a math guy, so the mathematical version helps a lot. =Uncool-