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  1. suyver

    Mean of sum of random numbers

    yes, I thought about that one too. But I got confused when I did a bunch of numerical simulations. Sometimes, the sum got very large (>1000). So I worry about the case where the sum may actually diverge: theoretically this is clearly possible (e.g.: sum of 1/n). Do we need to prove that this is...
  2. suyver

    Mean of sum of random numbers

    I choose a random number p_1 \in [0,1) and a subsequent series of (increasingly smaller) random numbers p_i \in [0, p_{i-1}). Then I can calculate the sum \sum_{i=1}^\infty p_i. Naturally, this sum is dependent on the random numbers chosen, so its particular result is not very insightful...
  3. suyver

    Limit of abc-formula for a->0

    OK, that makes sense. I had originally expected that both roots would converge to -c/b, but now that I think about it, it seems clear that the fact that b can be negative (so that I cannot just say \sqrt{b^2}=b) will spoil this. Oh well... too bad (for what I wanted).
  4. suyver

    Limit of abc-formula for a->0

    But for the other root, I get: \frac{-b-\sqrt{b^2-4ac}}{2a}=\frac{-b-\sqrt{b^2-4ac}}{2a}\cdot \frac{-b+\sqrt{b^2-4ac}}{-b+\sqrt{b^2-4ac}}= \frac{b^2-(b^2-4ac)}{2a(-b+\sqrt{b^2-4ac})}=\frac{2c}{-b+\sqrt{b^2-4ac}} which seems ok... but I don't think it is! After all, I multiply by...
  5. suyver

    Limit of abc-formula for a->0

    I was wondering someting that is so simple that it baffled me... When I have the equation a x^2+b x+c=0 this obviously has the solutions x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} And when I have the equation b x+c=0 this has the solution x=\frac{-c}{b} My problem now is the limiting case...
  6. suyver

    News American Civilian Beheaded in Iraq

    There is some doubt as to weather this video is real at all... http://www.infowars.com/print/iraq/berg.htm What do you guys think? Wag the dog all over again?
  7. suyver

    Mexican Air Force Pilots Videotape UFOs

    It's even on CNN (so it must be true... ;-) http://edition.cnn.com/2004/WORLD/americas/05/11/mexico.ufos.ap/index.html [Broken]
  8. suyver

    Another play with numbers website

    Good point! That must be why you are not allowed to choose a zero in the link that I gave.
  9. suyver

    Another play with numbers website

    OK, I think I completed the answer to my own question (great forum, this is! ;-) This trick is that the website divides the number that I imput by 9 to see what remainder is left. If it's 0, the missing digit had to be 9. If it's 1, the missing digit had to be 8. If it's 2, the missing...
  10. suyver

    Another play with numbers website

    OK, I got slightly further: My number Z=X-Y (X>Y) must be devidable by 9, right? Is it then just the case that because the website knows that the number I imput plus the unknown digit must be dividable by 9, the value of the unknown digit can be determined? I.E.: Because it knows that the...
  11. suyver

    Another play with numbers website

    Another "play with numbers" website http://digicc.com/fido/ It's probably related to the fact that we have a base-10 number system, but I fail to see how it works... This website does the following: 1) You write down a 3 or 4 digit number, say X=x1 x2 x3 x4 (where the x's denote the...
  12. suyver

    Saying pi is transcendental

    But I like LaTeX'ing! :)
  13. suyver

    Saying pi is transcendental

    No, this is not correct. You are saying that \pi + (1-2 i)\pi^2=-1 which would imply that \pi=\left(\mp\frac{1}{10}\pm\frac{i}{5}\right)\left(\mp 1+\sqrt{8i-3}\right) which is clearly not the case...
  14. suyver

    News US Presidential election

    Even though I am born and raised Dutch, I find this insulting. Shame on you.
  15. suyver

    Basics of neutrinos are they antimatter particles

    No, also 1/2. Negative spins are not possible: only the projection of the spin on a (z) axis can be <0.
  16. suyver

    Basics of neutrinos are they antimatter particles

    They are a particle: (almost) no mass, no charge, spin 1/2. No electromagnetic or strong interaction, only weak interaction. Typical strength of the interaction: you'd need about 1000 lightyears of lead to have a 50% probability for an interaction between a neutrino and the lead! On earth...
  17. suyver

    Proton: stable or unstable?

    Tachyons do not exist.
  18. suyver

    Numerical solutions to differential equations

    Hi, thanks for the response. I don't get the use of trying to find analytical solutions to a part of the problem first. It seems to be a lot of work and I don't see what use they'd have. After all, I am only interested in the numerical outcome (I want to fit the results, to obtain values for...
  19. suyver

    Numerical solutions to differential equations

    I've got a horrible system of 8 coupled differential equations: \frac{\partial}{\partial t} N_0=-R_{0,2}N_0Y_1+\sum_{j=1}^5W_{j,0}N_j-C_{0,1}^{4,2}N_0N_4 \frac{\partial}{\partial t} N_1=-R_{1,3}N_1Y_1-W_{1,0}N_1+W_{2,1}N_2+W_{4,1}N_4+C_{0,1}^{4,2}N_0N_4 \frac{\partial}{\partial...
  20. suyver

    News Draft poll .

    @phatmonky: Most of us in "old europe" tend to think of the UK as the 51st state.
  21. suyver

    News Draft poll .

    You've tried for 3 and a half hours and already gave up? ;)
  22. suyver

    Prove that light has no mass

    Can all the non-established "physics" please be moved to the Theory Development subforum (or at least be split off from this thread)? On-topic: @pmb_phy: regarding the Proca Lagrangian, is this the most accurate way to determine the upper-limit for the photon mass? Also, for the revised...
  23. suyver

    Substitution integral

    \int\frac{dx}{x^4+1}=\frac{1}{3\sqrt{2}} \left(2\arctan(1+\sqrt{2}x)-2\arctan(1-\sqrt{2}x)+\right. \left.\log(\sqrt{2}x+x^2+1)-\log(\sqrt{2}x-x^2-1)\right)
  24. suyver

    News Draft poll .

    1. No. 2. No. 3. No. 4. Mainly, yes. 5. Stop trying to make Irak the 52nd state of the US and let the UN take over.
  25. suyver

    Proton: stable or unstable?

    I think that would violate the CPT-theorem.... That would be bad news.
  26. suyver

    News Assassination of The Arab 'Pope'

    I choose to stop responding in this thread to prevent too emotional reactions / flamewars / ... (this certainly applies to me as well!).
  27. suyver

    News Assassination of The Arab 'Pope'

    Interesting... the Palastinians seem to have a legitimate claim against Sharon for possible genoside (I think from somewhere in the beginning of the 1980's). So, according to you they should just buy some gunships and blast him - and maybe a few of his children and some bystanders too - when he...
  28. suyver

    News Assassination of The Arab 'Pope'

    Even if all of this is true, then that STILL doesn't justify his murder in this way. He should have been arrested, tried in an oper court (with all the rules and so on) and he should only have been punished AFTER he had been found guily be an impartial judge (or jury, I have no idea how the...
  29. suyver

    A new point of view on Cantor's diagonalization arguments

    1905 is Einsteins "magic year": it is the year in which he published special relativity, the resolution of the photoelectric effect (for which he would get the Nobel prize later on), and the theoretical description of Brownian motion (that almost proved beyond doubt the existence of atoms)...
  30. suyver

    Was Einstein really a genius?

    I consider Einstein a genius. Not just because of SR, but also because of GR, the photoelectric effect, his proof of the Brownian motion, his contributions to laser-theory, ... ... ...
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