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1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. Saying pi is transcendental

But I like LaTeX'ing! :)
13. 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. News US Presidential election

Even though I am born and raised Dutch, I find this insulting. Shame on you.
15. 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. 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. Proton: stable or unstable?

Tachyons do not exist.
18. 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. 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. News Draft poll .

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

You've tried for 3 and a half hours and already gave up? ;)
22. 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. 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. 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. Proton: stable or unstable?

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