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"I would never die for my beliefs because I might be wrong."

-- Bertrand Russell

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 8h revised Prove that $\small\sin x\sin y\sin(x-y) + \sin y \sin z \sin(y-z) + \sin z \sin x \sin(z-x) + \sin(x-y) \sin(y-z) \sin(z-x) = 0$. added 13 characters in body; edited title Jul18 comment How to determine for which value of an unknown parameter, one eigenvalue is 0? "Always" was probably putting it too strongly. But I think it's important to guess. Besides, I am under the impression that because of the way I formulated the hint, you think that I first guessed the answer and then motivated my guess. Nothing is farther from the truth, I already had a certain approach in mind before making the guess. Jul18 comment How to determine for which value of an unknown parameter, one eigenvalue is 0? I don't know about you, but I always guess my answers before trying a more deductive approach. There's nothing wrong about guessing, and I think it's no use to give the full answer right now. Besides, hardmath's comment already gave more away even. Jul18 answered How to determine for which value of an unknown parameter, one eigenvalue is 0? Jul16 comment Evaluating the distance beween two vectors of different dimensions. Then, the question is, why pad one way rather than another? And if it does not matter, then, you might as well consider other embeddings. But in that case, it's always possible to embed one space into the other such that the two vectors coincide and hence the distance is zero. And that probably is not what you want. So we need more information about why you think it makes sense to compare the vectors to begin with. Jul14 comment Explaining Infinite Sets and The Fault in Our Stars @Link: $0.2=2 \times 0.1$ Jul14 comment Explaining Infinite Sets and The Fault in Our Stars @Link: It goes against your intuition because in mathematics, as one extends counting to infinite sets, the concept dissociates from that of inclusion. So while, the set of numbers between 0 and 1 is contained within the set of numbers between 0 and 2, each member of the former set can be matched with its double in the latter set, hence there is an equal amount of numbers in both. This cannot happen with finite sets which is what your intuition is built upon. Jul8 awarded Generalist Jun30 revised In the history of mathematics, has there ever been a mistake? deleted 2 characters in body Jun27 comment Is there a known evaluation of $\sum_{k=1}^{\infty} \frac{1}{k^k}$? @David: You're right, but I think the downvotes are aimed at the poor formulation of the question. Jun24 comment Is $0$ a valid number? This question is coming up every once in a while. It misses the point of what it is in mathematics that is so interesting: i.e. we make the rules, but surprise surprise, despite that, it seems like the entities we construct lead there own independent life. Take geometry or algebra. Who would have thought when abstracting the basic properties of elementary operations like addition and multiplication, that you'd get things like the Monster Group out of it? Jun21 comment What is integral of $x^x$? On a related note. Jun20 revised Why doesn't L'Hôpital's rule work here? added 8 characters in body Jun18 comment Explain the Birthday Paradox It's not so much a mistake as it is nonsense. You just divided the amount of ways you can select two different persons from 23 and then divided that by 365^2. Why does this have anything to do with the birthday problem? What happens with the other 21 persons? Jun18 comment Explain the Birthday Paradox What you computed is the probability of selecting two different persons out of 23 in a draw with replacement. This has nothing to do with the birthday paradox. What you should compute is the complement of the probability of drawing 23 birthdays out of 365 days with all birthdays different. Jun16 comment Is there any relation between Galois solvability and integrability of hamiltonian systems? There is a differential Galois Theory. Jun5 comment Unorthodox way of getting the average of two numbers I don't think, from a computational point of view, that the second method is a good method, though. May31 comment How many different ways are there to go from $(0,0,0)$ to $(3,3,3)$? The first step in solving a problem is always to formulate the problem correctly. May31 comment Logic behind cubic resolution of $x^4+px^2+qx+r=0$ But the trick predates Galois theory, so how did the person who came upon the trick for the first time, find it? Just sheer luck? May31 revised What is the length of GH? deleted 62 characters in body
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