# Luboš Motl

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bio website motls.blogspot.com location Czech Republic age 40 member for 2 years, 11 months seen Mar 12 at 7:48 profile views 2,481

Hi, I am a string theorist and a publicist.

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 Jun14 comment Compute $\lim\limits_{n \to \infty }\sin \sin \dots\sin n$ No, @Sam, the statement is obviously correct for any $|x|$ smaller than one, whether it comes from sines or not. This is a rigorous proof. Jun14 revised Compute $\lim\limits_{n \to \infty }\sin \sin \dots\sin n$ added 621 characters in body; deleted 2 characters in body Jun14 revised Compute $\lim\limits_{n \to \infty }\sin \sin \dots\sin n$ added 79 characters in body; added 1 characters in body; added 92 characters in body; added 3 characters in body Jun14 comment Compute $\lim\limits_{n \to \infty }\sin \sin \dots\sin n$ I got two downvotes for my answer, even though my proof and answer are obviously correct. By the way, I just upvoted your question because it's a clever limit. Jun14 revised Compute $\lim\limits_{n \to \infty }\sin \sin \dots\sin n$ added 128 characters in body; added 52 characters in body; deleted 40 characters in body Jun14 answered Compute $\lim\limits_{n \to \infty }\sin \sin \dots\sin n$ Jun14 revised Algebraic proof of a trig matrix identity? added 7 characters in body; added 1 characters in body Jun14 answered Algebraic proof of a trig matrix identity? Jun14 comment Maximum number of mutually orthogonal latin square pairs (definition provided) I may have misunderstood what it means for "all pairs to be distinct". I thought it meant that $x_{ij}\neq y_{ij}$ for all choices of $ij$. If it means something completely different, like that the same doublet $(x_{ij},y_{ij})$ can't occur for two choices of $ij$, then of course my comment is totally irrelevant. Jun14 answered Maximum number of mutually orthogonal latin square pairs (definition provided) Jun13 comment Prove that the product of a rational and irrational number is irrational It's surely not quite correct. For example, you missed factors of $1/z$ and $1/b$ in evaluating or "simplifying" $xy/z=a/b$. Otherwise the logic is OK. Jun12 awarded Nice Answer Jun12 answered How do I combine multiple sets of ratios in order to meet an overall “target” ratio? (word problem supplied to illustrate) Jun12 answered K3 surface criteria Jun12 comment Is there an analogue to the “Delta” symbol for ratios? Dear Theo, what I mean by "discontinuous" is that there is no continuous $f(x)$ such that $f(0)$ is positive and $f(1)$ is negative so that $f(k)/f(0)$ which is $\Delta^\times x$ at some moment would be well-defined for all $k$ between $0$ and $1$. That's a warning sign - if one uses $\Delta^\times$ for things that change sign, it could be an unnatural thing that can go awry at moment... I know that $\Delta$ is the Greek counterpart of $D$ but I think it's a good idea to distinguish them. Did your $D$ mean $\Delta$? Jun11 comment Is there an analogue to the “Delta” symbol for ratios? Dear Theo, $\log(-1)=\pi i$ and $\exp(\pi i)=-1$: is there any problem with that? Something's changing multiplicatively but changing sign would be a discontinuous process in the real numbers, anyway, so it only makes good sense in the complex realm. Concerning the notation, not sure whether I understand which $D$ you mean. Jun11 revised Is there an analogue to the “Delta” symbol for ratios? added 176 characters in body Jun11 comment Intersection of two vectors using perpedicular dot product This is really badly readable. Would it be difficult to translate the obscure object-oriented code into normal mathematical language? Jun11 answered Is there an analogue to the “Delta” symbol for ratios? Jun11 comment Combinatorial proof that binomial coefficients are given by alternating sums of squares? OK, sorry, I probably don't know what a combinatorial proof is. If that's pictures, I was taught that the most beautiful picture is an equation. ;-)