4,782 reputation
917
bio website motls.blogspot.com
location Czech Republic
age 40
visits member for 3 years, 6 months
seen Aug 4 at 12:45

Hi, I am a string theorist and a publicist.


Jun
14
comment Compute $ \lim\limits_{n \to \infty }\sin \sin \dots\sin n$
Dear @Theo, it's mutual, I would prefer not to have students or teachers who don't want to understand things and who are proud of having a limited intuition so that they always look for ways how to do things in mechanical ways that don't require intuition.
Jun
14
comment Compute $ \lim\limits_{n \to \infty }\sin \sin \dots\sin n$
Didier, do you actually claim credit for this answer, or do you admit that you copied it from my 20-minute older answer?
Jun
14
comment Solving for the implicit function $f\left(f(x)y+\frac{x}{y}\right)=xyf\left(x^2+y^2\right)$ and $f(1)=1$
Showing $f(0)=0$ is actually easy. Substitute $x=0$. Then the relation becomes $f(y f(0))=0$. If $f(0)$ were nonzero, then the argument $yf(0)$ could be any nonzero number and it would be true that $f(z)=0$ for all nonzero $z$ which contradicts $f(1)=1$.
Jun
14
revised What is Riemann-Roch in arithmetic all about?
rencently fixed
Jun
14
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.
Jun
14
revised Compute $ \lim\limits_{n \to \infty }\sin \sin \dots\sin n$
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Jun
14
revised Compute $ \lim\limits_{n \to \infty }\sin \sin \dots\sin n$
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Jun
14
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.
Jun
14
revised Compute $ \lim\limits_{n \to \infty }\sin \sin \dots\sin n$
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Jun
14
answered Compute $ \lim\limits_{n \to \infty }\sin \sin \dots\sin n$
Jun
14
revised Algebraic proof of a trig matrix identity?
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Jun
14
answered Algebraic proof of a trig matrix identity?
Jun
14
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.
Jun
14
answered Maximum number of mutually orthogonal latin square pairs (definition provided)
Jun
13
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.
Jun
12
awarded  Nice Answer
Jun
12
answered How do I combine multiple sets of ratios in order to meet an overall “target” ratio? (word problem supplied to illustrate)
Jun
12
answered K3 surface criteria
Jun
12
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 $\Delta$?
Jun
11
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.