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 May 24 comment A question on logic - where intuition can fail @amWhy: Thanks for finding such a good title. May 24 comment Modulo operation notation I would write it exactly like you, but add brackets. So $p(x) = (d(x) + b(x)\bmod w(x))$ but $p(x)\not=d(x)+b(x)\mod w(x)$. Notice also, that the spacing is also different. May 24 comment How to understand and appreciate the prime number industry? @Sebastien: I would not trust a prime I bought. It could be, that the vendor also sold it to someone else. May 22 comment Partial sum of ${A \choose i} {B\choose n-i}$, when $B=-1$? The formula holds for all integer $i$. (According to Knuth in Concrete Mathematics) May 21 comment How to prove that $\lim\limits_{x \to 0 }\;x^{-a}e^{\frac{-1}{x^{2}}} =0$ for all a? Why is it undefined? Then we have $\lim_{x\to0^-}{\sqrt x}/{\exp x^{-2}} = \lim_{x\to0^-}i\sqrt{|x|}/{\exp x^{-2}}$ which is the same except for an additional $i$. (Am I wrong?) May 21 comment How to prove that $\lim\limits_{x \to 0 }\;x^{-a}e^{\frac{-1}{x^{2}}} =0$ for all a? @Bill Dubuque: I am not very good at limits (I am still in highschool, they will teach these things next year). To prove that, I just sad, that $a\ln y$ grows slower than $y^2$ and thus $a\ln y - y^2\to-\infty$ as $y\to\infty$. I guess that's not a good solution. May 21 comment How to prove that $\lim\limits_{x \to 0 }\;x^{-a}e^{\frac{-1}{x^{2}}} =0$ for all a? @Bill: Quite similar to what you did. But I arrived at $\lim\limits_{y\to\infty}a\ln y - y^2=-\infty$... Maybe I calculated wrong. May 20 comment A question on logic - where intuition can fail @Asaf: Sorry. It's just that I am used to use both styles simutanously - Usually, it is more readable to use the bar notation for long expressions and the $\lnot$ notation for short expressions. May 20 comment A question on logic - where intuition can fail $\overline A = \lnot A$. It's just another syntax for negation. May 20 comment A question on logic - where intuition can fail Is $\bigwedge_{x\in\{\}}P(x)$ true? And what about $\bigvee_{x\in\{\}}P(x)$? It is supposed to be false, isn't it? But thank you for that answer. It helped me quite much. May 19 comment Is there an algorithm to find the roots of high-order polynomials? My question was, if the polynomial is expressable in terms of radicals, is it possible to give an algorithm to find them? May 18 comment Is there an algorithm to find the roots of high-order polynomials? I read the article and think, that you can certainly show that a polynomial's roots are describable in terms of radicands using the Galois Theory, but it doesn't explains you how to find them. May 10 comment Closed form for the sequence defined by $a_0=1$ and $a_{n+1} = a_n + a_n^{-1}$ I just tried to understand this answer again, but I didn't understood, why \$2n+1+\sum_{0\le k