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 Aug8 comment How many real roots are there to $2^x=x^2$? @Arturo This was meant because the answerer stated, that $x = 2, x = 4$ are the only solutions. Aug8 comment How many real roots are there to $2^x=x^2$? Why is $x\approx-0.76666469596212309311$ a solution? Jul7 comment Mathematical Career Advice to a young 16 year wannabe mathematician @sigma.z.1980 It's good to know, that other people have the same opinion as me. Jun15 comment All functions $\frac{1}{f\left(y^2f(x)\right)} = \big(f(x)\big)^2\left(\frac{1}{f\left(x^2-y^2\right)} + \frac{2x^2}{f(y)}\right)$ @J. J. Ah, thanks. I didn't read the ${}^+$ in $\mathbb R^+$. Jun15 comment All functions $\frac{1}{f\left(y^2f(x)\right)} = \big(f(x)\big)^2\left(\frac{1}{f\left(x^2-y^2\right)} + \frac{2x^2}{f(y)}\right)$ I just spotted a possible mistake: $1/f(0)=f(0)$ does not implies $f(0)=1$. It only implies, that $f(0)\in\{-1,1\}$. Jun14 comment Is such a cryptographic system possible? That's a great article! Jun14 comment How to solve this recurrence using generating functions? @muffel IIRC it's written by Graham, Patashnik and Knuth. Jun13 comment How to solve this recurrence using generating functions? @muffel Concrete Mathematics is an awesom book when it comes to sums and generating functions. Just if you're curios. Jun13 comment How to solve this recurrence using generating functions? @muffel For b) and c) recall that $\sum_{i=0}^ni^2=n(n+1)(2n+1)/6$. Jun13 comment Expected value for a random variable Oh, yes. You're right. May28 comment Convert any number to positive. How? In textbooks, the first one is often written $\lvert x\rvert$. May24 comment A question on logic - where intuition can fail @amWhy: Thanks for finding such a good title. May24 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. May24 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. May22 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) May21 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?) May21 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. May21 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. May20 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. May20 comment A question on logic - where intuition can fail $\overline A = \lnot A$. It's just another syntax for negation.