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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 $2n+1+\sum_{0\le k<n}a_k^{-2}=2n+1+o(n)$
May
10
comment Find a number $b$ such that $a\cdot b\equiv 1\mod m$
@Asag Karagila: Yes.
May
3
comment Need a result of Euler that is simple enough for a child to understand
Good idea. How about euler tours?
Apr
12
comment Solving a scrambled $3 \times 3 \times 3$ Rubik's Cube with at most 20 moves!
I would suggest looking on Wikipedia And also here
Apr
6
comment Please help me to show, that $(\ln x)'=\frac1 x$
Thank you. Great answer.
Apr
6
comment Please help me to show, that $(\ln x)'=\frac1 x$
@Arturo Magidin: Thank you very much.
Apr
6
comment Please help me to show, that $(\ln x)'=\frac1 x$
@quanta: Please don't cheat. I want to get an answer I can use to understand the derivation. But anyway, thanks for the definition.
Apr
6
comment Please help me to show, that $(\ln x)'=\frac1 x$
Ah... Okay. And how to show, that $\lim_{\delta\to\infty}\ln\left(1-\frac1{x\delta}\right)^\delta = x^{-1}?$