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Aug
8
comment How many real roots are there to $2^x=x^2$?
@Arturo Err, that would make it clearer, but the time for editing is up.
Aug
8
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.
Aug
8
comment How many real roots are there to $2^x=x^2$?
Why is $x\approx-0.76666469596212309311$ a solution?
Jun
15
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 $\mathbb R^+$.
Jun
15
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 $f(0)\in\{-1,1\}$.
Jun
14
comment Is such a cryptographic system possible?
That's a great article!
Jun
14
comment How to solve this recurrence using generating functions?
@muffel IIRC it's written by Graham, Patashnik and Knuth.
Jun
13
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.
Jun
13
comment How to solve this recurrence using generating functions?
@muffel For b) and c) recall that $\sum_{i=0}^ni^2=n(n+1)(2n+1)/6$.
Jun
13
comment Expected value for a random variable
Oh, yes. You're right.
May
28
comment Convert any number to positive. How?
In textbooks, the first one is often written $\lvert x\rvert$.
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.