1,687 reputation
926
bio website fuz.su/~fuz
location Berlin, Germany
age 20
visits member for 3 years, 11 months
seen yesterday

I am a student of computer science and mathematics at the Humboldt University of Berlin.


Oct
24
comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
@Gortaur: Well, that's not that difficult. You just need to find a geometrical interpretation of sine and cosine.
Oct
23
comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
Sorry for that.
Oct
23
comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
Thank you very much. I know that proverb, but I really wasn't able to find that out on my own.
Oct
23
comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
Hm... But now, how to prove that $\cos$ is continuous? (Read the question!)
Oct
23
comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
Okay. I had a look at the link Yuval provided. That proof works. Anyway, thanks for the effort.
Oct
23
comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
But how to prove that $\sin x<x<\tan x$?
Oct
23
comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
@mixedmath Sorry. That was indeed a typo.
Oct
12
comment Finding the number of newspapers
@Ramana It seems so, though I can't prove it.
Oct
10
comment A Tricky Limit: $(1 - \frac{c}{n}\log n )^{1-n}$
Wolfram Alpha says, $\lim_{n\to\infty}(1-\frac cn\log n)^{1-n} = \infty$...
Oct
10
comment Probability of a random $n \times n$ matrix over $\mathbb F_2$ being nonsingular
The number even appears on oeis.org as A048651
Oct
10
comment Probability of a random $n \times n$ matrix over $\mathbb F_2$ being nonsingular
It seems that there is something called $q$-Pochhammer symbol, such that $\prod^n_{k=1}(1-2^{-k})=(1/2;1/2)_n$. It seems that this actually converges: $(1/2;1/2)_\infty=0.2887880950866\dots$
Oct
9
comment Probability of a random $n \times n$ matrix over $\mathbb F_2$ being nonsingular
Sorry, I mistyped... It seems to converge to 0.288788..., but it might also be that it just falls infinitly, but extremly slow.
Oct
9
comment Probability of a random $n \times n$ matrix over $\mathbb F_2$ being nonsingular
At a glance from the plot, it seems that this function converges to something above 0.28; is that possible? And if not, is it possible to give asymptotics?
Oct
8
comment Simplifier Tool for Windows
Actually that's only true if you assume that $a\neq0$.
Oct
6
comment What types of functions do recurrence relations methods apply to?
This seems to be a typical recurrence relation. Concrete Mathematics has a good chapter about it, if you are interested.
Oct
6
comment Why are variables lowercased?
@Olivier oops... I forgot that $\mathbb N$ is not a field. You may use $\mathbb C$ as another example.
Oct
6
comment Why are variables lowercased?
You may also consider fields; they are usually denoted by double-struck capitals, like $\mathbb N$, $\mathbb Q$ and $\mathbb F_2$.
Oct
4
comment How many solutions does an equation system with binary values have?
Thank you. That was a missconception of mine. I thought that the echelon form would allow constructs like above.
Oct
4
comment How many solutions does an equation system with binary values have?
What if a row is not completely zero, just the coefficient $a_{k,k}$ is? In this case, it depends on how you set the free variables, whether the equation in row $k$ becomes $0=0$ or $0=1$... I don't know how to prevent that. If the row is full of zeroes, it is easy. Consider this system: $$\begin{array}{cccc|c}1&1&0&0&1\\0&0&1&0&1\\0&0&1&1&1\\0&0&0&0&0\\\end{array}$$ If you set the rightmost variable to $1$, it has no solutions. How to deal with such a case?
Sep
29
comment Fastest prime generating algorithm
You can't generate all prime numbers nor an infinite subset of all prime numbers in finite time...