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 Jun 21 comment Given a Turing Machine T, create another Turing machine T2 such that L(T) $\neq$ L(T2) Theorem of rice? Jun 21 comment An equivalent statement for convergence @clark Didn't knew that. Thanks for pointing that out! Please close my question. Mar 11 comment How to come up with the gamma function? Okay. Thank you! Mar 11 comment How to come up with the gamma function? YOur first interpretion is right. But your answer shows only that the integral satisfies the recurrence relation $\Gamma(x+1)=x\Gamma(x)$ and does not show how one can derive that integral. Mar 11 comment How to come up with the gamma function? Thank you for that answer although you don't point out how one get's to $\int_0^\infty t^ne^{-1}\;\mathrm dt$. Mar 11 comment How to come up with the gamma function? Sorry. I found out that the article actually contains an answer to my question, thus I removed my post. Feb 26 comment How does one easily compute the limit of $a_n=(n\cdot \ln(\frac{n+1}{n}))^n$? As $n$ goes to what? Feb 16 comment $y''=(y')^{3} e^{y}$, some easy way to solve this non-linear differential equation? Did you tried using Wolfram Alpha? It can also shows you a step-by-step solution. Jan 17 comment Question about a lemma on continuity @Arturo Sorry. That was a translation mistake. In German, one says "stetig" to say "continuous". stetig and steady are false friends... Jan 8 comment Given the cartesian coordinates of four points, how to calculate the interection of two lines they form? @J.M. Oh yeah. That looks good. THank you! BTW, is there a solution that use the $r,\vartheta$ representation instead? Jan 8 comment Given the cartesian coordinates of four points, how to calculate the interection of two lines they form? @J.M. Of course. This possibility is ruled out. Dec 2 comment Defining division by zero @picakhu You are going to run into problems when calculating limits. Just consider $\lim_{n\to0}\frac{2n}n$. Using your method, one gets $\frac{\infty_0}{\infty_0}=1$, while one gets $\frac21=2$ using the definition of limits. Nov 13 comment How to convert $\sqrt{\frac{5}{3}}$ to $\frac{\sqrt{15}}{3}$? @Max ${5\over3}\to{15\over9}$ Nov 13 comment How to convert $\sqrt{\frac{5}{3}}$ to $\frac{\sqrt{15}}{3}$? BTw, you can use LaTeX makeup by starting with an \$and ending with another \$, for instance $\sqrt{\frac{5}{3}}$ becomes $\sqrt{\frac{5}{3}}$. Nov 11 comment A lemma of convergence @André: yes. We already proved that. Nov 8 comment The Mathematics of Tetris That's an interesting question! I don't see any special reason for this, though. Nov 1 comment Prove the identity $\sum\limits_{s=0}^{\infty}{p+s \choose s}{2p+m \choose 2p+2s} = 2^{m-1} \frac{2p+m}{m}{m+p-1 \choose p}$ Hm... I recall that or a similar identity from Concrete Mathematics... maybe I find it again. 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.