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 May9 comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$? @CutieKrait We defined $\sin$ by geometrical means. Apr2 comment Why is it impossible to define multiplication in Presburger arithmetic? Ah, I see. Thank you for this answer. Mar31 comment Why is it impossible to define multiplication in Presburger arithmetic? @MJD How are these axioms? Mar31 comment Why is it impossible to define multiplication in Presburger arithmetic? @MJD Presburger arithmetic is an axiomatic system. People claim that it is impossible to define multiplication within this system. Why? Sep8 comment The inverse of the inscribed angle theorem I am sorry. I usually don't ignore the orientation of angles. I should've made that clear beforehand. Sep8 comment The inverse of the inscribed angle theorem Nice and easy. Thank you! Sep8 comment The inverse of the inscribed angle theorem In the second case, the sign of the angle $\angle ACB$ is negative. The equation $2\angle ACB=\angle AMB$ does not holds if the signs do not match. Sep8 comment The inverse of the inscribed angle theorem @Karolis I fixed the error. My bad :-( Sep8 comment The inverse of the inscribed angle theorem @KarolisJuodelÄ— No. C can be anywhere but the constraint on the angle $\angle ACB$ must hold. Jun21 comment Evaluating $\int_0^{\sqrt{3}}{\frac{\sqrt{1+x^2}}{x}}\,dx$ Try wolframalpha.com for evaluating integrals. It even shows a step-by-step-solution! Jun21 comment Given a Turing Machine T, create another Turing machine T2 such that L(T) $\neq$ L(T2) Theorem of rice? Jun21 comment An equivalent statement for convergence @clark Didn't knew that. Thanks for pointing that out! Please close my question. Mar11 comment How to come up with the gamma function? Okay. Thank you! Mar11 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. Mar11 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 $\int_0^\infty t^ne^{-1}\;\mathrm dt$. Mar11 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. Feb26 comment How does one easily compute the limit of $a_n=(n\cdot \ln(\frac{n+1}{n}))^n$? As $n$ goes to what? Feb16 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. Jan17 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... Jan8 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?