Hagen von Eitzen
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188,199
398/400 score
 Apr 25 comment Showing a recursively defined sequence is convergent @Dave Isn't that exactly what OP tries? Apr 25 answered Showing a recursively defined sequence is convergent Apr 25 awarded Nice Answer Apr 25 comment Direct Proof for sum of $n$ integers equation? +1 for invoking WWGD Apr 25 answered Construct a turing machine that accepts L = {ww : w belongs to {a,b}*} Apr 25 answered A problem in group theory_dsom Apr 25 answered Fourier series: can a function be odd and have a dc component? Apr 25 answered Polynomial division proof Apr 25 comment If $\lim_{x\rightarrow\infty}f(x)=0$, does $||f||_{L^2}=0$? Then how dare you write $\to$ after the fixed norm of a fixed function? Apr 25 comment Show that There exists a canonical injective homomorphism between $G$ and $G\times H$ Note that "canonical" more or less means that the solution is nearly impossible not to find. - So you are given an element $x\in G$ and nothing special from $H$. Which element $(g;h)$ of $G\times H$ could you write down with those givens and without knowing anything more detailed about $G$ and $H$? Well, $g$ must be an element of $G$ and we are given an element $x$ of $G$, so ... And $h$ must be an elemtn of $H$ and the only element of $H$ that wwe know to exist is ... Apr 25 answered Using the axiom of choice to choose bijections Apr 25 comment Why doesn't L'Hospital's rule work for this limit? The rule (for this particular indeterminate form) says: If $f(x)\to \infty$ and $g(x)\to \infty$ and $\lim\frac{f'(x)}{g'(x)}$ exists, then $\lim\frac{f'x)}{g(x)}$ exists and equals $\lim\frac{f'(x)}{g'(x)}$. Apr 25 comment The sum of two numbers is 5/9… I read the last instruction as asking for $(0.4 x)\cdot (0.4y)$ Apr 25 answered Does there exist a complex function which is differentiable at one point and nowhere else continuous? Apr 25 comment Has the polynomial distinct roots? How can I prove it? @drxy I found my counterexample by just playing around with $\gcd(f,f')$, motivated by mathguy's solution for real roots. I'm sure that playing around will also allow finding counterexamples (regarding complex roots) for higher $p$ values one by one - but the handling becomes impractical. Apr 25 comment Prisoners and hats variation Do they guess only once? OR is the game repeted (with the same hats) if nobody dared to guess? Apr 25 comment \$\sup\limits_{t>0}[\frac{g(t)}{\sup\limits_{t