Christian Ivicevic
Reputation
1,063
Top tag
Next privilege 2,000 Rep.
Edit questions and answers
 Nov 12 comment $\lim\limits_{x\to\infty}\frac{(x+7)^2\sqrt{x+2}}{7x^2\sqrt{x}-2x\sqrt{x}}$ @icurays1: I think I need a break... fixed this one, too. Nov 12 comment $\lim\limits_{x\to\infty}\frac{(x+7)^2\sqrt{x+2}}{7x^2\sqrt{x}-2x\sqrt{x}}$ @icurays1: That was just a typo, thanks for reminding me of that! Nov 11 comment Show that a matched set of nodes forms a matroid It will take some time to fully understand what you have written, i will come back in a few minutes if I have any questions - meanwhile you can have a look whether I made a mistake during the translation (you're from Berlin and probably know German ;) ) of the problem and confused everyone: i.imgur.com/sO8IU.png Nov 11 comment Show that a matched set of nodes forms a matroid I was now able to understand (1) and (2) but I have problems with the proof of (3). I was thinking about defining a basis $\mathcal{B}\in\mathcal{I}$ which contains all nodes of a perfect matching (which would be the entire set $V$), however this sounds incorrect because I think something would be missing here. Do you have any hint what I did misunderstand? Nov 11 comment Show that a matched set of nodes forms a matroid @joriki: I don't think that this is exactly what makes it difficult for me. We never had any exmaples in class because our prof just shows us some definitions without even explaining how to work with such structures. In the end this concept of a matroid is still a mystery to me and I don't know whether my thoughts on what to do suffice and furthermore I don't know how to proove this while having such abstract definitions without any imagination how my sets might look like. Nov 10 comment Extend functions such that they are continuous @martini: Oh again a typo... but nevertheless thanks. Nov 10 comment Extend functions such that they are continuous Oh typo. Fixed it now - may I ask you whether you can confirm my second result $b=4$ which I did determine the same way as $a$? Nov 9 comment Convergence of semi-telescopic series $\sum\limits_{k=1}^\infty\frac{1}{k(k+1)(k+2)}$ @BrianM.Scott: Did you forgot to add a $1/2$ to the partial sum at the end? Nevertheless this looks more familiar and comprehensible and I will try working on that later on. - Thanks! Nov 9 comment Convergence of semi-telescopic series $\sum\limits_{k=1}^\infty\frac{1}{k(k+1)(k+2)}$ @BrianM.Scott: We haven't even defined derivatives and integrals yet, currently attending "Calc. I" if you could say so. (Everything is different in Germany...) - However I still don't see how to determine the $1/4$ WolframAlpha has computed. By now I only know how to show, that my series converges. Nov 9 comment Convergence of semi-telescopic series $\sum\limits_{k=1}^\infty\frac{1}{k(k+1)(k+2)}$ @BrianM.Scott: Looking up in my textbook the $p$-series is prooved (in a part we did not work through yet) with approximations $1/n^k\leq 1/n^2\leq 2/(n(n+1))$ for $k>1,k\in\mathbb{N}$ and the last term converges because the telescopic series converges. You claim, that my series I have to work with does not converge, however WolframAlpha claims that it converges to $1/4$ - am I missing something? Nov 9 comment Convergence of semi-telescopic series $\sum\limits_{k=1}^\infty\frac{1}{k(k+1)(k+2)}$ We haven't discussed integrals yet in the context of limits and sequences and series so your hint does not help that much - so any easier way to show that? Furthermore I understand that I can show that the series will converge by your mentioned approximation, however I still don't know how to get the limit in the second step. Nov 5 comment $\lim\limits_{n\to+\infty}\frac{2^{n^3}}{n!5^{n^2}-n^n}$ without special means Oh I did some stupid mistakes - I have been able to get the desired result! Nov 5 comment $\lim\limits_{n\to+\infty}\frac{2^{n^3}}{n!5^{n^2}-n^n}$ without special means My results are always converging to 0 like $1/n!$ or $1/(5^{n^2}-1)$. Do you know what I might have done wrong? Oct 22 comment Is it possible to make a graph eulerian by adding exactly one node? This lemma and Michaels answer helped me out! Oct 22 comment Is it possible to make a graph eulerian by adding exactly one node? The handshaking lemma and your edit gave me a good clue to solve this. Thanks! Oct 22 comment Is it possible to make a graph eulerian by adding exactly one node? I am sorry, then I have translated it wrong. I have to work with a cycle - editing it now! Oct 22 comment Is it possible to make a graph eulerian by adding exactly one node? I know that a connected graph has an Eulerian path iff all vertices have even degree. I even proved that yesterday, isn't that contradicting with your mentioned property? Oct 22 comment Find the remainder of $128^{1000}/153$. @Rain: One can add LaTeX code between dollar signs. If you know how to write LaTeX code you will profit here ;) Oct 20 comment Relation of (un)bounded (in)finite sets and $\min$/$\max$ (1) As mentioned in fgp's answer I will reuse your idea. Quite easy, when being reminded of this fact with $1/n$. (2) I like $A=\{1\}$ more, but yeah quite complex what I did there. (3) I'm sorry, but I didn't really get everything you wanted to explain. fgp's description was more intuitive on the first look. (4) Ok :) Oct 20 comment Relation of (un)bounded (in)finite sets and $\min$/$\max$ (1) I do not want to use injective maps as proof though I like your idea. However I will use Brians general approach with \$\forall x\in\mathbb R,x>0:\exists n\in\mathbb N:0<1/n