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There is a command l available on my machine which appears to do nothing.  which l also produces no output. Is this a real command, and does it actually do anything? QGIS update from 2.14 to 2.16 failed on Ubuntu 14.04 Until yesterday my whole qgis and python-qgis worked fine with version 2.14 under Ubuntu 14.04. After a simple sudo apt-get update and sudo apt-get upgrade qgis failed to update... Several attempts to reinstall it with different versions failed.  Current error message (for version 2.14.3) goes like this:  qgis-providers (2.14.3+dfsg-2~trusty1) is configured ... /usr/lib/qgis/crssync: symbol lookup error: /usr/lib/libgdal.so.20: undefined symbol: GEOSDelaunayTriangulation_r   I also tried to reinstall all gdal libraries - not sure if I got all?!  Maybe it is somehow related to this one:  ?  UPDATE:  Trying to install version 2.16.0 it gives different but similar error:  /usr/lib/qgis/crssync: symbol lookup error: /usr/lib/libqgis_core.so.2.16.0: undefined symbol: GEOSNearestPoints_r   UPDATE Sources:  For version 2.16.0 there are these sources in /etc/apt/sources.list:  deb http://qgis.org/debian trusty main deb-src http://qgis.org/debian trusty main deb http://qgis.org/debian trusty main deb-src http://qgis.org/debian trusty main   which are all the same, right?   When I do apt-cache policy qgis it gives me:  qgis:   Installiert:           1:2.16.0+20trusty   Installationskandidat: 1:2.16.0+20trusty   Versionstabelle:  *** 1:2.16.0+20trusty 0         500 http://qgis.org/debian/ trusty/main amd64 Packages         100 /var/lib/dpkg/status      2.0.1-2build2 0         500 http://de.archive.ubuntu.com/ubuntu/ trusty/universe amd64 Packages How to evaluate $\int_{0}^{\infty}\exp(-x^2-1/x^2)dx$? Question :  $$\int_{0}^{\infty}\exp(-x^2-1/x^2)dx=?$$  I think the answer is $\sqrt{ \pi/2 \cdot \exp(-2)}$  If I change $-x^2-1/x^2$ to $-(x-1/x)^2-2$ then the above integral becomes    $$\exp(-2)\int_{0}^{\infty} \exp(-(x-1/x)^2)dx$$   integral of $\exp(-x^2)dx$ from $0$ to infinity = square root of $\pi/2$, but then is the   integral of $\exp(-(x-1/x)^2)dx$ from $0$ to infinity=integral of $\exp(-x^2)dx$ from $0$ to infinity ? I'm trying to re-learn my undergrad math, and I'm using Stephen Abbot's Understanding Analysis. In section 2.7, he has the following exercise:  Exercise 2.7.5 (a) Show that if $\sum{a_n}$ converges absolutely, then $\sum{a_n^2}$ also converges absolutely. Does this proposition hold without absolute convergence?  I'm posting about this here because my answer to that last question about whether the proposition holds without absolute convergence is "Yes", but my suspicions are raised by him merely asking the question. Usually questions like this are asked to point out that certain conditions are necessary in the statement of propositions, theorems, etc. I just want to see if I'm missing something here.  Anyway, here's how I prove the absolute convergence of $\sum{a_n^2}$, and note that I never use the fact that $\sum{a_n}$ is absolutely convergent:  Proof: Let $s_n = \sum_{i=1}^n{a_n^2}$. I want to show that $(s_n)$ is a Cauchy sequence. So, let $\epsilon &gt; 0$ and $n &gt; m$, and consider, \begin{equation}   \begin{aligned}     |s_n - s_m| &amp;= |(a_1^2 + a_2^2 + \cdots a_n^2) - (a_1^2 + a_2^2 + \cdots a_m^2)|\\                 &amp;= |(a_{m+1})^2 + (a_{m+2})^2 + \cdots + a_n^2|\\                 &amp;= |a_{m+1}|^2 + |a_{m+2}|^2 + \cdots + |a_n|^2\\   \end{aligned} \end{equation} Now, since $\sum{a_m}$ converges, the sequence $(a_m)$ has limit 0. Therefore I can choose an $N$ such that $|a_m| &lt; \sqrt{\epsilon/n}$ for all $m &gt; N$. So for all $n &gt; m&gt; N$,  we have, \begin{equation}   \begin{aligned}     |s_n - s_m| &amp;= |a_{m+1}|^2 + |a_{m+2}|^2 + \cdots + |a_n|^2\\                 &amp;&lt; \left(\sqrt{\frac{\epsilon}{n}}\right)^2 + \left(\sqrt{\frac{\epsilon}{n}}\right)^2 + \cdots + \left(\sqrt{\frac{\epsilon}{n}}\right)^2\\                 &amp;&lt; \left(\sqrt{\frac{\epsilon}{n-m}}\right)^2 + \left(\sqrt{\frac{\epsilon}{n-m}}\right)^2 + \cdots + \left(\sqrt{\frac{\epsilon}{n-m}}\right)^2\\                 &amp;= \epsilon   \end{aligned} \end{equation} Therefore $(s_n)$ is Cauchy and $\sum{a_n^2}$ converges. And since $\sum{a_n^2} = \sum{|a_n^2|}$, the series $\sum{a_n^2}$ is absolutely convergent. &#x220E;  Am I doing something wrong here? Am I right in thinking that $\sum{a_n}$ need not be absolutely convergent for $\sum{a_n^2}$ to be absolutely convergent? Why not introduce a donate button in Stack Exchange sites? Best way to parse RSS/Atom feeds with PHP Every finite subset of $\mathbb R$ contains its supremum (and its infimum)   Proof Let $A=\{a_1,...,a_n\}$ be a finite subset of $\mathbb{R}$. Since it is non-empty and it is bounded ($\max A$ is an upper bound), it has supremum, that is $\exists \sup A$ and by definition $\forall a \in A \;\, a \leq \sup A$. Let's suppose that $\sup A  \not\in A$ then, since $\max A \in A$ we have that $\max A &lt; \sup A$. But considering that $\mathbb Q$ is dense in $\mathbb R$ we can conclude that $\exists r \in \mathbb Q$ s.t. $\max A &lt; r &lt; \sup A$, but this is absurd since $r$ is an upper bound of $A$ and it is lower than the supremum. Necessarily, $\sup A\in A$.  Is there anything wrong? Is there any way to prove this without using density of $\mathbb Q$ or another property? Thanks in advance. How are self-replicating mines supposed to work? I have a list of integers, List&lt;Integer&gt; and I'd like to convert all the integer objects into Strings, thus finishing up with a new List&lt;String&gt;.  Naturally, I could create a new List&lt;String&gt; and loop through the list calling String.valueOf() for each integer, but I was wondering if there was a better (read: more automatic) way of doing it? dpkg error: "trying to overwrite file, which is also in..." Prove that $G$ is abelian iff $\varphi(g) = g^2$ is a homomorphism I'm working on the following problem:     Let $G$ be a group. Prove that $G$ is abelian if and only if   $\varphi(g) = g^2$ is a homomorphism.   My solution: First assume that $G$ is an abelian group and let $g, h \in G$. Observe that $\varphi(gh) = (gh)^2 = (gh)(gh) = g^2h^2 = \varphi(g)\varphi(h)$. Thus, $\varphi$ is a homomorphism.  I'm having trouble completing the proof in the reverse direction. Assume that $\varphi$ is a homomorphism. We then know that $\varphi(gh) = \varphi(g)\varphi(h)$ and $\varphi(hg) = \varphi(h)\varphi(g)$. However, I don't see a way to use this to show that $gh = hg$.  Could anyone lend a helping hand? Connected compact covering space of torus is homeomorphic to $S^1\times S^1$ Unable to get force:inputField or force:outputField to render inside other markup in Lightning Component when used in Lightning Experience Do descriptive statistics have p-values? If a friend wants to transfer $7000 to me, what is the best way to do it, especially if we don't share the same banks? We could do wire transfer, but that comes with its own fees. Could we also do direct deposit? Paypal doesn't allow such large lump sum transfers.  This would be US-to-US transfer. It seems to me that the terms "Teaching Assistant" and "Instructor" refer to a variety of positions. At some places, a teaching assistant is responsible for things like helping the actual lecturer by handing out papers, grading homework, etc., and instructors hold recitation sessions.  At other places, I saw the term "instructor" referring to the lecturer giving the course, while a teaching assistant is the person doing anything else (recitations, grading etc.).  Is there some widely accepted definition of the two positions?  For context: The question arose because I wasn't sure whether I'm using the correct terms in my CV -- I am a math graduate student, and I would like to make a distinction between jobs in which I only graded course assignments/final exams, and courses in which I held recitation classes* (and also participated in grading the final exams). Is it OK to use "Instructor" for the latter? What should the former be referred to as?  *In the course I'm currently teaching, the recitations are planned and written by the ones giving them (without the professors' supervision). Also, the people giving the recitations are not necessarily grad students (some already hold a PhD). I'm elaborating on that because from what I've seen, some of it could be relevant for the definition of the job. Graph Proof by induction. Can you prove via induction that there exists a node in a directed graph of n nodes that can be reached in at most two edges from every other node in the graph. Every node in the graph is required to have an edge with every other node that either points out or in (For every pair of nodes X and Y, either X points to Y or Y points to X). How do I display the nth result of an ls command? I used this command to display the first result of files in my directory.    ls | head -n 1   My simple question is, how can I modify this command to display say the nth result?  Thanks! Everytime I sudo apt-get update it always not complete and will say in the end  E: Read error - read (5: Input/output error) E: The package lists or status file could not be parsed or opened.   Same goes, when I try to install something and do sudo apt-get install &lt;some app&gt;  What should I do ? I admit, that my drive has bad sectors, could that be the reason? Is there anything else I can do? How can I convert the binary string $x_bin="0001001100101" to its numeric value $x_num=613 in Perl?