Windows command line emulator for Linux
Executing .bat file
Getting "System program problem detected" pops up regularly after upgrade This started to happen immediately after I had rebooted the first time after doing a system upgrade. It first starts with a dialogue that says "System program problem detected". Then when I try to hit 'report problem' not much happens. I am led through a dialogue that always ends up the problem cannot be solved.  I am aware this is not a lot of information, however I'm not sure which information I need to publish and how should I obtain it to debug this problem.  Here's a screenshot! Possible Duplicate:             Well, I remembered this after having Algebra II a year ago, is it possible that this is a valid proof that $1 = -1$?  $$ 1 = \sqrt{1} = \sqrt{-1\cdot-1} = \sqrt{-1} \cdot \sqrt{-1} = i \cdot i = i^2 = -1 $$  $$ \therefore 1 = -1 $$  So is this actually fully valid? Or can it be disproved? Why is this sequence of functions not uniformly convergent? For the following sequence of functions and its limit function, we can see that $f_n(x)$ is clearly pointwise convergent  $$f_n(x) = x^n\text{ }\forall x\in[0,1]\text{ and }\forall n\in\mathbb N^*\\ f(x) = \begin{cases}0&amp;\text{if } x\in[0,1)\\1&amp;\text{if } x=1\end{cases}$$  However, I was wondering why this is not uniformly convergent. The condition for uniform convergence is:  $$|f_n(x) - f(x)| &lt; \epsilon,\ \ \ \forall x \text{ when } n &gt; N$$  Now most sources present an argument along the lines of: assume that $f_n(x)$ is uniformly convergent and that $0 &lt; x &lt; 1$, this means that $x^n&lt;\epsilon$ whenever $n&gt;N$. Specifically, this would mean $x^{N+1}&lt;\epsilon$ for some fixed $N$. But if we now pick $x$ such that $1 &gt; x &gt; ε^{\frac{1}{N+1}}$, then this would lead to a contradiction, therefore $f_n(x)$ is not uniformly convergent.  However, I was wondering why couldn't we take $n$ to infinity. If $0 &lt; x &lt; 1$, then $\lim_{n\rightarrow \infty} |f_n(x) - f(x)| = 0$ (which is less than $\epsilon$). Now since $|f_n(x) - f(x)|$ will always be $0$ if $n &gt; \infty$, then wouldn't this be uniformly convergent? What can you say about $f$ and $g$ in the case that $fg$ is 1) Injective, 2) Surjective - Cohn - Classic Algebra Page 15 Question: Are my proofs below valid?   In both cases we are using: $f:A\to B, g: B\to C$  Notation of your type converted: $(g\circ f)(x)=g(f(x))=xfg$    If $fg$ is injective what can be said about $f$ and $g$?  If $fg$ is injective then $f$ is injective:  Proof:  $(x_1fg = x_2fg \implies x_1=x_2)$  $x_1fg=x_2fg$ is clearly true when $x_1f=x_2f$  Which requires $x_1=x_2$, hence $f$ is injective.  If $f$ were not injective, then $x_1fg\ne x_2fg$  $\blacksquare$    If $fg$ is surjective what can be said about $f$ and $g$?  If $fg$ is surjective then $g$ is surjective:  Proof:  $(\forall c\in C)(\exists a\in A) |( a(fg))=c$  This means for $g$ every element must have had been mapped to. How can this be proved Mathematically?  well $(af)g=c$ is surjective, hence $(af)=(b\in B)$ and $bg=c$  $(\forall c\in g)(\exists b\in B)|(bg=c)$  Hence $g$ is surjective.  $\blacksquare$ Monitor hard drive changes to files Several months ago I saw someone using an application that showed him files on the computer being modified in real time.  Basically there was an application that wasn't working correctly, so he installed the program, ran the application, and saw all the various files that the application either read from or wrote to.  He found out the application was writing a large debugging file it shouldn't be, which ended up being the problem.  I don't remember the application or the name of the person who used it, but I believe it's a freeware application.  Does anyone know what this program might be? What is the difference between 'git pull' and 'git fetch'? What are the differences between git pull and git fetch? I've got a simple Leaflet map with a basemap and one map-layer coming from my own hosted GeoServer.  I made the layers show up nicely in a map.  Now I want to add popups on the point layer showing information stored in MapService.  I couldn't find too much information about that topic.   There's one link to a working example but the link seems to be broken. I found another example which I addopted. You can see it on . I'd like to display the content of the name field in the attribute table but nothing happens when the user clicks the map.  Any idea? What HTML tags are allowed on Stack Exchange sites? Who are the diamond moderators, and what is their role? Some people have a diamond after their username (e.g. )    What special privileges do diamond moderators have? How can I become a diamond moderator? Who are the diamond moderators?  How many are there?      For more information, see  in the .     Note: not to confuse with certain Stack Exchange employees, for example  members or "community managers", who often have diamonds as well, but are not ordinary moderators. I read the answers in this question, but they still leave my question open:   I didn't find a way in the Google Webmaster Tools to invoke a re-download of my robots.txt.  Through some error, my robots.txt was replaced with:  User-agent: * Disallow: /   And now all my content was removed from Google search results.  Obviously, I'm interested in correcting this as soon as possible. I already replaced the robots.txt, but I can't find a way to make Google update the cached version. Let $A,B \subset \mathbb{R}$. Show that $\sup(A \cup B) = \max\{\sup A, \sup B\}$ Let $A,B \subset \mathbb{R}$. Show that $\sup(A \cup B) = \max\{\sup A, \sup B\}$   Here's what I did so far:  Let $\sup A, \sup B$, and $\sup (A \cup B)$ denote upper bounds of $A,B$, and $A \cup B$, respectively. If $x \in A$, then $x \le \sup A$. If $x \in B$, then $x \le \sup B$. In either case, $x \in (A \cup B)$. So either $x \le \sup A$ or $x \le \sup B$. In either case, $x \le \max \{\sup A, \sup B\}$. So $\max \{\sup A, \sup B\}$ is the upper bound of $A \cup B$, which means $\sup (A \cup B) \le \max\{\sup A, \sup B\}$.  I do not know if there's a better way to go at it, but all I did was show the inequality. Can I do this, and show the reverse inequality? If so, how can I go about doing that? How to determine the optimal control law? Given the differential equation $$\dot x = -2x + u$$ determine the optimal control law $u = - kx$ that minimizes the performance index $$J = \int_0^{\infty} x^2 \, \mathrm d t$$  My approach was to find the state feedback $k$. But since the value of $R$ (positive semidefinite Hermitian) is not given, that means $R=0$. How do I determine the optimal control for this system where $R=0$? Do we have to tune the number of trees in a random forest? Is their a way to move multiple vertices gradually at a time? I have moved multiple vertices gradually but a set of vertices at a time not all at a time, as shown in the animation below (First I moved the four vertices from top, then three, then two and at last the last vertex).  I wanted to do the same thing as shown in the animation below but all at a time. Imgur is over capacity - some user avatars fail to load I see a lot of 'white' avatars in the question lists, e.g.  and . Some user avatars aren't loaded, e.g.  and  – they just timeout for me. Sometimes (but not always) I do get a nice "Imgur is over capacity!" image, which I'm (rather surprisingly) able to upload to imgur - but you might not see it. Java: Detect duplicates in ArrayList? how to fill intersection of 2 shapes in latex tikz package I have to fill a specific region as given in the following figure.  The code I have written is   \begin{tikzpicture}  \draw (0,0) rectangle (10,10);  \draw (3.5,3.5) circle (5) node {A};  \end{tikzpicture}   Now, how to fill the intersecting area (area of circle overlapping the square) Definite article, repetition in lists Which would be correct?        The fridge, the shelves, the walls, the floor, and John himself, were all covered in foam.   The fridge, shelves, walls, floor, and John himself, were all covered in foam.      The the can be applied to all the nouns, so is there a need to repeat it? Removing nodes from graphs such that one is dependent on other - ZIO $2010$, P$1$ Greetings Community! The above problem you see is a combinatorics problem I could not solve. :( This problem is from ZIO $2010$, P$1$.     Here is what I did: Observe that every graph can be divided into "sub-groups" which may help in solving. We first remove the empty set. Then the singleton set. Consider the bigger but smaller than the sub-parts example:    The singleton sets are $\{4,5,6\}$ which are at the least position in the graph.   The dual sets are $\{2,4\}, \{3,5\}, \{3,6\}$, the bottom - two portions in the graph. The triplet sets are $\{2,4,5\}, \{4,5,6\}$ which we may manually count but for the bigger graphs in the sub-part, this may prove to be difficult and this is where I am stuck.   Any help would be appreciated. Thanks. I have an internal microphone in my laptop. I think it uses Intel High Definition Audio. But I can't get it to work with Ubuntu. It doesn't work with either the Sound Recorder or Skype.  On the Input tab in 'Sound Preferences', I just see Internal Analog Input Device...