Let $f\colon \mathbb{R} \mapsto   \mathbb{R}$ be a function with the property that the image of every connected set is connected. Is $f$ necessarily continuous?  I've recently learned the definition of connected set and i'm still not totally confortable with it. I thought about the function $f(x)=\sin(1/x)$ for all real non zero $x$ and $f(0)=0$ (obviously discontinuous) for a counterexample but i'm not certain that the image of every connected set is connected...  Thank you in advance for your help!
Continuity $\Rightarrow$ Intermediate Value Property. Why is the opposite not true?    It seems to me like they are equal definitions in a way.    Can you give me a counter-example?    Thanks
Best way to compare 2 XML documents in Java I'm trying to write an automated test of an application that basically translates a custom message format into an XML message and sends it out the other end.  I've got a good set of input/output message pairs so all I need to do is send the input messages in and listen for the XML message to come out the other end.  When it comes time to compare the actual output to the expected output I'm running into some problems.  My first thought was just to do string comparisons on the expected and actual messages.  This doens't work very well because the example data we have isn't always formatted consistently and there are often times different aliases used for the XML namespace (and sometimes namespaces aren't used at all.)  I know I can parse both strings and then walk through each element and compare them myself and this wouldn't be too difficult to do, but I get the feeling there's a better way or a library I could leverage.   So, boiled down, the question is:  Given two Java Strings which both contain valid XML how would you go about determining if they are semantically equivalent?  Bonus points if you have a way to determine what the differences are. I'be been running 18.04 since a clean SSD install on the day of it's official release, without issues. Power on to login was seconds (max 10)  Then, I did a regular upgrade this morning:  $ sudo apt update &amp;&amp; sudo apt dist-upgrade   The packages installed/upgraded were:  Install: linux-headers-4.15.0-24:amd64 (4.15.0-24.26, automatic), linux-headers-4.15.0-24-generic:amd64 (4.15.0-24.26, automatic), linux-modules-extra-4.15.0-24-generic:amd64 (4.15.0-24.26, automatic), linux-modules-4.15.0-24-generic:amd64 (4.15.0-24.26, automatic), linux-image-4.15.0-24-generic:amd64 (4.15.0-24.26, automatic) Upgrade: gnome-control-center-data:amd64 (1:3.28.1-0ubuntu1.18.04.1, 1:3.28.1-0ubuntu1.18.04.2), linux-headers-generic:amd64 (4.15.0.23.25, 4.15.0.24.26), gnome-control-center:amd64 (1:3.28.1-0ubuntu1.18.04.1, 1:3.28.1-0ubuntu1.18.04.2), linux-image-generic:amd64 (4.15.0.23.25, 4.15.0.24.26), linux-signed-generic:amd64 (4.15.0.23.25, 4.15.0.24.26), gnome-control-center-faces:amd64 (1:3.28.1-0ubuntu1.18.04.1, 1:3.28.1-0ubuntu1.18.04.2), linux-generic:amd64 (4.15.0.23.25, 4.15.0.24.26)   I rebooted once the upgrade had completed, and noted a 2-3 minute delay on the Ubuntu loading/splash screen (prior to login) (without any progress/activity indicated on the dots).  I powered off and tried to boot again, but am getting this delay consistently now. Also close down is much slower too.  Update #1 (2018-07-03): Analysis on systemd:  $ sudo systemd-analyze blame 3min 53.073s plymouth-quit-wait.service     2min 20.699s snapd.seeded.service          49.949s snapd.service           6.186s NetworkManager-wait-online.service           1.148s dev-sda2.device           1.098s plymouth-start.service   Showing that plymouth-quit-wait.service (which I now believe is related to the Ubuntu loading/splash screen) and snapd.seeded.service were by far the longest running services to initiate. So I compared the times before the dist-upgrade and after:  $ journalctl -u plymouth-quit-wait.service --since today -- Logs begin at Fri 2018-04-27 13:01:30 BST, end at Tue 2018-07-03 12:38:05 BST. -- Jul 03 04:15:43 user-laptop systemd[1]: Starting Hold until boot process finishes up... Jul 03 04:15:46 user-laptop systemd[1]: Started Hold until boot process finishes up. -- Reboot -- Jul 03 04:21:17 user-laptop systemd[1]: Starting Hold until boot process finishes up... Jul 03 04:24:52 user-laptop systemd[1]: Started Hold until boot process finishes up.   Before the upgrade plymouth-quit-wait.service took 3 seconds. After the upgrade it took 3 minutes 35 seconds  $ journalctl -u snapd.seeded.service --since today -- Logs begin at Fri 2018-04-27 13:01:30 BST, end at Tue 2018-07-03 12:42:14 BST. -- Jul 03 04:15:43 user-laptop systemd[1]: Starting Wait until snapd is fully seeded... Jul 03 04:15:43 user-laptop systemd[1]: Started Wait until snapd is fully seeded. -- Reboot -- Jul 03 04:22:47 user-laptop systemd[1]: Starting Wait until snapd is fully seeded... Jul 03 04:24:49 user-laptop systemd[1]: Started Wait until snapd is fully seeded.   Before the upgrade snapd.seeded.service took 0 seconds. After the upgrade it took 2 minutes 2 seconds.  Update #2 (2018-07-06): This morning's boot saw the return of the delay. So I guess we're still waiting for the kernel/plymouth/snapd update.  Update #3 (2018-07-12): The problem seems to be resolved, but I didn't see any update to snap or plymouth, and I'm still running 4.15.0-24 kernel. So I'm not sure which package update fixed the problem, or if it just resolved itself somehow. Reading the bug updates on launchpad it's unclear to me what was done (or is being done) to what package/s. If anyone can clarify that would be very useful. I've just upgraded my computer hardware(cpu + motherboard + graphic card + memory + hard disk), so that install a new OS is needed. I tried to download debian-6.0.6-amd64-netinst.iso with wget command but the speed is so slow that I could not bear. 4Kb/s ~ 17 Kb/s, slow like a running turtle, or even more slower if I use Chrome.  I've read the help information of wget, it seems like there are no options could make it more faster.  Is there anyway to make wget faster? Or is it possible to make it multi-threading download?  PS: my bandwidth is 4M. I use this command:  wget -c url  http://hammurabi.acc.umu.se/debian-cd/6.0.6/amd64/iso-cd/debian-6.0.6-amd64-netinst.iso List files sorted by the number of lines they contain How can I list the number of lines in the files in /group/book/four/word, sorted by the number of lines they contain?   ls -l command lists them down but does not sort them Consider the question :    The large number of down-votes displays as 199 rather than a score of -199.  This is clearly unintentional (and unfortunate for questions that possess such voting!), but can this be&nbsp;corrected? I'm rewiring a a small part of a wall and I'm confused about a combination of the NEC and the products that I'm able to find.  I'm working on a 20 amp circuit (with 12g wire of course).  I'm connecting 4 receptacles each in their own box, 15 amp receptacles for normalcy.  But the terminals don't seem to accept 12g wire, even on the screws.  My first reaction was to make pigtails 14g pigtails, so that the 14g tap goes directly to the receptacle and is not used to feed the rest of the circuit.  12g in the box, 12g out of the box, and 14g inside the box only.    Is that type of splice allowed, or should I look harder for a 15 amp outlet that can more easily accept 12g wire? How do I install and manage GNOME Shell extensions? This is fairly easy.  If I go to https://webserver.com/someurl?a=b, will the someurl?a=b part be protected, or just the contents of the site? What counts as an attack? I was looking over the class feature of the 'fiend' patron warlock in 5e. I'm a bit confused on what actions the player needs to take before they can use the 'Hurl Through Hell' ability on an enemy. The PHB states:     Starting at 14th level, when you hit a creature with an attack, you can use this feature to instantly transport the target through the lower planes.   I'm not clear on what an 'attack' means in this context. Does it have to be a physical attack like a sword or crossbow? Do magical attacks like Eldritch Blast that require an attack roll count? What about spells with no attack roll? I'm trying to insert a figure into my LaTeX file using the following syntax:  \begin{figure}   \centering   \includegraphics [width=3in]{fig1.png}   \caption{Calculation of shortest path betweenness}   \label{Fig.3:Shortest path betweenness} \end{figure}   It worked for me before but this time I'm getting the following error:   LaTeX Error: \begin{figure} on input line xxx ended by \end{document}   Also, hovering over the red cross symbol indicating error in Eclipse, I see this message    paragraph ended before Gin@iii was completed.   It's obvious that I have the \end{figure} to end my \begin{figure} so I don't understand how I still get that error.  Can someone please tell me what the problem is?  Edit: Add more details for debugging. The problem went away if I remove '[width=3in]'. Here is the detail error:  pdflatex&gt; Runaway argument? pdflatex&gt; width=3in]{fig1.png} \caption {Caption} \label {Fig.1}  pdflatex&gt; ! Paragraph ended before \Gin@iii was complete. pdflatex&gt; &lt;to be read again&gt;  pdflatex&gt;                    \par  pdflatex&gt; l.40  pdflatex&gt;        pdflatex&gt;  pdflatex&gt; Underfull \vbox (badness 10000) has occurred while \output is active pdflatex&gt; (./document.bbl pdflatex&gt;  pdflatex&gt; Package natbib Warning: Empty `thebibliography' environment on input line 3.   Added sample code:  \documentclass[10pt,psfig,letterpaper,twocolumn]{article} \usepackage{geometry} \usepackage{graphics} \usepackage{setspace} \usepackage{natbib} \usepackage{verbatim} \usepackage[scaled=0.9]{helvet} \singlespacing \paperwidth 8.5in \paperheight 11in \oddsidemargin 0in \headsep 1.3cm  \geometry{left=0.75in,top=0.75in,right=0.75in,bottom=1in} \textwidth 7in  \textheight 9.25in \columnsep 0.4in \footskip 0in  \renewcommand{\bibname}{REFERENCE} \pagestyle{empty}  \begin{document} \bibliographystyle{acm}   \title{\fontfamily{phv}\selectfont{\huge{\bfseries{Title here}}}} \author{ {\fontfamily{ptm}\selectfont{\large{\bfseries{author name}}}}\thanks{contact info }}  \maketitle \thispagestyle{empty}  \section*{\fontfamily{phv}\selectfont{\normalsize{\bfseries{Section name}}}}  \begin{figure} \centering \includegraphics[width=3in]{fig1.png} \caption{Caption} \label{Fig.1} \end{figure}  \pagebreak[4] \vspace*{5.52in} \bibliography{ref} \end{document} I was writing a program in C++ to find all solutions of ab = c, where a, b and c together use all the digits 0-9 exactly once. The program looped over values of a and b, and it ran a digit-counting routine each time on a, b and ab to check if the digits condition was satisfied.  However, spurious solutions can be generated when ab overflows the integer limit. I ended up checking for this using code like:  unsigned long b, c, c_test; ... c_test=c*b;         // Possible overflow if (c_test/b != c) {/* There has been an overflow*/} else c=c_test;      // No overflow   Is there a better way of testing for overflow? I know that some chips have an internal flag that is set when overflow occurs, but I've never seen it accessed through C or C++.    Beware that signed int overflow is undefined behaviour in C and C++, and thus you have to detect it without actually causing it. For signed int overflow before addition, see . Synonym for "Fellow Sufferers"? Low Quality review queue erroneously showing "Close" instead of "Recommended Close"? I was in the Low Quality Review queue, and the following review confused me:    It's showing eight "Close votes", which should be more than enough to close a question.  I checked the question's , and it wasn't somehow closed, then re-opened in the middle of the review.  So I then checked on each of the users, and noticed that the majority of them are under 3000 reputation, meaning they can only "Recommend Close".    However, all reviews are simply showing as "Close", which is extremely confusing.  Is this a bug, or possibly an undocumented change related to ?    Another recent example: Help Understanding How Long It Will Take To Heat My Wire Future Simple and Future Perfect I've read  about Future Simple and Future Perfect, but I still can't understand the exact usage of these two tenses. Is there any diffrence between the following?     I will do my homework by 6 p.m.   I will have done my homework by 6 p.m.       I will do my homework after school   I will have done my homework after school   Also, I've checked the word 'by' in  and there're some confusing examples:       By the time (that) this letter reaches you I will have left the country.   Can I use 'By the time (that) this letter reaches you I will leave the country' instead? Proving that the Hopf map $S^3 \to S^2$ is a submersion I need to show that the Hopf map $H : S^3 \to S^2$ is a submersion. There are many ways to define it, but for now I've gone with the restriction of the function $F : \mathbb{R}^4 \to \mathbb{R}^3$ mapping $$(x,y,u,v)\mapsto (2(xu+yv), 2(xv-yu), x^2+y^2-u^2-v^2).$$ It wasn't too bad to show that $F$ is a submersion, but is there a way to go from here to show that $H$ is a submersion? I can write down $H$ as the composition $$S^3 \overset{\iota}{\hookrightarrow} \mathbb{R}^4 \overset{F}{\to} \mathbb{R}^3 \overset{\pi}{\to} S^2,$$ and define $\pi(p) = p/\lVert p\rVert$, but I don't really know where to go after computing the Jacobian of $\pi$, and I don't know if this will even work for my purposes (I don't see how to argue that the composition of the corresponding differentials here isn't rank $1$ — I know $d\iota$ has trivial kernel but things seem to break down once I get to $d\pi$). I'm really just trying to avoid having to compute the Jacobian of $H$ with respect to the stereographic projections and show that that beast of a thing is full rank. Am I on the right track, or is there a better way? tmux: shared session, one user in a pane, another in another pane, two different cursors I've decided to try tmux: have been reading the docs and googling around, trying to find a way to have two users sharing a session, each with a different cursor.  However, giving 777 permissions to the socket, or creating a group, chgrping the socket and adding both users to it, seems to let that same socket be used to share a session with only one cursor: both users can write, but always in the same cursor position.  Right now both users are in the same home server over ssh, and the idea is to be able to have:   A terminal in a, let's say, left pane, where I can type commands Another terminal in a right pane, where I can see another user typing commands  in his own terminal The same thing for the other user   What I'm doing at the moment is using two sessions (not shared) and a script -f and tail -f combination that kinda works for reading each other's key strokes, but I reckon there is probably some way of doing this using tmux sharing capabilities.  Is there a way to get this idea working with write support in each other's terminal?  What is the better way to do this? Align equation left I'm having a problem rendering the environment map. I downloaded a sample project that has the same settings as my project but it renders without a problem. I tried using both a .hdr and .png image. Attached are screenshots with node settings. First is the incorrect render and 2nd image is the project the renders correctly. How do I go about fixing this? How to change the shadow color in Blender Cycles? I want to change the color of the shadow casting by a cube to green. While it's very easy to do it in Blender Internal (you select the lamp, go to the Lamp data header and change the shadow's color in the Shadow panel) in Cycles there're no such options. How to achieve it in Cycles?