Ubuntu won't boot after a file system check
"Welcome to emergency mode!" Think it is a fsck problem
I am trying to prove that all vector spaces can be written as the direct sum of two subspaces.  My attempt: If each vector in vector space V can be uniquely written as the sum of two other vectors in V, the two vectors can be categorized into subspaces and thus V can be written as the direct sum of these subspaces. I am not sure how to show that this is true for all cases though. Edit Sorry for the confusion,to clarify I meantGiven a vector space V with a subspace W, prove that there exists a subspace W' such that the direct sum of W and W' is V.I am not sure about my proof method at all. Thank you. We have 10 PC with some version of Ubuntu and only remote access. While doing some upgrades to custom software I did not notice that the line endings in some scripts were Windows version (CR+LF) and not the Unix version (LF). So now when I want to launch the script it gives an error:   bash: /usr/local/bin/portsee: /usr/bin/python^M: bad interpreter: No such file or directory   Is there a way to change all line endings in a script from terminal. The thing is that I can not install any new software to this group of PC-s. Story where vampires are created by drop absorbed on neck? I have been trying to identify a book that I read maybe 25-30 years ago (1987-1992), in which there are vampire or vampire-like creatures, but instead of being created in the traditional way (e.g. bite on the neck), something drops a drop of a fluid on the back of their neck, which is then absorbed into the body and transforms them. I have a vague notion that some sort of tree is what creates these drops. The drops may have had a shiny metallic appearance.  I've tried to find this book before and always came up short. I'm starting to think the whole thing was a dream and I never read it at all. But I really feel like it was a book or at least a short story. I have a Asus ROG G551VW laptop and I'm trying to install Ubuntu 16.04 on my laptop, but when i try to load the installer, my laptop just freezes and its fan starts working for no reason. I have tried to install Ubuntu 14.04 on my laptop and the installation went smoothly. What should I do if I want to install Ubuntu 16.04 on my laptop?  Any help would be greatly appreciated. My trackpad is broken so I can tap-to-click but i cannot drag and drop. This is really a problem when it comes to doing certain things.   Does anyone know how to program a sticky key to turn a click into a click-select that can then be dragged about?   I can't resize my browser or open window and I can't drag applications into the folder when installing etc.  free solutions only please.  A mid 2009 macbook-pro 13". 2.53 Ghz Intel Core 2 Due.   Running os lion (grudgingly). How to completely remove Garage Band from macOS? ERROR running force:source:pull: Entity of type 'CustomApplication' named 'Contact' cannot be found What are "first class" objects? When are objects or something else said to be "first class" in a given programming language, and why? In what do they differ from languages where they are not?  EDIT. When one says "everything is an object" (like in Python), does he indeed mean that "everything is first-class"? An integer is a $n$'th power if that holds true for all moduli. I have not been able to solve this problem. Any insights would be appreciated!   Let $x, n > 1$ be integers. Suppose that for each $k > 1$ there exists an integer $a_{k}$ such that $x − a_k^n$ is divisible by $k$. Prove that $x = A^{n}$ for some integer $A$. Calculating $\sum_{n=1}^\infty\frac{1}{(n-1)!(n+1)}$ I want to calculate the sum:$$\sum_{n=1}^\infty\frac{1}{(n-1)!(n+1)}=$$  $$\sum_{n=1}^\infty\frac{n}{(n+1)!}=$$ $$\sum_{n=1}^\infty\frac{n+1-1}{(n+1)!}=$$ $$\sum_{n=1}^\infty\frac{n+1}{(n+1)!}-\sum_{n=1}^\infty\frac{1}{(n+1)!}=$$ $$\sum_{n=1}^\infty\frac{1}{n!}-\sum_{n=1}^\infty\frac{1}{(n+1)!}.$$  I know that $$\sum_{n=0}^\infty\frac{1}{n!}=e$$  so $$\sum_{n=1}^\infty\frac{1}{n!}=\sum_{n=0}^\infty\frac{1}{n!}-1=e-1$$  But, what can I do for $$\sum_{n=1}^\infty\frac{1}{(n+1)!}$$ ?  Am I allowed to start a sum for $n=-1$ ? How can I bring to a something similar to $$\sum_{n=0}^\infty\frac{1}{n!}$$? 30" monitor has black border around desktop I have been using a 24" monitor with my macbook pro early 2011 connected via a mini display port to DVI adaptor.  I recently received an HP Z30i 30" monitor.  When I connect to it with an mini display port to display port adaptor, although it displays at the monitors native 2560x1600 resolution, the mac is scaling the desktop display down so as to leave a 1cm or so black border around the desktop.  The mac reports using a resolution of 2560x1600 and the display reports this also.   This makes the display blurry as single pixels become sub pixels.   The display looks like the same effect as having "under scan" turned on when using an HDMI cable at 1080p.  I thought that maybe there was a hardware or display problem, but when I boot off a previous system partition from a different hard-drive using the same OS (10.8.5) release, the monitor set up works perfectly.  This proves the OS release, display and the hardware, so I'm thinking that there must be a preferences problem with my current setup.  Perhaps the under scan setting is somehow being applied to this display when it's not using HDMI?  I've tried deleting /Library/Preferences/com.apple.windowserver.plist, ~/Library/Preferences/ByHost/com.apple.windowserver.HostNumber.plist and rebooting but no results.   The scaling is applied before the login screen and logging in as a different user has the same problem.  Any ideas?  It's driving me nuts, I've got this nice 30" screen and I can't use it! I have 12.10 ubuntu and when I try to remove / install programs I get notification :      Software can't be installed or removed because the authentication service is not available.    (org.freedesktop.PolicyKit.Error.Failed: ('system-bus-name', {'name':  ':1.104'}): org.debian.apt.install-or-remove-packages   When I log in as root user (instead of user account that I regulary use) i have no problems. Exercise on infinite series: pointwise product between convergent serie and unbounded sequence I am not able to solve this exercise. I've tried everything.     Exercise Let be $a_n &gt; 0$ a sequence and suppose that $\sum a_n$ converges. Prove that exists a sequence $c_n &gt; 0$ such that $\lim c_n = \infty$ and $\sum c_na_n &lt; \infty$   I don't even know if I have to find an "always-valid" closed form for $c_n$ (maybe in function of $a_n$?) or prove its existence in another way.  Thanks in advance. How can I make a plane's edges taper inwards? How can I deform one edge or multiple edges of a plane or cube so they are tapered in and rounded equally? Within a set of directories, how do I find a file whose name includes a given string, such as "abcde"? Can bug reports and feature requests requiring SE Dev attention be reported on per-site metas, or do they need to all go here? How to upload string as file with jQuery or other js framework How to run scripts on start up? How can I get id,class or name attr an element with jquery How do I specify unique constraint for multiple columns in MySQL?