Sequence of fractions $c_n = a_n / b_n$ converges to irrational $x$, prove $a_n$ and $b_n$ diverges to infinity.
Sequence of rationals with an irrational limit have denominators going to infinity
I am looking for a solution/technology which allows remote screencast display and control from desktop. My goal is to provided remote mobile device display through a browser. I found some existing solutions:   AndroidScreenCast: Based on ADB interface. this is just screenshots using a simple primitive provided by ADB. low display. VNC client &amp; server. works for both rooted android and jailbroken iphone. low display. iDemo + ScreenSplitR: Better, jailbroken iphone only. HDMI/TV output: No remote control.   I've heard about "direct-to-device" technology which is used by DeviceAnyWhere. Are there any other solutions? Checkout one file from Subversion How to create nested loops in x86 assembly language How to sail downwind faster than the wind? Recently a  set a record for sailing a wind-powered land vehicle directly down wind, and a speed faster than wind speed. Wikipedia has a  talking about it, but it doesn't explain exactly how it works.  I can imagine some configurations, but I don't get how a system could be set up to push forward with a tailwind (when the cart is moving slower than the wind) and push forward with a head wind (when the cart is moving faster than the wind).  Could someone help explain how this is possible? induction with 2 recursive sequnces I'm having trouble solving this problem. I have relation for two sequences of natural numbers.   $$a(n)+\sqrt3\cdot b(n)=\left(1+\sqrt3\right)^n$$  and I have to prove that recursions:  $$\begin{align*} &amp;a(n+1)=a(n)+3b(n)\\ &amp;b(n+1)=a(n)+b(n) \end{align*}$$  will satisfy relation mentioned above. I tried solve it using induction but I failed. Can anybody help with some other ideas? Unable to install any updates through update manager/apt-get upgrade I have been running Ubuntu 12.04 for the past few weeks. I recently tried to download and install some files through the Update Manager. It located a few files, downloaded them, but then failed to install them. It gave the error:  installArchives() failed: (Reading database ...  (Reading database ... 80% dpkg: unrecoverable fatal error, aborting:  reading files list for package 'libasn1-8-heimdal': Input/output error   I tried using apt-get upgrade but a similar error was produced:  Reading package lists... Done Building dependency tree        Reading state information... Done The following packages will be upgraded:   icedtea-6-jre-cacao icedtea-6-jre-jamvm openjdk-6-jre openjdk-6-jre-headless   openjdk-6-jre-lib 5 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. Need to get 0 B/34.6 MB of archives. After this operation, 1,024 B of additional disk space will be used. Do you want to continue [Y/n]? y (Reading database ... 80% dpkg: unrecoverable fatal error, aborting:  reading files list for package 'libasn1-8-heimdal': Input/output error E: Sub-process /usr/bin/dpkg returned an error code (2)   Any help would be greatly appreciated. Thanks in advance.  Edit: Here's some extra information that may be useful. My original problem was that the Ubuntu Software Centre would not open. I found that the Update Manager and Synaptic Package Manager also failed to open. They all gave an error along the lines of:   "installArchives() failed: dpkg: error: reading package info file '/var/lib/dpkg/available': Input/output errorError in function:"   After much googling I seemed to fix that problem as the package managers would open again. When I then tried to download and install any updates from the Update Manager I got the error at the beginning of this post. The Stack Overflow search shows questions twice. See  for example.  Results include "A: Add Search Engine into MVC Music Store" and "Q: Add Search Engine into MVC Music Store".  Why is search displaying the question twice, and what does "Q" and "A" mean?  Edit:   @Stephen answer :  The search is returning both a question (Q) and an answer (A) to the question, as both posts match your search criteria.  and my another question  If the question have multiple (like 100) answer ,then the answer link(A: Question Link) shown 100 times?  Is it correct functionality ? But i saw only one answer link , not a other answer link .. why ? How to resize partitions? What is the opposite of "preaching to the choir"? Showing that $|f(z)| \leq \prod \limits_{k=1}^n \left|\frac{z-z_k}{1-\overline{z_k}z} \right|$ How can I identify an anonymous inner class in a NotSerializableException 'apt-get' does not work with Proxy For the command   sudo apt-get update   I get following error:  W: Failed to fetch http://ch.archive.ubuntu.com/ubuntu/dists/maverick-updates/multiverse/binary-i386/Packages.gz   407  Proxy Authentication Required (The ISA Server requires authorization to fulfill the request. Access to the Web Proxy filter is denied. )   I am running Ubuntu 10.10 installed on Windows XP using VirtualBox. For Internet connections I am using proxy server with an authentication. I tried to use gnome-network-proxy tool to set proxy settings system-wide.   After that /etc/environment has been updated by http_proxy variable with the format http://my_proxy:port/, there were no authentication data.  I checked this with Firefox. Browser asked my for login and password and everything was working fine. It was unfortunately not the case for apt-get. I have also tried to do as described . Unfortunately it does not work.  May it be somehow related to the fact that a proxy is in a Windows domain, any ideas?  My proxy name is http-proxy. Is '-' a special character here? How to scp in Python? How do I log in if my OpenID is not available, or maybe even no longer exists? Can I restore my lost account, or do I need to start over?  See also: Film where aliens looking like humans are waiting in an airport closed due to snowstorm I saw the movie 6 - 7 years back on cable tv, from the looks of it it seemed to be made in the late 1990's or early 2000's. Unfortunately I could not see the complete movie. The story goes like--   Some people are waiting at a small airport because snowstorm activity has cancelled all flights in and out. There are two children in the group as well (one boy and a girl). Somehow they discover there are aliens looking like humans among them. They decide to check passengers through baggage scanners (checking the skeletal structure via x-ray). They find and kill 2 aliens.   and the big twist:      5. They then realize the two children are also aliens.   any ideas what the name of the movie is ??? When do I pronounce a non-existent “r” between adjacent vowel sounds? If I say two words consecutively, with the first ending in a vowel sound and the second starting with one, when is it correct to include a non-existent r between those two words?  Examples from phrases I've heard:        I saw (r)a movie   They saw (r)us   Law (r)and order   That's the idea, (r)anyway.      I heard the last one in the movie Edge of Tomorrow yesterday.  Is this grammatically correct? If so, is the omission of the r grammatically incorrect? Are there any rules regarding this? What is the difference between sector and cluster? I have gone through wikipedia and other sites and here's the information I have obtained.  Sector: Smallest Addressable Unit (mostly 512 bytes) Cluster: Smallest Allocation Unit (equals to 1 or more sectors and the number of clusters depends on the file system).  Let's say in the below example:  sector =512 bytes and a cluster =8 sectors=4096 bytes. Now, I am having a hard time figuring out, when I am trying to create a file what does the file system do? Does it consider 4096 bytes as the smallest write/read unit or 512 bytes?  If the answer is 4096 bytes: When the manufacturer of the disk drives has provided 512 bytes as the smallest addressable unit, why does the file system consider cluster as the smallest unit? I mean, what are the advantages in doing so? Under Windows 7, how can I delete a folder whose name ends with "..."? The problem from Burton: show that the equation $n^2 + (n+1)^2 = m^3$ has no solution in the positive integers.  So far, I can see that gcd($n$,$n+1$)$=1$ and $m \equiv_4 1$ and $m=a^2 + b^2$ for some integers a,b. I'm guessing I need to reach a contradiction.  At this point, I am stuck. Any hints? Shell script- To fetch the content from the specific tag at all occurrence using shell scripting I have an XML file on my server. In that file, I have many tags in which there is a tag for example, "container" tag. I need to fetch the content of all the container tags content separately. Many thanks in advance.