Prove/Disprove $\lim \sup a_n = -\lim \inf -a_n$
Prove that $\liminf x_n = -\limsup (-x_n)$
I wonder which of the two is correct:        I have a red and a blue car.   I have a red and a blue cars.      or        Everyone has a left and a right arms.   Everyone has a left and a right arm.      My (non-native) inclination would be for option 1, as it sounds better.  On the other hand, in the following examples, the plural sounds better to me.    Everyone has left and right arms. I have old and new cars. (when I only have only one old car and one new car) The left and the right arms are...   But are they correct? I am using  to show the branch name in gnome terminal (Ubuntu 15.10) when working in a git repository. Based on the above I now have the below in my ~/.bashrc file:  # uncomment for a colored prompt, if the terminal has the capability; turned # off by default to not distract the user: the focus in a terminal window # should be on the output of commands, not on the prompt #force_color_prompt=yes    ...  # Add git branch if its present to PS1 parse_git_branch() {  git branch 2&gt; /dev/null | sed -e '/^[^*]/d' -e 's/* \(.*\)/(\1)/' } if [ "$color_prompt" = yes ]; then  PS1='${debian_chroot:+($debian_chroot)}\[\033[01;32m\]\u@\h\[\033[00m\]:\[\033[01;34m\]\w\[\033[01;31m\]$(parse_git_branch)\[\033[00m\]\$ ' else  PS1='${debian_chroot:+($debian_chroot)}\u@\h:\w$(parse_git_branch)\$ ' fi unset color_prompt force_color_prompt   As a result I now get:    so it works. But why has the coloring of my user@host been removed? And I would also expect that the branch name should be colored. Before it looked like this:    UPDATE: I have now tried this guide instead:    adding this to .bashrc:  parse_git_branch() {      git branch 2&gt; /dev/null | sed -e '/^[^*]/d' -e 's/* \(.*\)/ (\1)/' } export PS1="\u@\h \[\033[32m\]\w\[\033[33m\]\$(parse_git_branch)\[\033[00m\] $ "   and that works:    Notice in .bashrc I also have this (default):  # uncomment for a colored prompt, if the terminal has the capability; turned # off by default to not distract the user: the focus in a terminal window # should be on the output of commands, not on the prompt #force_color_prompt=yes   I have yet to find the reason why that snippet gives the correct result and the other version does not. Any input on this?  Here is the version of my .bashrc that has the old snippet enabled that does not work: Two load icons simultaneously appearing in Android app This  confirms that the Android app is using two different loaders since last year, but just today I've noted that, at the questions page, it is using them simultaneously. I've never noted this, so I believe this bug was recently created.  I hope the following gif is clear enough to show the issue. Also, note that the bigger loader is "freezing".    SE Android App Version: 1.0.60 My Android OS Version: 5.0.2  Still observed in version 1.0.89 I’m currently in the process of reconsidering how I do bibliography management. It seems to be most sensible to use biblatex with biber. I’d like to know what tools are available on which I can build a solution that works for me. I’m interested in everything from full-blown bibliography management suites to pretty-printers for .bib files; both as traditional programs and online services.  Tools in question should fulfill the following criteria:   Unicode support. Support for the additional entry types and fields that biblatex supports. Support for biber’s improved cross-referencing. Best way to strike out a text I have two shapefiles, Point and Polyline. I'm trying to populate my polyline layer with the point data ID (systemID) where the lines start to where they end; eg. create two columns (from and to). The lines already have flow direction assigned to them. I am using ArcHydro tools but Arcpy is also fine.  In ArcHydro I have tried using Attribute Tools > Generate From/To Nodes for lines but it creates values for To and From that are not from my point data. My other alternative was using Feature to Vertices and joining the result to my point data table to get the systemID. But then I would have to update the polyline layer as well. I am sure there is a easier way of doing it.  Note: not all the lines have points at the vertices, blank values are fine for them. Did Stephen Baxter or Arthur C. Clarke's estate ever comment on continuing "A Time Odyssey"? 2007 book "Firstborn", the third and last book of "" trilogy by Stephen Baxter and Arthur C. Clarke - an "orthoquel" to "2001: A Space Odyssey" - ends with a cliffhanger which obviously implies continuation:      Myra said, “My God.Charlie? ”  Bisesa stared. “Who is ‘we’?”  “We call ourselves the Lastborn. We are at war. We are losing.” She held out her hands. “Please. Come with me now.”  Bisesa and Myra, still hugging each other, reached out their free hands. Their fingertips touched Charlie’s.  A clash of cymbals.   However, sadly, Sir Arthur died in 2008, with no further books forthcoming.  Did Stephen Baxter  or Arthur C. Clarke's estate ever comment on continuing "A Time Odyssey" after 2008?  Wikipedia has no info:     The 2008 Gollancz edition of the most recent book describes itself on the cover as the "Conclusion" of the series, but the plot is not concluded in the book. The immediate threat is averted but the enemy is not defeated, suggesting that further novels in the series were intended. With the death of Clarke, one of the two authors, it is not clear whether these will be written. How can I tell how long (more or less) it will take me to complete a game? I'm going down my huge backlog of unplayed Steam games and I'm thinking the best way to tackle the list is to go through the shortest games first and then concentrate on the 20+ hour ones. I'm wondering if there's a website or something else that has an estimated amount of gameplay time for games.   Is there anything like that? Cannot get to a new line by hitting Enter I am using a Mac machine.  I asked a question, and then, someone answered it.    I clicked "Edit" to add a comment, and I would like to press Enter to go to a new line, but doing so submitted my comment and ended the edit instead. How can I change the default location for bluetooth file transfers? I have an Android 2.3 device (Samsung Galaxy Y Duos, S6102) and want all files that I receive via bluetooth to save to my SD card.  How can I do that? Best Place to put Feature Requests? The only place I am aware of is the . How do you clone a Git repository into a specific folder? Executing the command git clone git@github.com:whatever creates a directory in my current folder named whatever, and drops the contents of the Git repository into that folder:  /httpdocs/whatever/public   My problem is that I need the contents of the Git repository cloned into my current directory so that they appear in the proper location for the web server:  /httpdocs/public   I know how to move the files after I've cloned the repository, but this seems to break Git, and I'd like to be able to update just by calling git pull. How can I do this? What does "period" mean when someone says "Sth... Period"? I often hear US citizens say something like this:     &lt;Some phrases>. Period.   What does period mean when it appears in a sentence by itself in this type of situation? Is there a rule in British English about how to pronounce "either"? There are two common pronunciations of "either": British /ˈaɪðər/ and American /ˈiːðər/. If Americans are more or less consistent in this regard, then the Brits seem to be freely using both. In fact, from what I can tell, "either this or that" is more often in the first form, whereas "me either" is in the second. But I may be wrong. Is there any kind of an informal rule in the modern British English with regard to this? Unemployed person applying for UK visa A map is continuous if and only if for every set, the image of closure is contained in the closure of image How does a magnet work? What to do before root and flash my phone? I am using different operating systems on different machines on different locations. I am using a USB flash disk to keep my files (source codes etc.).  I am new to Mac OS X and now I realize there are lots of files created with a dot underscore ._ prefix.  Questions  Why are ._ files created?   What are their purpose?   How can I avoid them? multiple choice question on number theory