Show $f^{-1}(A^c)=(f^{-1}(A))^c$
How to approach proving $f^{-1}(B\setminus C)=A\setminus f^{-1}(C)$?
put (a) and (b) to one in subfigures booting windows 10 spends too long Make account merges propagate to chat When two accounts are merged, all the posts/votes are moved over to the "master" account, and the other account ("slave"?) is deleted. The merge is propagated network-wide, so a similar thing happens on each site.  But, this does not happen to the chat user. The "slave" chat user is kept, with a 404 parent profile link. I feel that the chat user should be merged as well, re attributing all the chat messages.  Thoughts? What is the limit of this sequence? How does it relate to the exponential function? Find $$\lim_{n\to\infty} \left(1+\frac{x^2}{n^2}\right)^n$$   I particular, I am hoping to find the above to be $1+x^kg(x/n)$ where $g(\cdot)$ is a function with uniformly bounded derivatives.  Edit: I'm trying to prove a result that would be true if  $(1+x^2/n^2)^n -1 = x^kO(x/n).$ How to create nested loops in x86 assembly language Duplicate explanation should encourage improvement of original When I look in sys.sql_logins, I see a column called is_policy_checked. Can I trust that my password policy has been checked for all of the logins where this column value is 1? How do I mail merge from Google Spreadsheet to a Google Document? Search engines and browser accept-language I'm building a web portal where language content will generally depend on the "accept-language" sent by the browser. The same content-URI will thus serve different content to different users depending on their browser setting.  I'm very curious to know how this will affect search indexing. Does Google index using all languages, and is it handled well? Kernel Panic - not syncing: VFS: Unable to mount root fs on unknown-block(0,0) Upon trying to upgrade from 10.10 to 11.04 all seemed to go well until the restart. This error message is what comes up:  Kernel Panic - not syncing: VFS: Unable to mount root fs on unknown-block(0,0)   How do we fix that? Print composer custom grid label problem In answer to  Klas Karlsson puts forward a solution to the problem of formatting print composer grid labels for projected maps.  I'm very weak on scripting, but in QGIS 2.14 I've tried to enter the text as shown in Klas's illustration, which generates error messages. In my case I'm working with a coordinate system that has a six-digit Easting and a six-digit Northing and I'm trying to get a result similar to that shown in Klas's picture (but with a six-digit Northing). Can anyone help me with this? How can the petrification from the Flesh to Stone spell be removed? I have two identical folders, with same structure and contents like this:  folder_1   hello.txt   subfolder     byebye.txt  folder_2   hello.txt   subfolder     byebye.txt   if I compress them as tar.xz formats I get two different archives with two different file sizes (just a few bytes, but they're not identical).  $ cd folder_1 &amp;&amp; tar -Jcf archive.tar.xz * $ cd folder_2 &amp;&amp; tar -Jcf archive.tar.xz *   I get:  folder_1/archive.tar.xz != folder_2/archive.tar.xz   and of course if I md5sum or sha1sum them I'll get two different hashes  And that's my problem... I need to check if a provided archive is identical to the one I have in my storage. I cannot use hashing nor just check file sizes.  Using zip instead of tar.xz works as zip always produces identical achives from identical files. Why is this happening? Is there a way to prevent it? In a script I'm trying to find the Terminal.app window containing a specific tty device and raise that window to the top. Here's what I have in Applescript so far:  tell application "System Events"   set foundWin to false   if (name of processes) contains "Terminal" then     tell application "Terminal"       set theTabs to first tab of every window where tty is "$(tty)"       repeat with theTab in theTabs         if class of theTab is tab then           set theWin to (first window whose tabs contains theTab)           set selected tab of theWin to theTab           set foundWin to true         end if       end repeat     end tell   end if   if foundWin then     --RAISE THE WINDOW?!   end if end tell   Where I'm getting stuck is the "raising the window" part.  Here are some things that are not quite what I want:  set frontmost of theWin to true -- this brings the window to the front of the group of Terminal.app windows but doesn't raise it above any other windows.  tell application "Terminal" to activate -- this brings every Terminal window to the front in a big stack. I just want the one window.  tell application "System Events"     set theSysWin to first window of process "Terminal" whose name is (name of theWin)     perform action "AXRaise" of theSysWin end tell   This almost does it, but what it does is to raise the terminal window to the #2 position, still underneath the active window (if the active app is something other than Terminal.app.)  click theSysWin at {10,50} -- doesn't seem to do anything.  click first static text of theSysWin -- doesn't seem to do anything.  Is there a way to do this? It doesn't have to be in Applescript.  EDIT I did find this web page (  ) quoting an Obj-C/Cocoa call:  SetFrontProcessWithOptions(&amp;psn, kSetFrontProcessFrontWindowOnly);  I'm not familiar with either ObjC or Cocoa, and this is (ultimately) getting invoked from a shell script, so not sure where to go from there. By the end of The Force Awakens, who knows about Kylo Ren's family? Can a fired moderator be elected as a moderator? While this question is inspired by recent events, it is an independent question and not tied down to any specific moderator or situation.  There's precedent for a moderator who resigned their diamond to simply ask Stack Exchange for their diamond back, without having to stand for reelection. Obviously, this may not apply if the moderator did not resign, but was removed for cause by Stack Exchange.  If a moderator has been "fired" by Stack Exchange (has had their diamond removed involuntarily by corporate action), is the person eligible to pull a  and regain a diamond through the democratic process on one of our sites, or would any such attempt be blocked? I'm aware that there is a restriction on  from standing for election, but this is not the same thing as being stripped of a diamond (fired moderators, IME, aren't also given a full site suspension unless their behavior goes beyond "possibly not a very good moderator" into "supervillain" territory).  If there is no particular rule, what should that rule be?   Should fired moderators be immediately eligible to stand for election, subject only to community approval of them returning? Should fired moderators have to go through a separate re-vetting process with Stack Exchange to regain eligibility to stand for office? Should fired moderators have an ineligibility window in a similar way that suspended users have one (e.g. after X months or years after being fired, they may stand for election). Should fired moderators be forever banned from election?   In no way am I asking about the process for a fired moderator to seek restoration through corporate appeals, etc. I'm asking only about the community election process - if a site's community wants to elect a previously fired moderator, is this inherently objectionable to Stack Exchange? Assume two black holes in the most common size range, spiraling into each other until they merge. The event releases significant amounts of energy via gravitational waves, which warp the space-time.  If the distortion is powerful enough, it would get noticed in daily life, or perhaps even detected by the proprioceptors in the human body.  How close, as an order of magnitude estimate, would you have to be to the merger to perceive it like that, without any instrument? If $X$ follows a Binomial distribution with parameters $n$ and $p$, what can we say on the distribution of $n\choose x$ and $x\choose n$ ? ($x$ is realization of $X$). Comparing two Lists and returning the distinct values and the differences Age replacement policy for hard disks and SSDs at servers I'm planing an age replacement policy for our storage and servers. Most of them are for DBs and some for images (static content) so yes, they have an huge I/O everytime.  Also, we use Samsung 840 Pro SSDs for the RAID Controllers (PERC H700i) as CacheCade.  Are you guys managing the replacement of old hard drives and solid state drives?