How do I get \DeclareMathOperator to put the limit beneath?
Define additional math operators to be typeset in roman
What is the symbolic significance of the Night King's message? In Game of Thrones S8E1,        Ned Umber is found pinned to a wall by the Night King with a symbolic message, which looks like tentacles coming out of the body of Ned.   Is there some meaning to that symbolic message? If yes, then what is that? My Panda USB wi-fi adapter works just fine on 16.10, but when I try to connect to my wi-fi router in 17.04, GNOME network manager reports "Connection failed." I did some tinkering, and noticed that my MAC address for my wifi adapter, according to GNOME, is DIFFERENT every time I make it forget my wifi settings and try to reconnect. Any leads on a possible fix or work-around?   I'm running Ubuntu GNOME 17.04, kernel 4.10.0-19-generic, GNOME 3.24.0. What does a dot after the file permission bits mean? I performed an ls -la on directory on my CentOS 6.4 server here and the permissions for a given file came out as:  -rwxr-xr-x.   I understand what -rwxr-xr-x means, what I don't understand is the . after the last attribute.  Can someone explain it to me? Is it harmful in any way? Can it be removed? Initially, my question was: is "focussed" or "focused" the correct past tense of "focus", but since this applies to a lot of words, I would like to generalize and ask: is there supposed to be a rule when to double the consonant? Given $$1\cdot 2^1 + 2\cdot 2^2 + 3\cdot 2^3 + 4\cdot 2^4 + \cdots + d \cdot 2^d = \sum_{r=1}^d r \cdot 2^r,$$ how can we infer to the following solution? $$2 (d-1) \cdot 2^d + 2. $$   Thank you Is it possible to save `bc` command line history? bash has a handy file .bash_history in which it saves the history of commands and on the next execution of bash the history is populated with saved commands. Is it possible to save bc command history to a file in the same way and then load it on startup so that bc history is preserved? I tried reading  and it mentions readline and libedit. From ldd /usr/bin/bc I see mine uses readline and readline has  and read_history functions. Is this functionality implemented in bc or to do it I'll need to patch bc? I'm looking at buying a second-hand Mac, probably one that does not include an OS installation disk.  How can I scan it to make sure that it has not had security threats installed on it?  Is there a CD or DVD image I can boot it up with to perform this scan offline?  Edit: prospective machine would be a 2011- or 2012-vintage MacBook Pro.  Also note that I don't have reliable access to high-speed internet, so solutions that involve downloading 5GB over the Internet are not ideal.  For others, though,  may be helpful. Question of an isomorphism of $\epsilon_ 0$ and a subset of the rationals. I don't know if this question is appropriated for this site. Anyway, I'm searching for an isomorphism of order $f:K \longrightarrow \epsilon_o $, such that $(K, \leq)$ is a subset(proper or not) of $(\mathbb{Q}, \leq)$ and $\epsilon_o = \sup\{\omega, \omega^{\omega}, \omega^{\omega^{\omega}}, ... \}$. Actually,  I'm not finding neither an isomorphism between $K$ and $\omega^{\omega}$.  Thanks in advanced. Opposite of "straight talk" What is the opposite for the straight talk idiom? How do I best call the activity when someone makes a very long preamble before he says what he wants? Why do circuits work so fast? Drift velocity (explained to me as how fast the electrons are moving) is really slow. My book says the electrons move at around 10 mm/ s.  If electrons move so slowly how do circuits work so fast? If you make a basic circuit with just a light bulb, the bulb lights up almost immediately after you connect the wire to the positive terminal. Two layers, same coordinate system, wont show up I have vector two sets of vector layers that won't show up together. One set shows up together and the other set together etc but they are of the same area.  The layers I was given did not have a defined spatial reference which I manually projected as the same as the data frame I specified so all layers now have same CRS...yet not showing up together. I have noticed they appear to have different extents... What should I do? In Chamber of Secrets, in the first Duelling Club class, Snape suggests Malfoy use the Serpensortia spell against Harry. This of course reveals that Harry is a Parselmouth, but how could Snape anticipate this? Was there any reason for Snape to suspect Harry is a Parselmouth? Or was it just a way to laugh at how Harry would get frightened? As most of you know, in the Microsoft Store, there are . This means that on Windows I can emulate Ubuntu and have the Ubuntu command line directly on Windows.  The question is very easy: what can’t I do from the Ubuntu command line emulated in Windows that I can do on a proper Linux-based Ubuntu? Is it useful to download this Ubuntu application, install it, and work just with it instead of the real OS? Is it possible to install all the development libraries? Can I write (or not) device drivers? In other words: what are the limits?  What features of Ubuntu Linux-based are missing from Ubuntu-on-Windows?  New answers are welcome: I know that every software is always changing by improving characteristics and features! How best to sum up lots of floating point numbers? The "I Get It" Reputation Problem Proving the summation formula using induction: $\sum_{k=1}^n \frac{1}{k(k+1)} = 1-\frac{1}{n+1}$ A subring of the field of fractions of a PID is a PID as well. Let $A$ be a PID and $R$ a ring such that $A\subset R \subset \operatorname{Frac}(A)$, where $\operatorname{Frac}(A)$ denotes the field of fractions of $A$. How to show $R$ is also a PID?   Any hints? I've got a domain that I apparently forgot to set a preferred domain for, so I just tried to do it. Webmaster Tools instead popped up a little box:     Part of the process of setting a preferred domain is to verify that you own http://www.example.com/. Please verify http://www.example.com/.   I'm running into some problems following these instructions:   As far as I can tell I already did verify sometime in the past. There's a TXT DNS record with the gibberish Google tells you to set for it that I couldn't have come up with myself. …and nothing is telling me this information is bad. So let's assume the site is somehow not actually verified. All  instructions start with "click the Manage Site button next to the site you want, and then click Verify this site." That button doesn't even exist on my screens. (It presumably goes away when you successfully verify?) Those instructions were all updated pretty recently, and the DNS one in particular just a couple weeks ago so it seems a bit unlikely they're inaccurate.   I am not using Apps, and won't be, so can't try out the verification .   Note that I also have another domain that I have not done any verification for which is showing the same behavior(no such button, being told to verify when it seems impossible etc.) so something appears to just be broken.  I already have a no-www process in place server-side, so we can skip that. I'm just trying to get the box checked off in GWT.  If I don't get any resolution, I'll eventually scrap the TXT record and see if the site gets un-verified(or whatever since it thinks it isn't), and see if I can just restart the process.  It's not urgent so I'm just trying to figure out if I've gone blind to something or what. Did the button move? Reference to the Table of Contents page I thought that someone must have asked this, but my searches didn't find it.  I am looking to refer back to the table of contents from places in my document. How can I do this? Automatically login and lock