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Can you cast a 9th level spell if your multiclass spell slots have 9th level spell slots? How to print colored text to the terminal? Delete Duplicate Rows? I have a column in an Excel spreadsheet with several hundred entries, and some of these entries are duplicated.  I would like to remove all duplicate entries from the column so that each entry remaining is unique.   Is there a way to accomplish this automatically? This is a summary of the excerpt:  Given that we have:  *$10^9$ people  *each person has a chance of 0.01 of going to a hotel  *we have $10^5$ hotels, each hotel holds 100 people  *Thus, $P(2 \text{ persons meet on the same hotel in any given day}) = 0.01 \cdot 0.01 \cdot 10^{-5}$  *and $P(2\text{ persons on the same hotel in $2$ day}) = P(2 \text{ persons on the same hotel in any given days})^2 = 10^{-18}$  the book "Mining of Massive Dataset" said that the expected number of pairs who stay in the same hotel for 2 days is:  $P(2 \text{ persons on the same hotel in $2$ days}) \cdot ( \text{number of pairs of people} ) \cdot (\text{number of pairs of days})$  this is the part where I got stuck. Can't understand how it come to this derivation. Can anybody explain it in more elaborate detail.  You can find the content on page 6 of this link:  (it is freely available) I have an unused copy of Mass Effect 2 Collector's Edition bought via Amazon.com in the US, including a special code for Inferno Armour (also unused).  Will it work fine if I install and start playing the game in the UK? Does geographical location matter?  Thanks! My case here is that I was writing something for school, and my teacher explained an error which I really can't see. She referred to articles about &quot;dangling participles&quot;, which was previously unknown to me. I find it hard to relate the examples I've found about it to my situation. So this is a text I've written and the bold part is where the problem arises: (You could read only the bold part if you please)  Wandering, and lost in his thoughts, there is a deep despair occupying the mind of this man. He is barely aware of his surroundings, except for those few moments when the loud blissful voices break through the protective barriers, developed by his immense sadness and grave frustration, into his mind. ”How can they all possibly be so happy?” he thinks to himself. Staring blindly, with his head low, as he walks in a slow pace, whispering ”Mary, Mary, my Mary,” over and over again. Yesterday was her funeral. She had passed away from a severe type of cancer, at a relatively young age. It was his wife. They had been together since high school and were greatly attached to each other. Having spent nearly half his life by her side, we cannot but imagine his grief. Indeed, he could hardly picture a life without her. So, alone he roams in the midst of all the seemingly incessant cheering and noises, drowned by his sorrow.  Her comments on that part was:  we is slightly out of place here – see my comment below These few sentences are about him and his emotions, so ‘we’ seems out of place. If the sentence starts: ‘Having spent nearly half his life by her side’, the reader expects it to continue: ‘he’. After all we have not spent half our lives by her side.  Is she right? If so, could anyone try to explain why? How to detect if a variable is an array Proof of one inequality $a+b+c\leq\frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab}$ How to prove this for positive real numbers? $$a+b+c\leq\frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab}$$  I tried AM-GM, CS inequality but all failed. Prove every element of $G$ has finite order. It's driving me nuts! I just want to transfer one simple file from laptop to server.  I'm using ubuntu on both machines.  So I have:  -rwxr-xr-x 1 sandro    414622 2011-10-14 23:42 sandrophoto-html.tar.gz   And I'm sending it using:  sudo scp -P XXXX sandrophoto-html.tar.gz usern@server.local:/media/xx/xx/xx   And I get: scp: /media/xx/xx/xx/sandrophoto-html.tar.gz: Permission denied  p.s. I might be doing this other way around - I want to send file tar.gz that is located on my desktop, to remote server into the folder /media/yadayda Light "diode" and 2nd law of thermodynamics If I had a light "diode" - an object that only allowed light (at least for a range of frequencies) to travel through it in one direction, would this necessarily allow violations of the 2nd Law of Thermodynamics?  Or would it be possible to restrict other properties of the device such that it could be okay.  Why I think it should violate 2nd law:   I can place such devices at temperature T in a bath of thermal radiation at temperature T, such that it forms a box which only lets the light in or out.  This would appear to always allow one to create a thermal gradient.  Once a thermal gradient is formed, useful energy can be extracted.  This seems to allow useful energy to always be extracted from a thermal bath and thus give perpetual motion. Release one such device at temperature T in a bath of thermal radiation at temperature T.  Since the photons are absorbed or reflected in one direction, and undisturbed in the other, the device will start moving.  It can use a thermal bath to directly generate useful motion.   Why I think I'm missing something and such a device could potentially co-exist with the 2nd Law:   The above arguments seem valid if the diode was only 'partially' rectifying as well.  However there exist sunglasses which largely reflect on one side, but not from the other side. Researchers have succeeded in using meta-materials to create a "blackhole" for microwaves.   Can anyone help sort this out? Sums in math mode: how to display index under the sigma sign? I have a fraction with sums above and under the line. How can I convince LaTeX to write the indices of the sums under the sigma instead of next to it?  \begin{displaymath}   \frac{\sum_{s \in S} s^2}{\sum_{p \in P} p^2} \end{displaymath} I have a MacBook Pro 2009 running MacOS El Capitan. Recently the Wi-Fi has stopped working.   When I click on the Wi-Fi icon it displays the message "No hardware installed", but Ethernet still works.   Is there any way of fixing this by using a Wi-Fi dongle or something of the sort, if so do I need a specific dongle and how do I install it? How to find the magnetic field due to a revolving electron of hydrogen atom in first orbit Should I be offered the option to upgrade to 18.04.1? I understand that the first point release of Ubuntu 18.04, namely 18.04.1 is now available and that my system should now offer it as an update.  My current OS version is 16.04.5 LTS. In System Settings/Software and Updates I have set 'Notify me of a new Ubuntu version' to 'For long term support versions'. I have tried both the main server and the server for United Kingdom, neither offers an update when Software Updater is clicked or via the Ubuntu Software icon.  Can anyone please tell me why I don't get the option of updating to 18.04?  Edit:  I don't remember the details exactly, but I think that my last LTS point release update was offered automatically a lot sooner after the published release date than where we are now with 18.04.1.  Edit 10th August  It appears that there has been some problem with the update process and that it should be fixed next week, see:    Edit 14th August 18.04.1 LTS now available from UK server, I want to write a query like this:  SELECT o.OrderId, MAX(o.NegotiatedPrice, o.SuggestedPrice) FROM Order o   But this isn't how the MAX function works, right?  It is an aggregate function so it expects a single parameter and then returns the MAX of all rows.     Does anyone know how to do it my way? Here's an example of a Google Docs Spreadsheet script that sends emails using Google spreadsheets. I want the email Sent in HTML not plain text. Can someone help me out?  function sendEmails() {   var sheet = SpreadsheetApp.getActiveSheet();   var startRow = 2;  // First row of data to process   var numRows = 2;   // Number of rows to process   // Fetch the range of cells A2:B3   var dataRange = sheet.getRange(startRow, 1, numRows, 2)   // Fetch values for each row in the Range.   var data = dataRange.getValues();   for (i in data) {     var row = data[i];     var emailAddress = row[0];  // First column     var message = row[1];       // Second column     var subject = "Sending emails from a Spreadsheet";     MailApp.sendEmail(emailAddress, subject, message);   } } Prove recursively defined sequence converges I would like some advice on how to solve problems like the following: Let $(x_n)$ be a sequence defined by $x_1= 3$ and $x_{n+1} = \frac{1}{4-x_n}$. Prove that the sequence converges.  My strategy is to use the Monotone Convergence Theorem, but I am having trouble showing that the sequence is decreasing and bounded below. Here's my work so far:  Decreasing: The first 4 values are $3,1,1/3,3/11$, so let's assume $x_n \leq x_{n-1} \leq \ldots \leq x_1$. Want to show $x_{n+1} \leq x_n$. We have $x_{n+1} = \frac{1}{4-x_n}$. I want to have an upper bound for the RHS, but can't find one and don't really know where to go from here.  Bounded below: I wanted to show that all values are positive, but if we assume $x_n &gt; 0$, that doesn't rule out $x_{n+1}$ from being negative. Story whose final line is "Let there be light!" I read this series around 5-10 years ago. There were two parallel universes, ours and the universe of demons, and much of the series revolved around attacks in which demons created gateways to cross into our universe to kill people and wreak havoc, and had to be stopped by human magicians. Three youngsters (one guy from modern times, one from a few decades ago, and a girl from ancient Celtic times, all with funny names) end up being the key to the war when it's revealed that they are the three components of a mythical superweapon. These three are the only point-of-view characters in the series, each book being told from the PoV of just one of them. At the very end, they   destroy our entire universe so that, after killing all the demon masters, they can rebuild it and make sure everything happens as before up until the very last moment.  As they begin recreating the universe, the current PoV character (the one from modern times) says something like the following, the very last lines of the series. (sic on the quotation marks)  &quot;In the beginning, there was nothing but darkness. Then [name] said, 'Let there be light!'&quot; And there was light. Coolio! Hello,    This question is about the Command Line Developer Tools that are usually installed with xcode-select --install and updated via a software update from the Mac App Store (at least until macOS 10.13). I use the developer toolchain on a daily basis and it has always worked and updated without issues.    Today I've updated my mac from High Sierra 10.13.6 to Mojave 10.14.1, and I've lost the ability to update the Developer Tools.    After the update I've executed a terminal command that relies on the developer tools being installed. It was a command to update , although I don't think that the specifics matter, as I believe that any task that tried to access the developer tools would have triggered the same error message.    The error was:   xcrun: error: invalid active developer path (/Library/Developer/CommandLineTools), missing xcrun at: /Library/Developer/CommandLineTools/usr/bin/xcrun       The phrasing was new (maybe), but I thought that it was caused by the usual need to re-install the Developer Tools after some macOS updates.    Later I tried to dig a bit deeper into the failure, and found out that:  $ ls -l /Library/Developer/CommandLineTools/usr/total 0drwxr-xr-x  3 root  admin  96  4 Nov 19:32 share$ which xcrun/usr/bin/xcrun$ xcode-select -p/Library/Developer/CommandLineTools    Still, as I normally do, I entered the command to install and update the Developer Tools in the terminal:  xcode-select --install    This started the usual procedure: modal window to confirm, then request to accept the license agreement, followed by a progress bar. Except that it failed very quickly with an unexpected error:     Can&rsquo;t install the software because it is not currently available from the Software Update server.     I've tried several times, to no avail. It gets always stuck.    Sometimes, however, the failure causes the System Preferences to report a pending update:      If I open that preference panel it starts searching for updates, and it always finds nothing except the first time that it happened. The first time, it found this:          It literally suggested me to install the updates for macOS 10.11 and 10.13. I have no idea why.  I closed the preference without installing, and as I said it hasn't shown them again. There is also no update available in new Mac App Store.   Is this a known issue? Is there any way to resolve the problem?     Update  Of course I can download the Dev Tools for macOS 10.14 installer from .  Before installing them manually, though, I'm wondering if there is anything that's broken with the system.