Color definitions for CSS using listings
Color change of string delimiter in listings with macro
Is it possible to conditionally format a cell if the cell contains formula (to alert myself and other users when updating the cell)? Is there a way to do proportional editing only on specific vertices? Reputation misaligned in new topbar Cannot reach public WIFI login page in Ubuntu 18.04 Captive Portal Issue $n &gt; 2$ and $n$ is a prime number then $n$ is odd.  Prove by contradiction assume $n$ is even then there is some $k\in\Bbb N, n = 2k$ then $n &gt;2, 2k &gt; 2 , k &gt; 1$  Is this  a sufficient proof? What is the DC of the Tempest Cleric's Wrath of the Storm feature? What is exactly the density of a black hole and how can it be calculated? How do I query for posts by partial meta key? I have a function that stores the "like" status for a post as post meta. I want to associate that "like" with the user that liked it, so I setup a custom field called "like_status_{user_id}" (where {user_id} is the id of the currently logged in user) which I store as a 0 or 1. So for a post with several "likes" there would be several meta values in the db that are setup like this:  'meta_key' = 'like_status_0' 'meta_value' = 1 'meta_key' = 'like_status_2' 'meta_value' = 1 'meta_key' = 'like_status_34' 'meta_value' = 1   ....and so on.  There are potentially thousands of likes on a specific post. How would I run a query that showed if someone else also liked that post?  I was thinking something like this:  $query = new WP_Query(array(     'meta_key' =&gt; 'like_status_{user_id}',     'meta_value' =&gt; 1, ));   I'm trying to push a notification to everyone who has liked a post when someone else likes that post...something like, "Hey, someone else liked that post you liked. You should go check it out!" But I need a way to find out if anyone else has liked that post and if so, who they would be so I could notify them.  If it's not possible, could you suggest a better way of storing this data as post_meta while still keeping the efficiency of quickly updating a single user's like status on a post? What is the best practice for multiple button placement and emphasis? Usually, we only have 2 buttons at the bottom of a form or a page that requires an action: Submit &amp; Cancel.  This one is quite easy to style. However, what if we are dealing with multiple buttons at the bottom of a page? For example:   ← Back | Send Email | Booking Paid | Check-in Guest   I'm thinking of making "Back" just a link (not a button) and making "Send Email" / "Booking Paid" secondary buttons (light gray). Then I'd make "Check-in Guest" as the primary button (green).  I still feel that there's a better way of doing it or dealing with multiple buttons / actions. What do you think? For each $y \in \mathbb{R}$ either no $x$ with $f(x) = y$ or two such values of $x$. Show that $f$ is discontinuous. This is from Apostol's Mathematical Analysis.  Let $f$ be a function defined in $[0, 1]$ such that for each real number $y$ either there is no value of $x \in [0, 1]$ such that $f(x) = y$ or there are exactly two such values of $x$. Prove that a) $f$ must be discontinuous on $[0, 1]$. b) $f$ has an infinite number of discontinuities in $[0, 1]$.  Long back I had tried to solve the problem. I reasoned for a) as follows: Suppose that $f$ is continuous and let $m, M$ be its minimum and maximum values on $[0, 1]$. Clearly if $m = M$ then $f$ is constant and clearly for every $x \in [0, 1]$ we have $f(x) = m = M$ which contradicts given property of $f$. So we must have $m &lt; M$. Clearly there are now four distinct points $a, b, c, d$ in $[0, 1]$ such that $f(a) = f(b) = m, f(c) = f(d) = M$. By checking possible linear orderings of $a, b, c, d$ I could find a find a value of $y \in (m, M)$ for which there exist more than 2 values of $x$ such that $f(x) = y$. However this approach looks very clumsy and I suspect much simpler and easier proof is possible. Part b) seemed bit complex and my only guess was that probably $f$ was discontinuous on each subinterval of $[0, 1]$ but I could not prove this claim (may be the claim is wrong!). Perhaps there is a simpler solution to this part of the problem. Apostol's also asks to provide an example of such a function. Any hints on the overall problem will be appreciated.  Update: After looking at Marc's answer, I think I have found a way to show that there are infinitely many discontinuities. Earlier the solution was a part of the question itself but it made the question look quite lengthy hence I moved it to a separate answer. What are acceptable reasons for flagging as "Requires Moderator attention"? After reading , I feel I don't quite understand this function. What are the guidelines for flagging a question as &quot;Requires Moderator attention&quot;? Prove that the following inequality holds   $$a^a b^b c^c\ge (abc)^{\frac{a+b+c}{3}}$$   if $a,b,c$ are positive.   I'm not sure how to handle these kinds of powers. Are there any "famous" but not so advanced inequalities that involve this kinds of expressions?  I was trying to do something like ordering them without lost of generality because it's symmetric, but I get nowhere and I just make the thing even more complicated.  I'm asking for solution rather than hints since this is my first time encountering these kinds of problems. What is the max variance distribution with fixed mean and support Is there a upper bound on the variance for a distribution that is confined say, in $[0,1]$, and has fixed mean $\mu \in [0, 1]$ I am trying to create buffers around the Hurricane Sandy path I created in QGIS (points are lat/long).   I have both points from each day she was tracted and the line I created from it with Points2One.   When I go to make buffers around either the line or the points, the buffer takes up the whole screen. Its all just one color.   I have made buffers before but from data I did not create.   Right now all of my projections are set to WGS 84 EPSG 4326. Objective-C: Use singleton vs. use class as an object? Over the years I've written some libraries. These libraries sometimes depend on each other.  As a result, the "tex" directory is structured as follows:  tex ├── library |   ├── library1.sty |   ├── library2.sty |   └── library3.sty ├── project1 |   ├── master.tex |   ├── chapter1.tex |   └── chapter2.tex ├── project2 |   └── article.tex └── project3     └── paper.tex   The libraries depend on each other. As a result, in every library that depends on another library, this is part of the header:  %library2.sty \ProvidesPackage{library2} \RequirePackage{../library/library1}   In other words, the library is imported from the "root of every project". This is not a good design choice. What if someone copies the libraries in the folder of the root of a project, or what if the folder "library" is renamed...  It is however reasonable the "active directory" still remains in the project root.  What can be done to resolve such library dependencies? How to search inside files on Windows 7? In Windows XP we can search for files that contain a defined keyword (inside all files types).  Windows 7 can look inside files for a keyword, but only for text files. (*.doc, *.txt, *.inf, ...), not (*.conf, *.dat, *.*, ...).   don't contain any filter I can use for this.  How is this possible? I am trying to find the splitting field of $x^6+x^3+1$ over $\mathbb{Q}$.  Finding the roots of the polynomial is easy (substituting $x^3=t$ , finding the two roots of the polynomial in $t$ and then taking a 3-rd root from each one). The roots can be seen  [if there is a more elegant way of finding the roots it will be nice to hear]  Is is true the that the splitting field is $\mathbb{Q}((-1)^\frac{1}{9})$ ? I think so from the way the roots look, but I am unsure.  Also, I am having trouble finding the minimal polynomial of $(-1)^\frac{1}{9}$, it seems that it would be a polynomial of degree 9, but of course the degree can't be more than 6...can someone please help with this ? Rules for refreezing food What are the general rules regarding when can you refreeze food that was frozen and then thawed in the fridge? and what are the reasons behind them? (Hygiene? Food quality?). Let's assume for the sake of the argument that the items were in a non-frozen state only a few hours.  To be more specific, I'm interested in the application of these rules for  - Ginger garlic paste - Dough - Indian Curries - Green Chilly paste - Frozen green peas How can I get dramatic shallow DOF with a kit lens?