Can we use superlative when we are talking about 2 or more items? I'm not quite sure about that since the rule says: "Superlative adjectives are used to describe an object which is at the upper or lower limit of a quality".   I wanted to figure out this before talking to my student who wrote the following sentence:"Only a few games are the most popular in the world".
When speaking with my mother a couple of days ago, I read to her a message I was sending to my cousin on her behalf ending with: "... the birthday of your youngest." [implying her child]  She immediately leapt on this and said that as my cousin only had two children, the use of the superlative was not permitted and the comparative must be used instead: "... the birthday of your younger child."  She was adamant that this was a solid grammatical rule that she was taught throughout her education.  As a younger Briton, I have relatively little formal grammatical education to older people who were better taught in this regard, so I usually defer to her on grammatical rule knowledge.  Is she right?  Are superlatives not permitted when the domain of the object is only two?  To me it seems bizarre.  The minimum or maximum of any set does not only exist when there are different minima and maxima, or indeed something which is neither.
Cancel a vote so that the tally goes back to zero and not minus Given that every class gets a minimum of 5 ability score improvements each at levels 4, 8, 12, 16, and 19 (Rogue and Fighter get more at other levels), do these ability score improvements occur by character level or by class level?  For example, is it possible to create a character who never once gains a single ability score improvement by reaching level 3 in a class and then switching to a different class repeatedly?  I had originally thought the 5 that every class gets would occur by character level, so for example a sorcerer1/bard3 would earn an ability score improvement for reaching character level 4. But there are others who have expressed the opinion that this is wrong. Javascript function to convert color names to hex codes We know that the addition and multiplication operators are both commutative, and the exponentiation operator is not.  My question is why.  As background there are plenty of mathematical schemes that can be used to define these operators. One of these is   where $H_0(a,b) = b+1$   (successor op) $H_1(a,b) = a+b$   (addition op) $H_2(a,b) = ab $   (multiplication op) $H_3(a,b) = a^b$   (exponentiation op) $H_4(a,b) = a\uparrow \uparrow b$   (tetration op: $a^{(a^{(...a)})}$ nested $b$ times ) etc.    Here it is not obvious to me why $H_1(a,b)=H_1(b,a)$ and $H_2(a,b)=H_2(b,a)$ but not $H_3(a,b)=H_3(b,a)$  Can anyone explain why this symmetry breaks, in a reasonably intuitive fashion?  Thanks. How can you programmatically tell an HTML SELECT to drop down (for example, due to mouseover)? How can you programmatically tell an HTML select to drop down (for example, due to mouseover)? Missed the MyOpenID demise; account lost forever? Is there any way to get my old account + metadata back if I have lost an account ties to MyOpenID? In a Discord call on the desktop app and my voice cannot be heard by others. When I use Discord  through browser I can be heard. Any help appreciated. Does commutativity imply associativity? I'm asking this because I was trying to think of structures that are commutative but non-associative but couldn't come up with any. Are there any such examples?  NOTE: I wasn't sure how to tag this so feel free to retag it. Let $A$ and $B$ be $n\times n$ matrices such that $ABAB=0_{n\times n}$.  Can we conclude that  $BABA$ must be  $0_{n\times n}$?   I fail to give a counterexample when $n=2$， so I guess the answer is "yes" How small does a land-mass have to be before you live "on" it, rather than "in" it? I'm sure virtually everyone agrees that people live on the Isle of Wight, but in Ireland.  Apparently the usage depends somewhat on physical size, but that can't be the whole story. How exactly do we decide which form to use? And are there any really glaring 'outliers' that don't fit the normal pattern?  LATER - I must just add that the most uncertain case I've found so far is The Falklands. Most people go for in there, but a substantial minority (about 1 in 3) opt for on. I have the following code  &lt;?php if ($handle = opendir('C:/xampp/htdocs/movies')) {     while (false !== ($file = readdir($handle))) {         if ($file != "." &amp;&amp; $file != "..") {             echo $file."&lt;br /&gt;\n";         }     }     closedir($handle); } ?&gt;   When it does have mb language such as japanese, it doesn't display properly instead it display like kyuukyoku Choujin R ?????~? rather then kyuukyoku Choujin R 究極超人あ～る  Anyway to make it display the correct name or make it still download-able by others?  Thanks for helping me :) Identify this novel: youngsters psychologically tested for abilities/profession, hero wants to author the tests, society uses moving walkways dpkg -V , What does the output mean? I ran DPKG Verify on all packges and got this output and I don't know what it means :  ??5?????? c /etc/lightdm/lightdm-gtk-greeter.conf ??5?????? c /etc/default/chromium-browser ??5??????   /usr/local/etc/no-ip2.conf ??5??????   /var/lib/dokuwiki/data/cache/_dummy ??5?????? c /etc/xdg/menus/mate-settings.menu ??5?????? c /etc/apache2/apache2.conf ??5?????? c /etc/apt/apt.conf.d/10periodic ??5?????? c /etc/sysctl.conf ??5??????   /var/lib/xine/xine.desktop ??5??????   /boot/vmlinuz-4.4.0-21-generic ??5??????   /usr/lib/python3/dist-packages/cupshelpers/__pycache__/cupshelpers.cpython-35.pyc ??5??????   /usr/lib/python3/dist-packages/cupshelpers/__pycache__/xmldriverprefs.cpython-35.pyc ??5??????   /usr/lib/python3/dist-packages/cupshelpers/__pycache__/config.cpython-35.pyc ??5??????   /usr/lib/python3/dist-packages/cupshelpers/__pycache__/openprinting.cpython-35.pyc ??5??????   /usr/lib/python3/dist-packages/cupshelpers/__pycache__/__init__.cpython-35.pyc ??5??????   /usr/lib/python3/dist-packages/cupshelpers/__pycache__/ppds.cpython-35.pyc ??5??????   /usr/lib/python3/dist-packages/cupshelpers/__pycache__/installdriver.cpython-35.pyc ??5?????? c /etc/xdg/autostart/mate-volume-control-applet.desktop ??5?????? c /etc/libvirt/qemu/networks/default.xml How to get information about deb package archive? How to get information about .deb package archive?   Like: package information, version, installed-size, architecture, description and licensing information etc. from .deb package archive? Show that $a \star b=a \cdot b+a+b$ is binary operation for the group $\Bbb{ Q} \setminus \{-1\}$ The group $\left(\Bbb{ Q}\setminus\{-1\},\star\right)$ has as its underlying set the rational numbers different from $-1$ and the operation $\star$ is defined as $a \star b=a \cdot b+a+b$ where multiplication/addition are the usual operations with rational numbers.Show that this is a binary operation.  What I did (Please help verify):  identity element has to be 0 since $a\star 0 = a+0+a(0)$ so for $a\star b=0$ we have  $ab+a+b=0$ $$ab+a=-b \\ a(b+1)=-b \\ a=\frac{-b}{b+1}$$ so $b$ cant be $-1$ since that solution is not in $\Bbb{Q}$. Similar question might have been answered here. Is this operation true for all groups? I think so.  Thanks for the tips and help. An example for a homomorphism that is not an automorphism I am using wp_get_attachment_image_src to construct the srcset attribute of an img tag. In that attribute I want to output a comma separated list of image urls along with the image widths.  Using the Media Settings page, I have configured the image sizes to be as follows:   Thumbnail size: 150x150 Medium size: 640x480 Large size: 1024x768 Small size: 278x320   The wp_get_attachment_image_src function returns the correct urls and the correct widths for the image sizes full, medium and small. small is a custom size I added using add_image_size.  If I call wp_get_attachment_image_src( $image_id, 'large' ), the returned array looks like this:  array (     0 =&gt; 'http://localhost/wp-content/uploads/2014/10/image-1024x768.jpg',     1 =&gt; 640,     2 =&gt; 480,     3 =&gt; true, )   Checking the image which can be found at that url turns up the image with the correct dimensions.  Currently i am using the php builtin function  to circumvent this problem, but this function call takes significantly longer than simply accessing the index returned by wp_get_attachment_image_src:  Without getimagesize (mtime before and after execution):   '0.83761000 1415195440' '0.83831600 1415195440'   With getimagesize:   '0.34808000 1415195635'  '0.35323900 1415195635'   What can I do to make wp_get_attachment_image_src return the correct dimensions? Setting default values (conditional assignment) In Ruby you can easily set a default value for a variable   x ||= "default"   The above statement will set the value of x to "default" if x is nil or false  Is there a similar shortcut in PHP or do I have to use the longer form:  $x = (isset($x))? $x : "default";   Are there any easier ways to handle this in PHP? When I log in with LightDM on my laptop running Debian Unstable, it recently started to hang for around 2 minutes until journalctl shows the message kernel: random: crng init done. When I press random keys on my keyboard while it hangs, it logs in faster (around 10 seconds). Before I didn't have this issue, is there any way I can fix it?  Edit: using linux-image-4.15.0-3-amd64 instead of linux-image-4.16.0-1-amd64 works, but I don't want to use an older kernel. Codomain of function complete implies function space complete Let $(X,d_X)$ and $(Y,d_Y)$ be two metric spaces.   Let $(C_b(X,Y), d_C)$ be a function space with the metric $$d_C(f,g):=\sup\limits_{x\in X} d_Y(f(x), g(x)).$$  Prove that if $(Y,d_Y)$ is complete then $(C_b(X,Y), d_C)$ is complete.  Unfortunately, I have no idea how to approach this problem. I can think of something like this:  Let $(y_k)_k\subset Y$ be a Cauchy sequence converging to $y\in Y$. Then there exists some $f\in C_b(X,Y)$ such that $f(x_k)=y_k$ for all $k\in \mathbb N$. Since $f$ is continuous, $\lim\limits_{k\to\infty} d_Y(f(x_k), y)=0$.  But how do I go from here? As far as I understand, what needs to be proved is that any Cauchy sequence of functions in $C_b(X,Y)$ converges in $C_b(X,Y)$, that is, that the limit is bounded and continuous. But how do we devise such a sequence of functions?