In particular, think of the home air conditioner or the power setting on the kitchen refrigerator: the intensity of effort is opposite to the numbering of the related quality. So "Turn up the air conditioner" can be interpreted as a request to set it colder (make the machine work more) or warmer (change the control to a larger number).  What terms would be good to use instead, that are grammatically equivalent so they are drop-in replacements and don't require re-arranging the sentence, are succinct, and are understandable (even if  not immediatly familiar) by folks lacking a Chirchhillesque vocabulary? And, the whole point is that they are completely unambiguous.  Ideally the pair of terms should match nicely, but that's not necessary.  I know the confusion can be avoided by phrasing it differently, and that's what I actualy do if I notice it. But I've wondered if there's a better term that could be used in this place that is simply not ambiguous at all.
As the title says, I've heard two possible meanings for turning down the air conditioning: It could mean set the target temperature lower (i.e. colder) or make it work less (i.e. warmer).  Turning down the heat makes it colder, but both meanings are in agreement there.
System of congruences with variable I am looking over , and I came across a solution containing this:  Problem Bernardo chooses a three-digit positive integer $N$ and writes both its base-5 and base-6 representations on a blackboard. Later LeRoy sees the two numbers Bernardo has written. Treating the two numbers as base-10 integers, he adds them to obtain an integer $S$. For example, if $N = 749$, Bernardo writes the numbers $10,\!444$ and $3,\!245$, and LeRoy obtains the sum $S = 13,\!689$. For how many choices of $N$ are the two rightmost digits of $S$, in order, the same as those of $2N$? $\textbf{(A)}\ 5 \qquad\textbf{(B)}\ 10 \qquad\textbf{(C)}\ 15 \qquad\textbf{(D)}\ 20 \qquad\textbf{(E)}\ 25$ Solution 1 First, we can examine the units digits of the number base 5 and base 6 and eliminate some possibilities. Say that $N \equiv a \pmod{6}$ also that $N \equiv b \pmod{5}$ Substituting these equations into the question and setting the units digits of $2N$ and $S$ equal to each other, it can be seen that $b &lt; 5$ (because otherwise $a$ and $b$ will have different parities), and thus $a=b$. $N \equiv a \pmod{6}$, $N \equiv  a \pmod{5}$, $\implies N=a \pmod{30}$, $0 \le a \le 4$ Therefore, $N$ can be written as $30x+y$ and $2N$ can be written as $60x+2y$ Just keep in mind that $y$ can be one of five choices: $0, 1, 2, 3,$ or $4$, ; Also, we have already found which digits of $y$ will add up into the units digits of $2N$. Now, examine the tens digit, $x$ by using $\mod{25}$ and $\mod{36}$ to find the tens digit (units digits can be disregarded because $y=0,1,2,3,4$ will always work) Then we take $N=30x+y$ $\mod{25}$ and $\mod{36}$ to find the last two digits in the base $5$ and $6$ representation.[N \equiv 30x \pmod{36}][N \equiv 30x \equiv 5x \pmod{25}]Both of those must add up to[2N\equiv60x \pmod{100}] $N\equiv{30x\mod{36}}\\N\equiv{30x}\equiv{5x\mod{25}}$ Both of these must add up to $2N\equiv{60x\mod{100}}$ [...]  I'm not really sure which modular arithmetic rule to apply in the final three congruences, or where to start. How would I go about understand this? Renaming hundreds of files at once for proper sorting I am looking for a way to output all page IDs from the following menu:   &lt;?php wp_list_pages('depth=1&amp;exclude='3,5,11')); ?&gt;   Only top level pages needed, therefore the 'depth=1'.  Any help appreciated. How do I convert two lists into a dictionary? Ubuntu with full disk encryption - bad password after upgrade to 18.04 A few months ago I set full disk encryption during installation of Ubuntu 17.10. Now, I've decided to upgrade. The upgrade ran to the end without any problems. However, after reboot I am not able to log into my encrypted disk.  Where can be the problem? I am 100% sure I press the "right keys" on the keyboard, but technically I don't know what I am writing because of "*" characters and maybe after upgrade my keyboard layout changed. I use some characters which might be somewhere else on the keyboard. What language is default after upgrade?   By the way, I've already tried Caps-lock, but still no luck.  Help will be really appreciated. I am not a fan of installing my system and all backups over and over again. Html Textarea elements only wrap when they reach a space or tab character. This is fine, until the user types a looooooooooooooooooooooong enough word. I'm looking for a way to strictly enforce line breaks (eg.: even if it results in "loooooooooooo \n ooooooooooong").    The best I've found is to add a zero-width unicode space after every letter, but this breaks copy and paste operations. Anyone know of a better way?  Note: I'm referring to the "textarea" element here (i.e.: the one that behaves similarly to a text input) - not just a plain old block of text. Efficient Way to store images in android Are the units of the quotient ring $\mathbb{F}_2[x]/\langle x^k+1 \rangle$ known in general, where $\mathbb{F}_2$ is the finite field with two elements? I'm specifically interested in the case where $k$ is divisible by two, such as say $k=8$, or $k=12$.  If so, can they be constructed easily? I'd be grateful if you could provide a few examples. Best answer versus best solution What is better to have? A pokemon with higher IV but lower CP or vice versa? Me and my friends have encountered this situation many times. We need to decide which Pokemon to evolve. Take the following scenario:   Growlithe A: 20% more CP than Growlithe B. (898 instead of 743). Growlithe B: 26% more IV than Growlithe A. (87 instead of 69 in this case).   I didn't give more details about each Pokemon because I'd like a general answer that others can use.  Thank you kind folks!  P.S this is not a duplicate, since I understand what a higher IV interprets into.  Yes, a higher IV will define the MAX CP, but it's not the only thing to consider. A higher IV also means better chance of better moves for the evolved pokemon - and those are much more important than a high CP. Also consider that I have many Arcanines and I don't have the stardust to max them out (that is a different question). Motion Tracking objects that go out of frame and re-enter later I have successfully transferred "Killing Floor" from my brother's laptop to my own via external hard drive. The problem, now that I have all the files, is that I don't know how to launch the game through Steam. All I did was copy files from his Laptop to the hard drive, then from the hard drive to my laptop, then I put the files in the "Steamapps" folder under "Steam" in my laptops hard drive. So the question is, how do I start up the game through Steam? In general what is the approach to switch the desktop environment or window manager on Ubuntu? The main difference between stock Ubuntu, Kubuntu and Lubuntu is supposedly the use of Unity vs. KDE vs. LXDE.  However, in order to try various desktop environments and window managers I don't want to have to reinstall the respective flavor from scratch just to get a particular desktop environments or window manager. There probably is an easier method than that.  The question: How can I easily test different desktop environments and respective compatible window managers (say KDE, LXDE, Unity, GNOME, XFCE and StumpWM)? How can I resize an ext root partition at runtime? How can I increase the size of the root partition of a system at runtime?   I have a partition that is not allocated after the root partition (which is also ext4), how can I add that unallocated space to the space allocated to the root partition without having to shutdown the server? Measures: Atom Definitions Let $\Omega$ be a measure space with measure $\mu$. (Here, a measure is only meant to be countable additive!)  Consider a subset $A\in\Sigma$.  Then according to the  it is an atom if: $$(1)\quad\forall E\subseteq A:\quad\mu(E)&lt;\mu(A)\implies\mu(E)=0\quad(\mu(A)&gt;0)$$ and according to the  it is an atom if: $$(2)\quad\forall E\in\Sigma:\quad\mu(E\cap A)=0\lor\mu(E^c\cap A)=0\quad(\mu(A)&gt;0)$$  Now, these definitions agree for the really trivial cases: $$\mu\equiv0$$ $$\mu\equiv\infty$$ but they differ for the less trivial case: $$\quad\mu(E\neq\varnothing):=\infty,\,\mu(\varnothing):=0$$ namely the atoms are w.r.t. (1) all nonempty subsets whereas w.r.t. (2) only the singletons.  Excluding this pathological case, are the definitions equivalent? (More precisely, assume there exists a measurable subset $0&lt;\mu(F)&lt;\infty$.)  So far I checked that: $$(2)\implies(1):\quad\mu(E)&lt;\mu(A)\implies\mu(A\setminus E)&gt;0\implies\mu(E)=0$$ but what about the other direction? Windows 7 low and critical battery levels cannot be set lower than 10% I'd like to work on a bbcode filter for a php website. (I'm using cakephp, it would be a bbcode helper) I have some requirement.    Bbcodes can be nested. So something like that is valid.  [block]       [block]       [/block]       [block]           [block]           [/block]       [/block]   [/block]     Bbcodes can have 0 or more parameters.     Exemple:     [video: url="url", width="500", height="500"]Title[/video]   Bbcodes might have mutliple behaviours.     Let say, [url]text[/url] would be transformed to [url:url="text"]text[/url] or the video bbcode would be able to choose between youtube, dailymotion....  I think it cover most of my needs. I alreay done something with regex. But my biggest problem was to match parameters. In fact, I got nested bbcode to work and bbcode with 0 parameters. But when I added a regex match for parameters it didn't match nested bbcode correctly.   "\[($tag)(=.*)\"\](.*)\[\/\1\]"  // It wasn't .* but the non-gready matcher  I don't have the complete regex with me right now, But I had something that looked like that(above).  So is there a way to match bbcode efficiently with regex or something else.  The only thing I can think of is to use the visitor pattern and to split my text with each possible tags this way, I can have a bit more of control over my text parsing and I could probably validate my document so if the input text doesn't have valid bbcode. I could Notify the user with a error before saving anything.  I would use sablecc to create my text parser.   Any better idea? or anything that could lead to a efficient flexible bbcode parser?  Thank you and sorry for my bad english... How do I create a link? Say I am extending The blockBase class to create a custom block, and I am implementing the blockBuild method to create some markup for my block. Something like this:   class YourModuleBlock extends BlockBase {     /**      * Implements \Drupal\block\BlockBase::blockBuild().      */      public function build() {       return array(         '#markup' =&gt; 'This is a block!',       );      }    }   If I wanted to provide a link in this markup, in D7 I would have used the l function, but this is no longer available (). So, I need to make available the new D8 method for generating links. I could just use an &lt;a&gt; tag, but this was never best practice in D7.  So, what is the right method to use for creating links and how do I make it available to my function? “have found” vs. “found” 3D bodies in TikZ Is there like a library that has default geometric figures like the ones shown below. Am not acquainted yet with 3D diagrams in TikZ.