What is a term which refers to the areas in the back or rear, with the same scope as the word "frontal"?  The satirical/humorous term backal exists, but is not really a word (or appropriate to use in writing).
When we lie down, the "back part of the body" is in contact with the bed. It includes the heels, the calves, the backside, the back, and the back of the neck, and the back of the head etc.  How do we refer to the entire "back part" of the body?
Is  purely conceptual or does it represent some real "thing"?  Said another way, is superposition thought to have some tangible physical manifestation or is it simply the lack of physical determinism, except as defined by a wave function?  It seems like my question might be semantic.  For example, it is said that   superposition is obeyed, like a law superposition can be observed, like a phenomena superposition describes behavior   I guess my question is, can superposition be measured like an electrical charge, or is it simply the lack of knowable position. Proof for $A \cup B = B$ if and only if $A \subset B$ I am trying to define a proof for  $A \cup B = B$ if and only if $A \subset B$  I started with:  $$A \cup B$$ $$x \in A \lor x \in B$$   but I am unsure on how to continue. I just failed these   in First Post, I read the question and thought it seemed reasonable but the user was deleted so to be on the safe side I clicked add comment and I failed the audit.  I'm not sure why adding a comment would be considered a negative action, is the correct option to click No Action Needed or edit?  What was I supposed to do in this situation?  Adding a comment should not be a review audit fail. One of the most common security best practices these days seems to be . I've never really found a good explanation for that, but I'm assuming it's to minimize the risk of a  malicious or infected script within the webroot from reading the database password.  But, you still have to let WordPress access it, so you need to expand open_basedir to include the directory above the document root. Doesn't that just defeat the entire purpose, and also potentially expose server logs, backups, etc to attackers?  Or is the technique only trying to prevent a situation where wp-config.php would be shown as plain-text to anyone requesting http://example.com/wp-config.php, instead of being parsed by the PHP engine? That seems like a very rare occurance, and it wouldn't outweigh the downsides of exposing logs/backups/etc to HTTP requests.  Maybe it's possible to move it outside the document root in some hosting setups without exposing other files, but not in other setups?    Conclusion:  After a lot of back-and-forth on this issue, two answers have emerged that I think should be considered the authoritative ones. Aaron Adams makes a good case in  wp-config, and chrisguitarguymakes a good . Those are the two answers you should read if you're new to the thread and don't want to read the entire thing. The other answers are either redundant or inaccurate. How to install Wi-Fi driver for Realtek RTL8821CE on Ubuntu 18.04? I'm trying to install drivers for my Wifi on my HP All-in-one desktop. I've been told to show the output of the command "sudo lshw -C network" so here it is:  *-network description: Ethernet interface product: RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller vendor: Realtek Semiconductor Co., Ltd physical id: 0 bus info: pci@0000:01:00.0 logical name: enp1s0 version: 15 serial: 48:ba:4e:5c:06:5f size: 100Mbit/s capacity: 1Gbit/s width: 64 bits clock: 33MHz capabilities: pm msi pciexpress msix bus_master cap_list ethernet physical tp mii 10bt 10bt-fd 100bt 100bt-fd 1000bt 1000bt-fd autonegotiation configuration: autonegotiation=on broadcast=yes driver=r8169 driverversion=2.3LK-NAPI duplex=full firmware=rtl8168h-2_0.0.2 02/26/15 ip=192.168.1.21 latency=0 link=yes multicast=yes port=MII speed=100Mbit/s resources: ire:31 import:e000(size=256) memory: fea04000-fea04fff memory:fea00000-fea03fff  *-network UNCLAIMED description: Network controller product: Realtek Semiconductor Co., Ltd. vendor: Realtek Semiconductor Co., Ltd. physical id: 0 bus info: pci@0000:02:00.0 version: 00 width: 64 bits clock: 33MHz capabilities: pm msi pciexpress cap_list configuration: latency=0 resources: import:d000(size=256) memory:fe900000-fe90ffff   Output from "lspci -nnk | grep -A2 0280":  02:00.0 Network controller [0280]: Realtek Semiconductor Co., Ltd. RTL8821CE 802.11ac PCIe Wireless Network Adapter [10ec:c821] Subsystem: Hewlett-Packard Company RTL8821CE 802.11ac PCIe Wireless Network Adapter [103c:831a] 03:00.0 Unassigned class [ff00]: Realtek Semiconductor Co., Ltd. RTS5229 PCI Express Card Reader [10ec:5229] (rev 01) I am creating a controller for a 12 V system using an Arduino Uno microcrontroller. For the outputs I am using a relay shield to switch the 12 V components. I have a 12 V toggle switch that turns on some 12 V components in the system and I want to use a trigger signal off of this same switch to send to an Arduino digital input. I know that the Arduino can only handle 5 V max. What would be the best way to step down the 12 V coming off of the switch to the 5 V for the input?  EDIT: The system is for use in a car. Would the amperage of the car battery need to be lowered somehow as to not blow up the components? How do I see the extensions loaded by PHP? I believe this to be fraud — hired, then asked to cash check and send cash as Bitcoin I have been "hired" by Nissan Motor as a key account specialist.  My first assignment is to cash two checks that I have received. Both were written by a customer who has already received the engines. The total is $2500. I am to cash the checks, get the money, take out my bonus and any other related expenses and deposit into a Bitcoin ATM. Then make copy of receipt and electronically send to my "manager".  I contacted a lawyer, was told to talk to the Department of Labor, who said they will not get involved, as this is between me and my employer. Any advice? I use wubi to install Ubuntu 10.10 on my ntfs partition. So I want to change the home folder to a folder on the ntfs partition. I could keep the personal configuration, software and so on after reinstalling the Ubuntu.  So I use ntfs-config to manage the disk partition, it's mounted when system is startup. And the permission of all files and directories are 777.  Then I modified the /etc/passwd to set the home folder to the folder on the ntfs partition. I can successfully login the account, however it looks like the .bashrc and .profile are not loaded correctly. I can't use the input method(even can't configure ibus), no sound device. However everything works well after changing the home folder back to /home/.  Could anybody give me a hint to make it work? Thanks. Proof of when is $A=X^TX$ invertible? Say we have an $n\times m$ matrix $X$. What are the specific properties that $X$ must have so that $A=X^TX$ invertible?  I know that when the rows and columns are independent, then matrix $A$ (which is square) would be invertible and would have a non-zero determinant. However, what confuses me is, what sort of conditions must we have on each row of $X$ such that $A$ would be invertible.   It would be very nice to have a solution of the form:   when $n &gt; m$ then $X$ must have... when $n &lt; m$ then $X$ must have... when $n = m$ then $X$ must have...   I think in the 3rd case we just need $X$ to be invertible but I was unsure of the other two cases. I've searched the net for such information and found different command lines, like these ones:  sudo apt-get remove application sudo apt-get remove application*  sudo apt-get remove --purge application sudo apt-get remove --purge application*  sudo apt-get purge application sudo apt-get purge application*   So, what is the correct way? Is it necessary to use that "*"?  After that, I also found these commands:  sudo updatedb sudo locate application sudo rm -rf (file/folder name) Let $R$ be a Artinian commutative ring with $1 \neq 0$. If $I$ is prime, then $I$ is maximal. Prove: Let $R$ a Artinian commutative ring with $1 \neq 0$. If $I$ is prime, then $I$ is maximal.     I got stuck on this. I understand that every ideal is generated by finitely many elements. Here is my approach:  It's enough to prove the following implication: $$ R/I \ \text{is a domain} \quad \Rightarrow \quad R/I \ \text{is a field}$$ Then only finding an inverse is left. So let $x \in R$ in arbitrary. We have to find an inverse element of $x+I \in R/I$, that as an element y so that $x \cdot y \in I+1$. We denote $I = (x_1, x_2, \cdots, x_n)$.  Now I have to find y so that $xy -1 = r_1 x_1+ r_2 x_2 + \cdots + r_n x_n$. This is where I no more knew what to do.   Your advise will be appreciated. Placeholder for body off in Android app The placeholder for the body field (the word "Body") is strangely placed in the Android app, seems a bit too high:    Could reproduce using:   Samsung Galaxy 4a.  Android version 4.4.2  App version 1.0.54 Moto X (2013), Android 4.4.4 App version 1.0.60 Most people say I wish I could, I wish you would.    Can we use I wish I can, I wish you will?    I'd like to know what the main differences between the usage of can/will and could/would are when wishing.  Is it related to the subjunctive? Because one says “I wish I were”, not “I wish I am”, so are would and could the subjunctive forms of can and will?  Or is it something else entirely? MySQL Error 1093 - Can't specify target table for update in FROM clause Lately my laptop (HP g42 247sb) screen is damaged, so I hook it up with an external monitor (LG something) and it works fine now.  The only annoying thing is I cannot navigate the BIOS menu for some tweaking because the BIOS not shown on the external monitor, instead, it only shown on the broken laptop screen, and  it only output to my external monitor when Windows/OS is logged-on.  So, is there anyway I can force output during BIOS/BOOT/POST to my external monitor?  Things I have done and didn't work:   Set my LG monitor as primary display on both window properties and Intel Graphics panel  Enter the BIOS (F10 key) and press the Fn+F4 key (change display output). Disable and uninstall my internal screen (broken laptop screen) using device manager and restart, but Windows (BIOS?) install it back on log-on. Closed lid/Magnet on sensor. What is going on with pgfpages and page labels? I’m using a feature of beamer that shows notes beside slides, but the page numbers that are coming out are crazy, making it impossible to extract specific slides into other documents with \includegraphics[page=n]{presentation.pdf}.  For example, in this MWE, there are two frames that are each 1 slide, and then one frame that is four slides. The PDF page labels that show up in Acrobat are, as indicated, 2, 3, 3, 3, 3, and 7. It starts at page 2 instead of 1, and then there are four page 3s, but they don’t even all belong to the same frame!  \documentclass{beamer} \usepackage{pgfpages}  \setbeameroption{show notes on second screen=left} \setbeamertemplate{note page}{frame \insertframenumber \\ \insertnote} \def\pg#1{pgfpages says this is page #1 but it is really page \arabic{page}}  \begin{document}  \setcounter{page}{0}  \frame{hi \note{\pg{2}}}  \frame{there \note{\pg{3}}}  \frame{how \pause are \pause you \pause today \note&lt;1-3&gt;{\pg{3}} \note&lt;4&gt;{\pg{7}}}  \end{document}   Here’s what the output looks like:    I know that the manual says, “pgfpages will produce wrong page numbers in the .aux file” and gives a manual workaround. But the page counter still works, so shouldn’t there be some way to pass that through to the PDF? I’d like to fix this, but don’t know where to start. Specifically, when the manual says that “TeX instantiates the page numbers when writing an .aux file only when the physical page is shipped out,” what exactly is it talking about? Where is the source code for that? Jointly Complete Sufficient Statistics: Uniform(a, b) Let $\mathbf{X}= (x_1, x_2, \dots x_n)$ be a random sample from the uniform distribution on $(a,b)$, where $a &lt; b$.   Let $Y_1$ and $Y_n$ be the largest and smallest order statistics.  Show that the statistic $(Y_1, Y_n)$ is a jointly complete sufficient statistic for the parameter $\theta  = (a, b)$.     It is no problem for me to show sufficiency using factorization.   Question: How do I show completeness? Preferably I would like a hint.    Attempt: I can show $\mathbb E[g(T(x))] = 0$ implies $g(T(x)) = 0$ for the one parameter uniform distribution, but I am getting stuck on the two parameter uniform distribution.   I tried playing around with $\mathbb E[g(Y_1, Y_n)]$ and using the joint distribution of $Y_1$ and $Y_n$, but I am not sure if I am going in the correct direction, as the calculus is tripping me up. Let $(a_n)$ be a strictly increasing sequence of positive integers such that: $a_2 = 2$, $a_{mn} = a_m a_n$ for $m, n$ relatively prime. Let $(a_n)$ be a strictly increasing sequence of positive integers such   that: $a_2 = 2$ and $a_{mn} = a_m a_n$ for $m, n$ relatively prime. Show that $a_n = n$, for every positive integer $n$.   This is a result apparently due to Paul Erdős, and  has a proof by induction.  I tried like this, $a_{10}=a_2a_5$. After this what we can do?    [Editor's comment] Possibly due to the apparent simplicity of the conditions it may be difficult to appreciate the subtleties of this question. If we try and construct a counterexample like $a_3=4$, $a_4=5$, $a_5=6$, then the requirements dictate $a_6=8$, $a_{10}=12$, $a_{15}=24$. At this point we realize that we have been speeding. For monotonicity forces $a_9\le 11$, and therefore $a_{18}\le22&lt;a_{15}$, violating the requirements. It is not obvious why something similar ruins all the modifications to the sequence $a_n=n$. [/comment, JL] ... namely that if $n &gt; 1$ and $(n − 1)!\equiv−1\pmod{n}$, then $n$ is prime.  This is for a number theory class I'm in at Penn State. My idea is to follow accordingly, but I can't get it concretely..  Reason by contradiction, suppose that $n$ is not prime.   Then $n = ab$, where $1 &lt; a, b &lt; n$  In particular $(n-1)! = ai$ for some $i\in\Bbb{Z}$. $\\$ If $(n-1)! = nj - 1$ for some $j\in\Bbb{Z}$ then it follows that a probably doesn't divide $-1$?