Find all solutions to the equation functional $f(x)+f(x+y)=y+2$
Find all solutions to the functional equation $f(x) +f(x+y)=y+2 $
VMWare: This host doesn't support VT. Can not play 64-bit VM due to lack of VT flag I have an Intel E7300 Core2 Duo processor with 2.66GHz speed. I need to run a 64-bit WinXP SP2 VMWare image. My host operating system is Win 7. So I just installed the VMPlayer from www.vmware.com.  The problem is when I run the VM image it says This host doesn't support VT.  If I continue I see Windows shows an error message saying     Attempting to load an x64 operating system, however this CPU is not compatible with x64 mode.   My question is how do I run this VM without buying a new processor? Any other tools or software? Confusion about the definition of function Yesterday I was talking to one of my friends about the definition of function. The formal definition of function is given by Cartesian Products but my friend's question was whether it is possible to define a function without being acquainted with any concept of Cartesian Products.   To answer this question I told him the definition of a function may be given by defining a function $f$ from the set $X$ to $Y$, denoted by $f:X\to Y$, to be some "rule" (the word rule being an undefined concept) which associates, to each member of $X$, exactly one element of $Y$.     But my friend said that the definition using the concept of "rule" isn't rigorous and there are examples that don't obey the definition but still is a function in the Cartesian Product sense.    My questions are,   Why the definition of function using concepts such as "rule" isn't rigorous?  Is there really any example which doesn't obey the definition but still is a function in the Cartesian Product sense? How do I update Custom Label's value using apex? Which one would be a better option metadata api or tooling api? Please provide example I'am working on post deployment automation process in salesforce. I am stuck on how should I update values in custom labels which needs tobe updated manually after a sandbox refresh. Feature Request: Could 7.5K users have the privilege of proposing synonyms without the 5 upvotes per tag requirement?  (in other words unrestricted synonym suggestion)  Background: I would like to be able to suggest tag synonym suggestions.  I do not however, have the required , but someday I will.  Yet many 2.5K users do not have the requisite 5 upvotes in each tag in order to propose synonyms.  I realize that this  for low-rep users.  But could it be made available to users with 7,500 rep?  At this level, they've clearly demonstrated an understanding of the Stack Exchange site.  Note: I'm not requesting the ability to create synonyms -- merely synonym suggestions.  I believe this privilege is currently only available to moderators? (and  )  Lastly, please note that  clearly demonstrates the breadth of simple synonym suggestions which could be made (almost every Stack Exchange site has some), but many haven't even been suggested yet. Python idiom to return first item or None I'm sure there's a simpler way of doing this that's just not occurring to me.  I'm calling a bunch of methods that return a list.  The list may be empty.  If the list is non-empty, I want to return the first item; otherwise, I want to return None.  This code works:  my_list = get_list() if len(my_list) &gt; 0: return my_list[0] return None   It seems to me that there should be a simple one-line idiom for doing this, but for the life of me I can't think of it.  Is there?  Edit:  The reason that I'm looking for a one-line expression here is not that I like incredibly terse code, but because I'm having to write a lot of code like this:  x = get_first_list() if x:     # do something with x[0]     # inevitably forget the [0] part, and have a bug to fix y = get_second_list() if y:     # do something with y[0]     # inevitably forget the [0] part AGAIN, and have another bug to fix   What I'd like to be doing can certainly be accomplished with a function (and probably will be):  def first_item(list_or_none):     if list_or_none: return list_or_none[0]  x = first_item(get_first_list()) if x:     # do something with x y = first_item(get_second_list()) if y:     # do something with y   I posted the question because I'm frequently surprised by what simple expressions in Python can do, and I thought that writing a function was a silly thing to do if there was a simple expression could do the trick.  But seeing these answers, it seems like a function is the simple solution. Is "funnest" a word? I recently got a computer from school. It came with Windows 8.1 installed. I then installed another copy of Windows 8.1 (so it would use the built-in Windows Pro license) and upgraded it to Windows 10. I then installed Ubuntu alongside both Windows 8 and 10. Note that I made a separate 255MB ext2 partition for /boot. Now, when I boot the computer, I first see a GRUB prompt (I already un-hid the grub prompt 'cuz I like it that way) with Windows 8 and Ubuntu options. However, there is no Windows 10 option. If I select Ubuntu, the computer boots into Ubuntu. However, if I select the Windows 8 option, I then get sent to the Windows bootloader, where it then gives me options to boot either Windows 8 or Windows 10. (However, by this point, the computer has already loaded the kernel and all. Apparently Microsoft misunderstood the concept of a bootloader and decided that that meant &quot;boot practically the entire system before actually showing the bootloader&quot;. Typical Microsoft.) How can I disable the Windows bootloader and add a Windows 10 option to GRUB? EDIT: Someone has answered telling me to disable the Windows bootloader. However, I still do not know how to add Windows to the GRUB OS list. Can anyone help with this? EDIT 2: After removing Windows 10 from the Windows bootloader with EasyBCD, it seemed that, after a few reboots, it would continually unhide itself and Windows 10 would reappear. However, I then later deleted Windows 10 from the list of OSes in msconfig, and it seems to have stayed deleted. However, I STILL have not managed to get Windows 10 to appear in GRUB. It's as if GRUB simply doesn't detect it. Also, I'll put this in the question so that people see it - I have tried using boot-repair, however, it has NOT helped any. Does one wing of fly contain harmful microbes and the other contain only antibodies? There was  study but the conclusion and it's source's relability seemed a bit off. How come a house flies one wing contain all microbe and the other don't. Are there any other methods to apply to solving simultaneous equations? We are asked to solve for $x$ and $y$ in the following pair of simultaneous equations:  $$\begin{align}3x+2y&amp;=36 \tag1\\ 5x+4y&amp;=64\tag2\end{align}$$  I can multiply $(1)$ by $2$, yielding $6x + 4y = 72$, and subtracting $(2)$ from this new equation eliminates $4y$ to solve strictly for $x$; i.e. $6x - 5x = 72 - 64 \Rightarrow x = 8$. Substituting $x=8$ into $(2)$ reveals that $y=6$. I could also subtract $(1)$ from $(2)$ and divide by $2$, yielding $x+y=14$. Let $$\begin{align}3x+3y - y &amp;= 36 \tag{1a}\\ 5x + 5y - y &amp;= 64\tag{1b}\end{align}$$ then expand brackets, and it follows that $42 - y = 36$ and $70 - y = 64$, thus revealing $y=6$ and so $x = 14 - 6 = 8$. I can even use matrices! $(1)$ and $(2)$ could be written in matrix form: $$\begin{align}\begin{bmatrix} 3 &amp;2 \\ 5 &amp;4\end{bmatrix}\begin{bmatrix} x \\ y\end{bmatrix}&amp;=\begin{bmatrix}36 \\ 64\end{bmatrix}\tag3 \\ \begin{bmatrix} x \\ y\end{bmatrix} &amp;= {\begin{bmatrix} 3 &amp;2 \\ 5 &amp;4\end{bmatrix}}^{-1}\begin{bmatrix}36 \\ 64\end{bmatrix} \\ &amp;= \frac{1}{2}\begin{bmatrix}4 &amp;-2 \\ -5 &amp;3\end{bmatrix}\begin{bmatrix}36 \\ 64\end{bmatrix} \\ &amp;=\frac12\begin{bmatrix} 16 \\ 12\end{bmatrix} \\ &amp;= \begin{bmatrix} 8 \\ 6\end{bmatrix} \\ \\ \therefore x&amp;=8 \\ \therefore y&amp;= 6\end{align}$$  Question Are there any other methods to solve for both $x$ and $y$? How to print results in SQLcmd window The ring $\Bbb Z\left [\frac{-1+\sqrt{-19}}{2}\right ]$ is not a Euclidean domain Let $\alpha = \frac{1+\sqrt{-19}}{2}$. Let $A = \mathbb Z[\alpha]$. Let's assume that we know that its invertibles are $\{1,-1\}$. During an exercise we proved that:     Lemma: If $(D,g)$ is a Euclidean domain such that its invertibles are $\{1,-1\}$, and $x$ is an element of minimal degree among the elements that are not invertible, then $D/(x)$ is isomorphic to $\mathbb Z/2\mathbb Z$ or $\mathbb Z/3\mathbb Z$.   Now the exercise asks:     Prove that $A$ is not a Euclidean Domain.   Everything hints to an argument by contradiction: let $(A, d)$ be a ED and $x$ an element of minimal degree among the non invertibles we'd like to show that $A/(x)$ is not isomorphic to $\mathbb Z/2\mathbb Z$ or $\mathbb Z/3\mathbb Z$.  How do we do that? My problem is that, since I don't know what this degree function looks like, I don't know how to choose this $x$!  I know that the elements of $A/(x)$ are of the form $a+(x)$, with $a$ of degree less than $x$ or zero. By minimality of $x$ this means that $a\in \{0, 1, -1\}$. Now I'm lost: how do we derive a contradiction from this? How do I install "non-free firmware" (wifi driver) from USB? (Debian) Can't install Oracle JDK 9 I uninstalled jdk packages and now can't install them back. I managed to install oracle-java7-installer and oracle-java8-installer but can't install oracle-java9-installer. It seems that my computer tries to download wrong version of oracle-java9-installer 177 when version i would be able to download is 178.    $ wget http://download.java.net/java/jdk9/archive/178/binaries/jdk-9+178_linux-x64_bin.tar.gz --2017-07-21 11:00:02--  http://download.java.net/java/jdk9/archive/178/binaries/jdk-9+178_linux-x64_bin.tar.gz Connecting to 10.144.1.10:8080... connected. Proxy request sent, awaiting response... 200 OK Length: 293348142 (280M) [application/x-gzip] Saving to: 'jdk-9+178_linux-x64_bin.tar.gz'  jdk-9+178_linux-x64_bin.tar.gz     1%[&gt;                                                          ]   5.42M  5.04MB/s               ^C  $ wget http://download.java.net/java/jdk9/archive/177/binaries/jdk-9+177_linux-x64_bin.tar.gz --2017-07-21 11:00:16--  http://download.java.net/java/jdk9/archive/177/binaries/jdk-9+177_linux-x64_bin.tar.gz Connecting to 10.144.1.10:8080... connected. Proxy request sent, awaiting response... 404 Not Found 2017-07-21 11:00:17 ERROR 404: Not Found.   Can you help? apt-get tries to install Oracle JDK 9.  I run Ubuntu 16.04 in virtual machine hosted by win7  Full error message:  sudo apt-get install oracle-java9-installer Reading package lists... Done Building dependency tree        Reading state information... Done oracle-java9-installer is already the newest version (9b177-1~webupd8~0). 0 upgraded, 0 newly installed, 0 to remove and 147 not upgraded. 1 not fully installed or removed. After this operation, 0 B of additional disk space will be used. Do you want to continue? [Y/n] Y Setting up oracle-java9-installer (9b177-1~webupd8~0) ... Using wget settings from /var/cache/oracle-jdk9-installer/wgetrc Downloading Oracle Java 9... --2017-07-21 10:54:11--  http://download.java.net/java/jdk9/archive/177/binaries/jdk-9+177_linux-x64_bin.tar.gz Connecting to 10.144.1.10:8080... connected. Proxy request sent, awaiting response... 404 Not Found 2017-07-21 10:54:13 ERROR 404: Not Found.  download failed Oracle JDK 9 is NOT installed. dpkg: error processing package oracle-java9-installer (--configure):  subprocess installed post-installation script returned error exit status 1 Errors were encountered while processing:  oracle-java9-installerE: Sub-process /usr/bin/dpkg returned an error code (1) Speed of light in a gravitational field? How do I solve the speed of light in gravitational field?  Should I just add gravitational acceleration in speed of light?  $$c'=c_0+g(r)t~?$$ How to use Launchctl for schedule application I try to work with Launchctl and have a question:  How can I set up an application to run in a few minutes using Launchctl? (for example, open the program MyApp.app with arguments "hello" "world" Every 10 minutes)  I know that it can easily be done by creating Launch Agent, I looking for a way to do it using Launchctl directly to programmatically. Using the variable "name" doesn't work with a JS object Seatpost Overextension I've been riding with my very short seat post extended well past its maximum extension line for quite a while now. Looking at the seat post itself I don't see any signs of deformation or damage other than some very minor surface rust.   Could my bike frame have been damaged? Could the lever force have damaged the frame? I can post some pictures of the frame if needed. My bike is all aluminum. How to clear bash history completely? Does a capacitor store charge? There're some easy concepts which I don't get exactly in my mind. I'm afraid I've been studying these things for two years of my engineering but they still bother me. Capacitor is one of them. Can someone explain?    What does a capacitor do? Does it store charges? If so, then how does it do?   I have searched it on Google and Yahoo but didn't find any helpful thing there (for me). So I will be glad if I got my problem solved here.  P.S. I hope that the question would not again be an off-topic, as it always does and moreover people don't suggest then where to go. It's a real sad thing. There are many beings that have very big powers. There are beings that are worshipped as gods (Asgardians; and I would lump Azazel into that as well since Marvel seems to imply that he's - while a mutant - someone people consider to be "Devil"). There are mutants whose power would clearly have been considered as "god like" by people worshipping Greek or other polytheistic pantheons where the threshold to what made you a god was pretty low.  But are there any actual major "Gods" in Marvel universe?  Since there are many different definition of what a "god" is, the one that is pertinent to this question:   Power wise, being able to create Universe(s); e.g. gods more in a sense of Christianity/Judaism scale rather than "Pan" or "Hestia" in Greek pantheon who merely have some limited supernatural powers over small domain of natural events. Effectively immortal, at least excluding specific exotic attacks. Origin-wise, be "supernatural", not merely a human mutant or a powerful alien with advanced technology. Desire/demand/like followers' worship or prayers.