My confused mind swapped old/new state in suggested edit and I've approved an edit that introduced rubbish when I was thinking I was approving an edit that removed rubbish. How can I undo this?
I accidentally clicked reject on the suggested edit on this question(). I can't find the button to change it to Approve?
I think I have managed to work this out, however there is no solution provided with the question so I thought it best to check.   My working:  Let $(x,y) \in (A \times B) \cup (C \times D)$  $\Rightarrow x \in (A$ or $C)$ and $y \in (B$ or $D)$  $\Rightarrow (x, y) \in (A \cup C) \times (B \cup D)$  $\Rightarrow (A \times B) \cup (C \times D) \subseteq (A \cup C) \times (B \cup D)$  Now let $(x,y) \in (A \cup C) \times (B \cup D)$  $\Rightarrow x \in (A$ or $C) $ and $y \in (B$ or $D)$  $\Rightarrow (x, y ) \in (A \times B) \cup (A \times D) \cup (C \times B) \cup (C \times D)$  $\Rightarrow (A \cup C) \times (B \cup D) \nsubseteq (A \times B) \cup (C \times D)$  $\Rightarrow (A \times B) \cup (C \times D) \not= (A \cup C) \times (B \cup D)$  Is this correct?  Thank you. I have a fairly modern desktop computer, an AMD Athlon II X2 based silent PC, that does not work.  When turned on, it will start physically (all fans are rotating, disks start up...) but not give a signal on any of the graphics ports (DVI, VGA, and HDMI, I tried all three). Also, the reset button does not seem to have any effect.  I have stripped the mainboard bare of all SATA connections, extension cards, and the one 2GB RAM chip to eliminate them as the problem source, but to no avail, so I think it's fair to assume it's either the mainboard or the processor that are at fault.  However, I have neither a replacement mainboard, nor a replacement processor handy to identify which one is broken. The cause of the defect is unknown, so for all I know, it could be both. Therefore, I'm reluctant to buy replacement hardware blindly before knowing more.   Is there any way to further diagnose (or at least get some indication) which component is broken without buying replacement hardware? Remotely changing hard drive boot order, windows 7 I have one workstation chassis with two hard drives.  Depending on which one I boot from, I get one of two different operating systems: both are windows 7, but they have different static IPs, serve totally different purposes, etc.    The workstation has a modern asus motherboard, core i7 intel CPU, 32 GB ram.   Is there a way to remotely change which hard drive is booted from on a reboot?  Both systems have remote users, and i'd like a solution that is more elegant than being physically present and selecting boot order manually. What is the point of Refresh if Dynamic has an UpdateInterval option? I installed Ubuntu on my Windows 7 Sager laptop using Wubi. Hibernate (i.e. suspend to disc) is not an option from the power icon, only suspend, shutdown, etc. Hibernate is also not an option from my battery/lid close options. I understand that hibernation is disabled by default in Ubuntu 12.04. I tried running pm-hibernate but I get the following message:  Looking for splash system... none  s2disk: Snapshotting system   and then the computer just hangs with a black screen. According to the documentation  if this fails then I can't enable hibernate but it offers no help in making pm-hibernate succeed.  Could swap be my problem? It looks like I have very small swap:  user@ubuntu:~$ cat /proc/swaps Filename                Type        Size    Used    Priority /host/ubuntu/disks/swap.disk            file        262140  0   -1   The advice on  is only for the author's set up (e.g. I don't have an Ubuntu install disk since I used Wubi) and he says that 'INFO: This will not work for 12.04, resume from hibernate work differently in 12.04.'  Any advice? I really need to get hibernate working to use my laptop as a, er, laptop.  Thanks Orphaned tag wiki edits have broken activity entries I need some advice as I am struggling with the following combinatorics exercise.  Let $k$ be a given positive integer. Show that any non-negative integer $N$ can be written uniquely in the form $$N=\binom{x_k}{k}+\binom{x_{k-1}}{k-1}+\dots+\binom{x_1}{1},$$ where $0 \leq x_1 &lt; \dots &lt; x_{k-1} &lt; x_k$.  The exercise is accompanied by this advice:  Let $x$ be such that $\binom{x}{k} \leq N &lt; \binom{x+1}{k}$. Then any possible representation has $x_k = x$. Now use induction and the fact that $N-\binom{x}{k} &lt; \binom{x}{k-1}$ to show the existence and uniqueness of the representation.  I am really stuck and thus grateful for the slightest hint on how to solve it. The strange thing about the maximum in Planck's law Is it possible to dual boot two instances of Ubuntu 16.04? I've been programming for about a year and I'm very new to Ubuntu. I'm currently working on a project with a mentor who suggested partitioning part of my drive with a fresh Ubuntu install. I've never done anything like this and most of the guides I've seen are for dual-booting Ubuntu and Windows/MacOS.  I'm currently running Ubuntu 16.04 on my laptop. I was wondering If I could keep my current setup and also partition part of my drive with a fresh install of Ubuntu 16.04? If I push or hit an object in space will it rotate or move along a straight line? How to add a small rounded rectangle around a word inline I want to add a box with a very light pink background and red border around a word but inline and  within a sentence.   i.e. something like this (drawn with inkscape)    I know the mdframed package can be used for placing boxes around paragraphs, but it does not seem to work inline and also give colored boxes.   Possibly TikZ is a solution? From the little I know of TikZ, it can be used to draw pictures inline inside a sentence. It is asked to solve the PDE  $$u_x + u_y + u = e^{x+2y}$$  My attempt: We have that $$\frac{dx}{1}=\frac{dy}{1}=\frac{du}{e^{x+2y}-u} $$  $\Rightarrow \frac{dy}{dx}=1 \Rightarrow y=x+C_1 \iff C_1=y-x$  $\Rightarrow \frac{du}{dx}= e^{x+2y}-u \iff \dot{u}+u=e^{x+2y} \iff \\ \frac{d}{dx}(e^x u) = e^{2x+2y} \iff u = e^{-x} ( \frac{1}{2}e^{2x+2y} + C_2)$  As $u$ is constant along its characteristics:  $$u(x,y)=\frac{e^{-x}}{2}(e^{2x+2y} + 2C_2(y-x))$$  where $C_2$ is any function of one variable. But wolfram gave the following answer  $$u(x,y)=\frac{e^{-x}}{4}(e^{2x+2y} + 4C_2(y-x))$$  as you can check   What am I doing wrong? Trying to find a story about an unborn telepathic baby who can save a spaceship from doom There's a spaceship, nearing the end of its journey. Everybody on board is in cryosleep. For some reason the wake-up system malfunctions, and the ship will fly on indefinitely. The people at the space port realise this, and try to wake someone up. Their last resort is finding someone on board who is telepathic, and wake this person up. They find one, but it turns out to be an unborn baby. How to create a "heat distortion" effect with a cycles procedural node set up without compositing I know how to do a heat distortion effect in compositing.   What I am looking for is a way to do the same effect with a material set up in cycles.   What would be the best way to create a procedural material that can be placed in front of any object and make it look like heat is rising in front of it (without compositing)?  Any ideas would be greatly appreciated. How to tell M2Eclipse to install jar file as a maven dependency Lost my APFS partition after using EaseUS partition manager on Bootcamp I used macOS mojave(APFS partition) and Windows10(Bootcamp). And I tried to expand Bootcamp partition with moving Windows OEM partition by EaseUS partition master in windows. After this, I can’t find APFS partition installed macOS.  I use MacBook Pro 2016.  I think “disk0s2” was APFS partition, but now it is “Windows Recovery” partition.  Do you have any ideas to solve this? (I am Japanese, so I'm sorry for my poor English)  I tried “gpt show” and “diskutil list” on macOS Recovery   Additional information  I tried dd if=/dev/disk0s2 count=1 bs=512 command in a Terminal app of macOS Utility from network boot, and the terminal says,  -bash-3.2# dd if=/dev/disk0s2 count=1 bs=512 | vis -c 1+0 records in 1+0 records out 512 bytes transferred in 0.005472 secs (93568 bytes/sec) )us??-ҵ?\^A\0\0\0\0\0\0\0?\M^F\^Z\0\0\0\0\0\^A\0\0\M^@\0\0\0\0NXSB\0\^P\0\0?\M^B?\^B\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\^B\0\0\0\0\0\0\0"\^R???\M^_@}\M^Bvy57 ?(h?8\0\0\0\0\0?\M^F\^Z\0\0\0\0\0\^X\^A\0\0 l\0\0?\M^J\0\0\0\0\0\0\^R\r\0\0\0\0\0\0\a\0\0\0004*\0\0\^E\0\0\0\^B\0\0\0\^S*\0\0!\0\0\0\M^Qr8\0\0\0\0\0\M^U?\b\0\0\0\0\0\^A\^D\0\0\0\0\0\0\0\0\0\0d\0\0\0\^C\^D\0\0\0\0\0\0\M^T\M^N\^A\0\0\0\0\0\M^V\M^N\^A\0\0\0\0\0?0\^B\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0-bash-3.2#   . How do I rename all folders and files to lowercase on Linux? I am using ffmpeg to cut out a section of a large file like this: ffmpeg -i input.wmv -ss 60 -t 60 -acodec copy -vcodec copy output.wmv  The -ss part works fine but the -t is ignored. It correctly removes the initial specified seconds specified with -ss but then keeps going to the end of the input with the copy. Is there a way to use ffmpeg to cut off the end of a video without recoding it? I'm using OSX 10.9. I'm trying to set up Internet Sharing to connect my Android to my Mac directly over Wi-Fi. Every tutorial I've come across (including ) mentions checking a box for "AirPort" in a "To computers using" list. However, the option is simply not available on my machine:    I have a few related questions:   Why isn't the AirPort option available? Is there anything I can do to make it available? If there isn't, how can I work around it to finish setting up Internet Sharing so I can connect my Android and my Mac directly over Wi-Fi? Why would I buy a bond with a negative yield? The only reason that I can think of is because I expect the bond to appreciate in price thus offsetting the loss in yield. I could still end up with less money than I started with, if I hold the bond until maturity. Ultimately, the only scenario where I would want to buy a bond with a negative yield is because I anticipate deflation and even lower rates in the future. Is this correct, or is there another reason?  Currently, a lot of the global government bond market is trading on negative yield, and there are even some corporate bonds that are too.