By what means is space expanding?
What causes the expansion of space?
If $f$ is entire and $|f|\geq 1$, then show $f$ is constant. Intuition behind why order of a subgroup divides order of a group. I'm trying to setup a image decal in cycles, and I can't figure how to setup the nodes to work fine. Does anyone know the solution? Show that if $ R $ is an integral domain then a polynomial in $ R[X] $ of degree $ d $ can have at most $ d $ roots Show that if $ R $ is an integral domain then a polynomial in $ R[X] $ of degree $ d $ can have at most $ d  $ roots.  Thoughts so far:  I feel like I might be missing something here. If $ R $ is an integral domain, then so is $ R[X] $. The factor theorem gives a correspondence between roots and factors. Clearly (is this clear?) a polynomial of degree $ d $ can't have more than $ d $ irreducible factors. TikZ: What EXACTLY does the the |- notation for arrows do? I am currently trying to work out how the perpendicular arrows  work, and I fail.  Taking:  \draw [arrow] (node1) -- node[sloped, above] {Caption} (node1 |- node2.north west);   I suspected that the notation meant: Draw an arrow from node 1, to the north-west corner of  node 2. Make the arrow perpendicular to node 1.  Further attempts to draw arrows told me: No, that's not it. I have sadly failed to figure out what exactly the notation is supposed to be doing though! Is there any "explanation for dummies" that will lead me to understand what exactly    node1 |-   Is supposed to do?  Thanks! What is the title of a 80's (i believe?) movie where humans in the far future are going extinct, and are aquiring new humans by going back in time to todays world, kidnapping air travelers that are known to have died that day, from the flying passenger aircraft just before its crashing.  A key visual:    Inside a hangar, a time portal opened, and a tail of a (flying) passenger aircraft extruded into the hangar where a stairs provided access to the back door of the aircraft.  The kidnappers made sure the surviving passengers remain seated and would forget about the whole ordeal. Kidnapped humans got replaced by lookalike dummies, including things they had on them. They tried hard not to alter the timeline. Lower the amount of reputation needed to comment is a great example of people coming from Google and using answers as comments.  I understand the reputation threshold is there to prevent spam, but Answers are just as prone to spam as comments and you can post them at reputation 1. Furthermore there are already flags in place as a preventive measure for both.  Essentially the reputation threshold of comments is forcing people to use the site in ways the designers did not intend. Removal of the reputation cap would also make the site more new user friendly as newbies that use the site in this manner are commonly given a unfriendly welcome in the form of downvotes from people who forget you need 50 rep to post comments. Prevent Photos app on OSX from launching when plugging in device The Photos app opens whenever I plug in my phone.    How can this be prevented?  I have seen many solutions for the old iPhoto app that involve changing the "Connecting camera opens" option, but the new app has no such option. Closed form for the sequence defined by $a_0=1$ and $a_{n+1} = a_n + a_n^{-1}$ What I am working with: I am running my self-made Arduino board (in the sense that I use the Arduino bootloader and code editor) at 3.3V, and powered from a Lithium ion battery, which is USB-charged by a corresponding Microchip charger IC.  What I am trying to achieve: I want to measure battery capacity once every minute or so. I have an LCD attached, so the idea is that the overall setup lets me know how the battery is doing at a given moment. The datasheet of the battery has a voltage versus discharge-level curve, and so by measuring the voltage of the battery, I can estimate the remaining capacity (very roughly but enough for me!).  What I did:   (EDIT: Resistor values updated and P-MOSFET switch added based on @stevenvh and @Jonny's suggestions).  I connected a voltage divider from the battery V_plus, with the larger "portion" going to an analog-read-pin (i.e., ADC) on the Arduino/Atmega chip. The divider is 33 KOhm-to-10 KOhm, thus allowing measurement up to 4.1 Volts maximum of the Li-ion battery from my 3.3V level microcontroller. Also, using one of the I/O pins connected to an n-channel MOSFET, I can switch the current through the divider only when I need the measurement. Here is a rough schematic (updated for a 2nd time based on suggestions of @stevenvh and @Nick):     My question:   How is my current setup? My only constraints are: (1) I would like to make a rough measurement of the battery capacity based on the voltage reading, as described above. (2) I would like to prevent the voltage divider from interfering with my charging IC's reading of battery presence (in my original setup, the divider sometimes caused the IC to misread presence even when the battery was absent). Let's say we have $2$ particles facing each other and each traveling (almost) at speed of light.    Let's say I'm sitting on #$1$ particle so in my point of view #$2$ particle's speed is (almost) $c+c=2c$, double light speed? Please say why I am incorrect :)    EDIT: About sitting me is just example, so in point of view of #1 particle, the second one moves at (almost) $c+c=2c$ speed? There are several things that I don't understand. I know that zero is a real number, but I'm confused on the how and why aspects. What defines a real number, compared to a number that's considered non-real? For what reason is zero real, and how is it that a value such as infinity isn't when zero is?  Also, what purpose does zero even have? It's obvious that it's used as a place holder, but what value does it have alone? What makes it any different from other numbers? I realize that it is typically interchanged with nothing, but that would technically mean that zero is nothing—and that's not true. People have told me already so many times that zero does not necessarily mean nothing, and I figured it out a long while ago anyway. So, what I want to know is the actual value that can be associated with zero.  However, my question brings up another topic that has been argued and disputed about and disagreed on for years. Zero divided by zero, or 0/0. There are a lot of varying answers about this, but what's been constant throughout everything is that people claim 0/0 is not a real number. So, if I may ask, why is it that zero is considered a real number, and not 0/0? And why is it considered non-real in the first place? True, there is no defined value, but the expression is anything but meaningless; if it was, then there wouldn't be so many people trying to understand it. I guess what I'm trying to figure out is the reason behind the expression's classification as non-real—especially when the sole number of zero is real, despite not having an evident value.  This covers a few different things, so I was uncertain about what to make the title of these questions. I apologize for that. If anyone can answer, though, I'd be extremely grateful! Redefining "cited on" string (and others) in biblatex What should i use for better performance, nine-patch or drawable xml resource? Normalising Constant for exponentiated function What would the normalising  constant be of the following, or atleast an approximation? I would like to avoid sampling.  $$f(\theta)=\exp(-k_1e^{-k_2\theta^2}-\theta^2)\qquad\theta\in(-\infty,\infty), \quad k_1,k_2&gt;0$$  In the event that its not possible, what would be a valid polynomial lower bound on $\log(f(\theta))$, that would take into account $k_1$  For anyone, who is interested, I end up with this expresssion because I place a Gaussian prior over (a squared exponential) kernel parameters, and trying to use variational bayes (hence, a lower bound). I may not be coming in tomorrow...    I might not be coming in tomorrow...       When should I use "may" and "might"? When mounting an NFS share manually using mount and a path of the form &lt;domain/ip&gt;:&lt;path&gt;/&lt;path&gt; or &lt;domain/ip&gt;:/&lt;path&gt;/&lt;path&gt;, umount fails to find the path in /proc/mounts, despite the fact that the path is in fact listed in /proc/mounts.  This is the same problem as in this question:   Steps to reproduce:  # mount --version mount from util-linux 2.24.1 (libmount 2.24.0: debug, assert) # mkdir mountpath # mount 192.168.2.101:/devices mountpath # umount mountpath /home/.../mountpath was not found in /proc/mounts # grep mountpath /proc/mounts 192.168.2.101://devices /home/.../mountpath nfs4 rw,[snip],addr=192.168.2.101 0 0   How can I unmount this mount? What is causing disabled options when adding a mesh/curve object to the scene? Removing a list of characters in string How to interpret the significant interaction of two non-significant main predictors? I have two non-significant main binary variables in my binary logistic regression model, but their interaction is significant. The variables are centered and no multicollinearity is the case (all VIFs about 1.0). The main variables are nonsignificant, but their interaction is. I want to interpret that significant interaction of two non-significant estimates.   It would read something like this: the effect of the variable A is less visible in the level 1 of the variable B (B1) and more visible in the second level of B (B2). Or I can say the same thing about the effect of B being less visible in A1 and more visible in A2...  However, the problem is that neither the effect of A, nor the effect of B are significant! So the above interpretation, although seemingly correct, sounds inconsistent or strange. (How a non-significant effect is supposed to be boosted by the other variable?)...   On a second thought, it seems that it is actually possible. For example, if I exclude cases with B2 from my sample, now the effect of A in the sample would show up as significant (it is B2 cases in the sample that disallow A to appear as significant)... This is getting more clear in my head now, but do you still have something other than the above interpretation in mind?