Hi I have a quick question. I know this may be a common question. If N3L states that there's an equal and opposite force, why do things still move?  I have read up a lot and this is my understanding. If a finger exerts a force on a box, then box will move/accelerate. At the same time, box exerts an equal force on the finger. The motion of box(assuming no friction) is affected only by force from the finger. (I think the term is System = box). Thus, the reaction force from box only affects the motion of finger and has no relevance to the motion of the box.  However, I came to this question. If the reaction force from the box on the finger is equal to the force from the finger to the box, then there must be some other kind of force on the finger that is opposite to the reaction force and greater, since the finger is accelerating/moving. What is that force?
Given Newton's third law, why is there motion at all? Should not all forces even themselves out, so nothing moves at all? When I push a table using my finger, the table applies the same force onto my finger like my finger does on the table just with an opposing direction, nothing happens except that I feel the opposing force. But why can I push a box on a table by applying force ($F=ma$) on one side, obviously outbalancing the force the box has on my finger and at the same time outbalancing the friction the box has on the table? I obviously have the greater mass and acceleration as for example the matchbox on the table and thusly I can move it, but shouldn't the third law prevent that from even happening? Shouldn't the matchbox just accommodate to said force and applying the same force to me in opposing direction?
When to delete your 0 vote answers? I've been in the SO community a little over a month now - and having a great time!  As I grow into a contributing citizen of stackoverflow, i'd like to ensure that i'm being responsible with my answers.   I've answered a few questions, some without upvotes, some voted on and some accepted.  I feel that after a certain period of time, 0 vote answers are probably providing more clutter than value.  Apparently, nobody has found them useful, so they probably aren't (or are poorly written). Tonight I went through and deleted my answers with 0 upvotes where some answer was accepted.  That was an easy decision.   I left my 0 vote answers where nothing was accepted yet, well, because I think they could provide the information that the OP requested.  But at some point, I think my answers might just be cluttering the issue.  So my question to you is: How do you know when it's time to delete your 0 vote answers?  Or even 1 vote answers for that matter? Alright, I'm toying around with converting a PIL image object back and forth to a numpy array so I can do some faster pixel by pixel transformations than PIL's PixelAccess object would allow.  I've figured out how to place the pixel information in a useful 3D numpy array by way of:  pic = Image.open("foo.jpg") pix = numpy.array(pic.getdata()).reshape(pic.size[0], pic.size[1], 3)   But I can't seem to figure out how to load it back into the PIL object after I've done all my awesome transforms.  I'm aware of the putdata() method, but can't quite seem to get it to behave. How to determine $\int x^2 e^{-x^2}\mathrm dx$? I was wondering how to determine $$\int x^2 e^{-x^2}\mathrm dx?$$ I tried to move the exponential into the integrator, and apply integration by parts, but that will make the integrand more complicated. Thank you! What should my Objective-C singleton look like? I am trying to prove the following by Mathematical Induction:  $$\sum_{i=1}^n i\cdot i! = (n+1)!-1\quad\text{for all integers $n\ge 1$}$$   My proof by Induction follows: First prove $P(1)$ is true,  $$\sum_{i=1}^1 i\cdot i! = (1+1)! - 1$$  Then, for all integers $k &gt;= 1$, if $P(k)$ is true then $P(k+1)$ is also true,  $$ \sum_{i=1}^k i\cdot i! = (k+1)! - 1$$ Then, we must show that $P(k+1)$ is true   $$ \sum_{i=1}^{k+1} i\cdot i! = ((k+1)+1)! - 1\\ \sum_{i=1}^{k+1} i\cdot i! = (k+2)! - 1$$  I am currently struggling with the next step to show that $P(k)$ is equal to $P(k+1)$. How would I finish this prove by induction? I can show that for $x &gt; 0$ and $r_{i} &gt; 0$ we have $$ \left(\, x + r_{1}\,\right)\ldots\left(\, x + r_{n}\,\right)\ \geq\ \left[\, x + \left(\, r_{1}\ldots r_{n}\,\right)^{1/n}\,\right]^{n}.$$ However, I can't do this using straight up induction, strong or weak. Can someone do this?   You can show the inequality holds for $n$ if it holds for $n+1$ using $r_{n+1} = (r_1 \cdots r_n)^{1/n}$, so going down isn't a problem, but going up has eluded me. Additionally, you can show that if it holds for $n=a$ and $n=b$ then it holds for $n=ab$. Using powers of two and the above is sort of a way to prove the above by induction but it certainly isn't "normal".  You can also prove the above using Lagrange multipliers (which isn't surprising). The last proof I know is where you compare coefficients of $x^k$ and use the AM-GM inequality. FTPS versus SFTP versus SCP What's the proof that the Euler totient function is multiplicative? That is,     why is $\varphi(AB)=\varphi(A)\varphi(B)$, if $A$ and $B$ are two coprime positive integers?   It's not just a technical trouble—I can't see why this should be, intuitively: I bellyfeel that its multiplicativity should be an approximation at most. And why the minimum value for $\varphi (n)$ should be $ \frac{4n}{15} $ completely passes me by. Can a self-complementary graph on 100 vertices have precisely one vertex of degree 50? story on forest timescale I'm looking for the title of a short story by Ursula Le Guin about a scientist (?) who is given a drug that slows the timescale of his perception enormously, so that he can perceive that an alien (?) forest is actually behaving as a sentient being, reacting to current events, but at an enormously slow (from a normal human point of view) timescale. It might be in , but I don't remember the title (and it doesn't jump out at me from the list of titles) and don't have access to that collection right now. It is not &quot;The Word for World is Forest&quot;, nor &quot;Direction of the Road&quot; (from ), nor &quot;Vaster than Empires and More Slow&quot;, the latter two of which look at similar plant perception/time-scale issues. Update: it turns out that the description was right, but I had most of the details wrong: not Le Guin, not alien, not a scientist ... Python element-wise tuple operations like sum Is there anyway to get tuple operations in Python to work like this:  &gt;&gt;&gt; a = (1,2,3) &gt;&gt;&gt; b = (3,2,1) &gt;&gt;&gt; a + b (4,4,4)   instead of:  &gt;&gt;&gt; a = (1,2,3) &gt;&gt;&gt; b = (3,2,1) &gt;&gt;&gt; a + b (1,2,3,3,2,1)   I know it works like that because the __add__ and __mul__ methods are defined to work like that. So the only way would be to redefine them? Converting string to tuple and adding to tuple Possible Duplicate:             TL;DR: sudo apt-get install ... saying "Unable to correct problems, you have held broken packages."   The problem  I was trying to get the WebApps feature for PP and QQ following .  I ran the sudo add-apt-repository ppa:webapps/preview command to add the repository, but i got a connection error. Since I know my current ISP gives a shaky connection, I tried again and sure enough, it worked.  Then I ran sudo apt-get install unity-webapps-preview, but I realized we had to update apt-get first, so I hit Ctrl + C to stop it. Then I ran sudo apt-get update which worked w/o a fuss, but when I ran sudo apt-get install unity-webapps-preview again later, it showed an error message. Here's the dump:  Reading package lists... Done Building dependency tree        Reading state information... Done Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  unity-webapps-preview : Depends: xul-ext-unity but it is not going to be installed                          Depends: xul-ext-websites-integration but it is not going to be installed                          Depends: xul-ext-webaccounts but it is not going to be installed E: Unable to correct problems, you have held broken packages.   I think this might be because of me interrupting the earlier command. It hadn't got a chance to output anything, though — I stopped it pretty fast.  What I tried  Commands  I tried these:-   sudo apt-get install --fix-broken sudo apt-get autoclean sudo apt-get autoremove sudo apt-get -f install   But even after running sudo apt-get upgrade after every try, none of them worked.  Purging  I tried purging the repository, but that didn't work either. First, I got the package using sudoapt-get install ppa-purgeand then tried to purge the WebApps repo usingsudo ppa-purge ppa:webapps/preview`.  Manually installing dependencies  If you look at the error dump carefully, it says:     Depends: xul-ext-unity but it is not going to be installed   Depends: xul-ext-websites-integration but it is not going to be installed   Depends: xul-ext-webaccounts but it is not going to be installed   So I tried installing them manually. I ran sudo apt-get install xul-ext-unity, but got this:     Depends: xul-ext-websites-integration but it is not going to be installed   Breaks: firefox (>= 15.+) but 16.0~b6+build1-0ubuntu0.12.04.1~mfn4 is to be installed   I have no idea what the second part means, but I tried resolving the first. Running sudo apt-get install xul-ext-websites-integration gave:     xul-ext-websites-integration : Breaks: firefox (>= 15.+) but 16.0~b6+build1-0ubuntu0.12.04.1~mfn4 is to be installed   As a last resort, I tried sudo apt-get install xul-ext-webaccounts, but that gave the sane message too:     Breaks: firefox (>= 14.+) but 16.0~b6+build1-0ubuntu0.12.04.1~mfn4 is to be installed   What does Breaks: firefox (&gt;= 14.+) but 16.0~b6+build1-0ubuntu0.12.04.1~mfn4 is to be installed mean?  Research  I tried searching , looking at a couple of , looking at  and searching on AU, but to no avail. Help would be appreciated. Create a table with LaTeX I am trying to write a condition into a SQL WHERE clause that forces the column comparison to a variable to be compared in lowercase. However the addExpression function isn't accomplishing this (since that is putting the expression in the field selection, not the where clause.  Here is what I have tried:  $category = 'mobile wifi'; $query = db_select('taxonomy_term_data', 'ttd')     -&gt;fields('ttd', array('tid')); $query-&gt;innerJoin('taxonomy_vocabulary', 'tv', 'ttd.vid = tv.vid'); $query-&gt;addExpression("LOWER(ttd.name) = $category"); $result = $query-&gt;condition('machine_name', 'images_cat', '=')     -&gt;execute()     -&gt;fetchAssoc();   And this:  $category = 'mobile wifi'; $query = db_select('taxonomy_term_data', 'ttd')     -&gt;fields('ttd', array('tid')); $query-&gt;innerJoin('taxonomy_vocabulary', 'tv', 'ttd.vid = tv.vid'); $result = $query-&gt;condition('machine_name', 'images_cat', '=')     -&gt;condition('LOWER(ttd.name)', $category, '=')     -&gt;execute()     -&gt;fetchAssoc();   The second one becomes invalid and the first one causes the problem I mentioned above. Any thoughts or suggestions?  Thanks, Patrick Finding singularities of a complex function and the respective residues Consider the function,   $$f(z) = \frac{\sin(\frac{1}{z})}{z^2+a^2} \text{ where } a&gt;0$$  I know that this has two simple poles at $z = \pm ia$ and an essential singularity at $z = 0$ because of $\sin(\frac{1}{z})$ in the numerator. For $\operatorname{Res}(f,ia)$ and $\operatorname{Res}(f,-ia)$, it is relatively easy to find the these values using   $$a_{-1} = \lim_{z\rightarrow z_0} ((z-z_0)f(z))$$  However, I am finding it much more difficult to determine the residue at an essential singularity.  From what I have read, it seems that the easiest way to determine the residue is to explicitly find the Laurent Expansion and then get it from there. Would this be the case for this function as well? How do I kill a process that won't die? I'm unable to kill a process using any of the techniques I'm aware of ("Force Quit" in Activity Monitor, top, killall from the Terminal) and wonder if there are some additional steps I can take.    ~ $ sudo killall -KILL 77439 Password: No matching processes were found ~ $ killall -KILL 77439 No matching processes belonging to you were found ~ $ killall 77439 No matching processes belonging to you were found ~ $ killall Mathematica No matching processes belonging to you were found   FWIW the process is "Mathematica" which I cannot relaunch, Quit, or Force Quit, or sample, either by name or PID, and it appears to have some odd side effects (screenshots don't appear, can't empty trash, and can't even shut down the system).  Are there additional steps that can be taken to really really kill a badly behaved process? LAN not working on 17.04 Actually yesterday I've upgraded from Ubuntu 16.04 to 17.04 and I got a problem that, if connect LAN cable it does not showing anything and  remains disconnected. But i can connect with WiFi. I don't know what's the problem. Actually its showing "device not managed" under the "Ethernet Network" and both were disabled. I've searched for the solution, but did not found yet. biblatex and new line for DOI, URL and Eprint Is an empty set equal to another empty set?