How can I bring back the original version of a file in git? Even though I have commited the file and had been pushed?
How can I reset or revert a file to a specific revision?
Is $\sum_{n=1}^\infty \frac{\sin(2n)}{1+\cos^4(n)}$ convergent? As I was just checking this 'child prodigy' out on Youtube, I stumbled upon  video, in which Glenn Beck asks the kid to do the following proof:    Further on, the kid starts sketching a proof (without a shadow of a doubt regarding the accuracy of his solution ) including the Integral Test. I don't know much about improper integrals since I just finished highschool, but this integral approach seemed, intuitively, pretty inaccurate to me since this is not a strictly decreasing function. Then I found this out from Wikipedia !   Furthermore, the blunt assessment that the series are convergent seems dubious as well..Upon a few computations of my own(mostly partial sums) , I tend to believe that the series are, in fact, divergent .  Can anyone suggest a rigurous take on this problem (easy as it may seem to some amongst you) ? A Riemann integrable function must have infinitely many points of continuity Finding all group homomorphisms of $S_n\to\mathbb{C}^*$ and $A_n\to\mathbb{C}^*$ I need to find all group homomorphisms of $S_n\to\mathbb{C}^*$ (for $n\ge2$), and also all group homomorphisms of $A_n\to\mathbb{C}^*$ (for $n\ge2$).  Someone on this site, two years ago, seems to have already asked the same question (). I understand what the questioner says there, but I don't understand it when he says:     Therefore there is exactly one $g:\mathbb{Z}/2\mathbb{Z}\to\mathbb{C}^*$, so all elements of $a\in\mathbb{C}^*$ give us $\operatorname{ord}(a)\mid g[\mathbb{Z}/2\mathbb{Z}]$, so $a$ can only be $-1$ or $1$. Now we know that $f:S_n\to\{-1,1\}$ &hellip;   What is he saying there? And how to go on from there? (I do not understand the answer given either &hellip;)  I hope that someone here can help me further. (And if I'm not allowed to ask this question because is has already been asked two years ago, please tell me what to do instead).  Thank you in advance! I have a mouse with lots of buttons, but it's not a mainstream make like Logitech. For Windows, I have a driver that lets me assign actions like close-window (Ctrl+W) or next-tab (Ctrl+Tab), but I don't have a Linux driver. Since Linux is so flexible, I thought perhaps there is a general way to do this, regardless of brand?  Update: Based on input from Cyrex, I installed and ran sudo apt-get install btnx which found several but not all mouse buttons. Found: left, right, wheel, wheelclick, thumb fwd, thumb back. Not found: wheel left, wheel right, thumb middle button. Vendor ID is 0x04d9, Model ID is 0xa015.  Update 2: In System>Prefs>Mouse there's a lightbulb icon for testing double-click speed. Every working button can turn the bulb on&amp;off, but the missing buttons can't. It would seem that Ubuntu isn't aware of these buttons and thus doesn't register their clicks. I guess I need to hunt for a driver, though a mainstream mouse is probably the easier way. This question and answer is a response to a request from Joseph Wright.   Why shouldn't I use getnonfreefonts to install additional fonts? Why shouldn't I use updmap when installing or removing fonts?     Background  There are a number of questions on the site concerning problems caused by people installing additional fonts and using updmap to update the 'map' files on which TeX depends.  One common cause of these problems is the use of getnonfreefonts.  Other causes are the use of other font installation scripts or executing updmap directly. I am in 1.13 Pre-Release 7 trying to make a one command creation and I need an item with a specific name. The command I use is /give @p diamond_sword{display:{Name:"Sword of Power"}} and it gives my a diamond sword, but it doesn't have the name.   This is me running the command.   This is the command not working. I have a problem with the interpretation of a test result in which the p-value is 8.6e-28. How should it be interpreted? What is the e for?  Specifically, I used White's Test for the homoscedasticity assumption of a linear regression:  White's general test statistic :  150.0535  Chi-sq( 9)  P-value =  8.6e-28 Prove $\int_0^{\infty}\! \frac{\mathbb{d}x}{1+x^n}=\frac{\pi}{n \sin\frac{\pi}{n}}$ using real analysis techniques only I have found a proof using complex analysis techniques (contour integral, residue theorem, etc.) that shows $$\int_0^{\infty}\! \frac{\mathbb{d}x}{1+x^n}=\frac{\pi}{n \sin\frac{\pi}{n}}$$ for $n\in \mathbb{N}^+\setminus\{1\}$   I wonder if it is possible by using only real analysis to demonstrate this "innocent" result?  Edit A more general result showing that  $$\int\limits_{0}^{\infty} \frac{x^{a-1}}{1+x^{b}} \ \text{dx} = \frac{\pi}{b \sin(\pi{a}/b)}, \qquad 0 &lt; a &lt;b$$ can be found in How can I set Excel to always import all columns of CSV files as Text? Though I try to avoid it, I occasionally have to open a CSV file in Excel. When I do, it formats columns containing numbers, which makes them useless for my purposes. As far as I can tell, the only way to prevent this from happening on import is to rename the file so the extension isn't .csv and use the import wizard to specify the format of each column individually. For files with 50-60 columns, this is impractical.  Since every answer for this oft-asked question on the internet suggests either some means of converting the formatted numbers back once the file is open (which won't work for me - I want to solve the general problem, not a few specific cases) or manually selecting the format type of each column (which I don't want to do), I'm looking for a way to set a global preference or style such that all columns of all CSV files opened are always formatted as text.  I know about "armoring" the numbers with quotes, too, but the files I get don't come like that and I was hoping to avoid having to pre-process the files so Excel doesn't screw them up.  Is there a way to do specifically this: Always format all columns in opened CSV files as text, without manually selecting each column every time during import?  I'm using Excel 2003, but I'll take answers for 2007 if that's what you know. Recently I bought a new laptop that came with Windows 10 installed but not activated. I use both Windows 10 and Ubuntu 18.04, so I tried making a dual boot with a USB flash drive. It was recognized by the BIOS, I tried Try Ubuntu without installing and Install Ubuntu. With both options the PC freezes, and I need to press the power button. It's shown very fast some errors that are listed below:  [ 0.064522] ACPI Error: Method parse/execution failed \_SB.PCID.RPOB.PXSX, AE_NOT_FOUND (20170831/parse-550)  [ 0.066316] ACPI Error: [_SB.PCID.RPOB.PXSX], Namespace lookup failure, AE_NOT_FOUND (20170831/download2-191)  [ 0.066325] ACPI Error: AE_NOT_FOUND, During name lookup/catalog (20170831/psobject-252)  [ 0.246232] ACPI Exception: AE_NOT_FOUND. Evaluating _PRS (20170831/pci_link-176)  [ 0.246248] ACPI Exception: AE_NOT_FOUND. Evaluating _PRS (20170831/pci_link-176)  [ 0.246260] ACPI Exception: AE_NOT_FOUND. Evaluating _PRS (20170831/pci_link-176)  [ 0.246272] ACPI Exception: AE_NOT_FOUND. Evaluating _PRS (20170831/pci_link-176)  [ 0.246285] ACPI Exception: AE_NOT_FOUND. Evaluating _PRS (20170831/pci_link-176)  [ 0.246297] ACPI Exception: AE_NOT_FOUND. Evaluating _PRS (20170831/pci_link-176)  [ 0.246310] ACPI Exception: AE_NOT_FOUND. Evaluating _PRS (20170831/pci_link-176)  [ 0.246322] ACPI Exception: AE_NOT_FOUND. Evaluating _PRS (20170831/pci_link-176)   I'm using NVIDIA GTX 1050 Ti graphics card and Intel i7-8750H processor.  I talked to the customer support and they just said that my laptop might not be compatible with Ubuntu. I also tried Ubuntu 16.04, but there were no changes.  EDIT: Thanks a lot for all the answers, but unfortunatelly I returned the PC to the store, neither the technical support found a solution for the problem, they just said: "Our PCs are just able to work with Windows, anyother OS might work but without our warranty". I followed the official step-by-step "Visual Studio Code and Unity" guide, but it seems I messed up something, because Intellisense doesn't see any Unity related stuff.  Like the MonoBehaviour class and its members (like .transform), or the Unity callbacks, like Start or Update. When should we use "and" and/or "and/or"? What's the difference between "and" and "and/or"?  How do we decide whether to use one or the other?  Note: Also it would be great if someone could explain how do we actually pronounce "and/or" verbally in a sentence... how to reduce DC voltage using resistors? How would one go about using a 12 V DC power source to power something which needs 4.5 V DC using resistors? Is there a way to determine how much adding a resistor would drop the voltage? Too many of your edits were rejected, try again in 7 days First time I've got the following message on SO:     Too many of your edits were rejected,   try again in 7 days.   Although, I have made ~50 accepted edits this day.  I'm sure that should outweigh the ~5 rejected edits, right?    My suggestion:  bool allowEdit(USER u) {     if(u.rejected * 5 &gt; u.accepted)         return(false);     else         return(true); }   Think of it this way: if I do a 1000 accepted edits, and mess up on 5 [rejected], does that mean I should get banned for 7 days?    Hmmm... There seems to be a bug; the message only appears when clicking edit from review.  But otherwise, I can't edit , even when going to it from the homepage. increasing impedance of headphones I have headphones with differential input and impedance of 8 ohms. I need to drive this headphone with some DAC with built in headphone driver (Currently I have chosen ADAU1772). DAC's datasheet mentions that the minimum impedance of headphones it supports is 16 ohms. Can I increase impedance of my headphones so that I can drive them through this chip? What will happen if I drive this 8 ohm headphone through a chip supporting minimum impedance of 16 Ohms? Item cannot be installed or removed until the package catalogue is repaired Every Hilbert space has an orthonomal basis - using Zorn's Lemma The problem is to prove that every Hilbert space has a orthonormal basis. We are given Zorn's Lemma, which is taken as an axiom of set theory:  Lemma If X is a nonempty  with the property that every  of X has an upper bound in X, then X has a maximal element.   Given a orthonormal set $E$ in a Hilbert space $H$, it is apparently possible to show that $H$ has an orthonormal basis containing $E$.   I tried to reason as follows: Suppose $E$ is a finite set of $n$ elements. Then one can number the elements of $E$ to create a totally ordered set of orthonormal elements. Then the span $&lt;E&gt;$ can be identified with $R^n$, where each element $v = v_1 e_1 + v_2 e_2 + ... + v_n e_n$ is identified with the vector $(v_1, v_2, ..., v_n)$. On $R^n$ we have a total order, namely the "lexigraphical order" $(x_1,x_2,...,x_n) \leq (y_1,y_2,...,y_n)$ if $x_1 &lt; y_1$ or if $x_1 = y_1$ and $x_2 &lt; y_2$ or if $x_1 = y_1$, $x_2 = y_2$ and $x_3 &lt; y_3$ and so on. Hence $E$ is a totally ordered subset of $H$ and $H$ is a partially ordered set. However, this set doesn't seem to have an upper bound. The set $E$ does have an upper bound. If we define a total order on $E$ only, then X is a partially ordered set satisfying the criteria so X has a maximal element?   This is as far as I got, and I am not sure the entire argument is correct. I don't see how what kind of maximal element I am seeking, since the orthonormal basis of a Hilbert space can have countably infinity number of elements. How to set systemwide "XP style DPI scaling" in Windows 8.1? I run my ThinkPad with a system DPI setting of 140%. In Windows 7 and 8, I enabled the "Use Windows XP style DPI scaling" checkbox in the Custom DPI Setting dialog. When this setting is off, non-DPI-aware applications get DPI virtualization via bitmap stretching, which results in large but fuzzy text. Turning on the checkbox disables this bitmap stretching, so non-DPI-aware apps get smaller text but without the fuzzy stretching. I find most apps to be more readable with the smaller crisper text, so I enable XP style scaling (i.e. disable DPI virtualization).  Windows 8.1 RTM has removed this option completely. After upgrading, all of my non-DPI-aware apps are running with ugly bitmap stretching. I'm able to fix this by going into the Properties for each app and setting the "Disable diplay scaling on high DPI settings" box in the Compatibility tab, but that is a bit of a pain.  Is there any way to restore the systemwide XP-style DPI scaling in Windows 8.1? Let $A$ and $B$ be two sets of real numbers. Define the distance from $A$ to $B$ by $$\rho (A,B) = \inf \{ |a-b| : a \in A, b \in B\} \;.$$ Give an example to show that the distance between two closed sets can be $0$ even if the two sets are disjoint. How to make 'python' program command execute Python 3? The python program command executes Python 2. Python 3 can be executed using the python3 command.  How can Python 3 be executed using the python command?