Is there a way in Git to rollback to a much earlier version of a file? I can roll back to the previous version with REVERT, but what if I want to go back to earlier versions?
I have made some changes to a file which has been committed a few times as part of a group of files, but now want to reset/revert the changes on it back to a previous version.   I have done a git log along with a git diff to find the revision I need, but just have no idea how to get the file back to its former state in the past.
what is PGP public key block? There's PGP public key block posted on some websites (eg. ).  It's not hex code. it uses much more alphabet characters. What is it?  Why is this information posted? how can i use it? Using the quadratic formula, we have either 0, 1, or 2 solutions. I wonder if we could use it this formula for congruence? Or is there a formula to solve quadratic equation for congruence?  Edit Assume that $ax^2 + bx + c \equiv 0 \pmod{p}$, where $p$ is prime with $(a, p) = 1$, then is there a formula for this equation?    Thanks, I have a really simple Java class that effectively decorates a Map with input validation, with the obvious void set() and String get() methods.  I'd like to be able to effectively call those methods and handle return values and exceptions from outside the JVM, but still on the same machine Update: the caller I have in mind is not another JVM; thanks @Dave Ray  My implementation considerations are typical    performance ease of implementation and maintenance (simplicity?) reliability flexibility (i.e. can I call from a remote machine, etc.)   Is there a 'right way?' If not, what are my options, and what are the pro/cons for each?  (Stuff people have actually done and can provide real-life feedback on would be great!) How come Mortarboard is bronze and Enthusiast is silver? :   Silver  Enthusiast    Visited the site each day for 30 consecutive days   56.9k awarded Bronze  Mortarboard   Earned at least 200 reputation in a single day      15.4k awarded    It would seem that earning Enthusiast requires almost no effort while Mortarboard is highly non-trivial. This appears to be reflected in the award count (almost 4:1 in favor of enthusiasts).  So, why is the first one silver and the second one bronze?  (A similar question can be asked about Epic vs Fanatic and probably many other). I have not been able to watch CBS all access for some time now. Error 2004. I have not found another browser for ubuntu that will play all access either. However firefox for windows plays it fine? Is there a fix in the works for ubuntu firefox? What is the difference between implication symbols: $\rightarrow$ and $\Rightarrow$? I do not understand the difference between $\rightarrow$ and $\Rightarrow$. Sometimes I see implication truth tables labeled with the former, sometimes with the latter.  Aren't they synonyms of logical implication or is there any difference? Is PCA still done via the eigendecomposition of the covariance matrix when dimensionality is larger than the number of observations? I have a $20\times100$ matrix $X$, containing my $N=20$ samples in the $D=100$-dimensional space. I now wish to code up my own principal component analysis (PCA) in Matlab. I demean $X$ to $X_0$ first.  I read from someone's code that in such scenarios where we have more dimensions than observations, we no longer eigen-decompose the $X_0$'s covariance matrix. Instead, we eigen-decompose $\frac{1}{N-1}X_0X_0^T$. Why is it correct?  The normal covariance matrix is of size $D\times D$, each element of which tells us the covariance between two dimensions. To me, $\frac{1}{N-1}X_0X_0^T$ is not even of the correct dimensions! It is $N\times N$ matrix, so what would it tell us? Covariance between two observations?! Gravitational slingshot of light using a black hole/massive object Wikipedia has this page on  using planets. In some cases this effect was used to accelerate the spacecraft to a higher velocity. This diagram shows this in a very oversimplified manner.   That got me thinking that if light is affected by gravity, and if it slingshots around the black hole/massive object, can't it gain a higher speed than $c$? What limitations are stopping it from doing this?  Forgive me if the answer to this question is pretty straight-forward or staring-you-in-the-face kind. I haven't fully understood the mechanics of the gravitational slingshot fully yet, but I couldn't wait to ask this. Note: If it is possible (I highly doubt that!), could you provide an explanation using Newtonian mechanics, I'm not very familiar with general relativity because I'm in high school. Does it give higher quality to shoot in low-res mode in-camera, or to downsize high-res photos later? Suppose you want to store your photos at some lower resolution, let's say about ~1 MB large.  You own a camera able to make photos at 5 MPix and more.  And, you want to have the maximum quality at the smaller size.  Would it be better to make a photo at highest resolution and then resize it with PC software (with a good filter of course), or to directly set the camera to make photos at 2 MPix only? Non-trivial cyclic group with unique generator Let $G$ be a non-trivial cyclic group with an unique generator. Show that $G$ has exactly two elements.   Let $g$ be a generator of $G$. My first idea to approach the problem was to show that if $|G|=n &gt; 2$ then there is an integer $k$ between 1 and $n$ such that $\langle g^k \rangle = G$ or, equivalently, $g \in \langle g^k \rangle$. My second idea was to analyse the problem in 2 separate cases. For the first one, if $n$ is prime, let $k$ be a positive integer then, by Lagrange's Theorem, $|g^k| \mid n$ and, therefore, $\langle g^k \rangle = n$. Hence, we must conclude that, if $n &gt; 2$ the generator cannot be unique. For the second case, where $n$ is composite, I was hoping to get to a contradiction, but could not advance any further. Is there a way to develop either of these ideas or is it necessary a new approach? A word for a worldly wise person who pretends to be naïve? What is a word for someone who is experienced and wise, but who deliberately acts naïve?    I don’t intend it for sarcastic use; I’m trying to describe someone succeeding in making people think that that person truly is naïve.   Is there a word for this? How fast does the sequence $y_t$ defined by $y_{t+1}=y_t(1-y_t)$ decay to zero? The question is in the title; I'm looking for the exact decay rate. Naturally, assume the starting point $y_0$ belongs to $(0,1)$.   This is motivated by one of the answers to . Is password confirmation necessary on a Change Password dialog? Somewhere on Stack Exchange I saw the equation     $$\gcd(2^m-1,2^n-1)=2^{\gcd(m,n)}-1.$$   I had never seen this before, so I started trying to prove it. Without success...  Can anyone explain me (so actually prove) why this equation is true?  And can we say the same when replacing the '$2$' by any integer number '$a$'? Capital letters in "Theorem", "Conjecture" etc This is my first post and as you can probably guess I am a mathematician so I have no clue about grammar. I am writing a mathematical document at the moment and I would appreciate some advice on my usage of capital letters. Can somebody please confirm if the following are correct?  1) "We know by T​heorem 4.6.1 that..."   2) "the following c​onjecture, due to..."  3) In order to prove the "Mckay-Stevens $k$-covering C​onjecture, once needs to show that..."  I'm particularly confused about 3).  Many thanks for any help Let $R$ be a Artinian commutative ring with $1 \neq 0$. If $I$ is prime, then $I$ is maximal. Prove: Let $R$ a Artinian commutative ring with $1 \neq 0$. If $I$ is prime, then $I$ is maximal.     I got stuck on this. I understand that every ideal is generated by finitely many elements. Here is my approach:  It's enough to prove the following implication: $$ R/I \ \text{is a domain} \quad \Rightarrow \quad R/I \ \text{is a field}$$ Then only finding an inverse is left. So let $x \in R$ in arbitrary. We have to find an inverse element of $x+I \in R/I$, that as an element y so that $x \cdot y \in I+1$. We denote $I = (x_1, x_2, \cdots, x_n)$.  Now I have to find y so that $xy -1 = r_1 x_1+ r_2 x_2 + \cdots + r_n x_n$. This is where I no more knew what to do.   Your advise will be appreciated. How do I allow long URLs to have line breaks at any point. This is in the bibliography not the main text. I am trying to save space so don't want extra spaces to be added to make it only break at slashes, for example, as it does by default.  I am using biblatex+biber. Question :   Determine all natural numbers n such that 3   divides $n\cdot2^{n}+1$  Actually I don't have any ideas to approach but  my efforts :   I see $n=1,2,7,8,13,14$ so I think :   $n=6k+1$ and $n=6k+2$ $k\in \Bbb{N} $  If I'm not wrong but I don't know how ? I prove it ? What is the function of "do" in this sentence? Rarely, though, do countries introduce a single reform alone.   What function does do have in this sentence? How much hard disk space should be needed for Xbox 360? I want to get a 360 and don't know wether to get the bigger (250GB), newer, more expensive Elite, or get one of the older, smaller (120GB), last gen ones. I know the arcade is going to be too small to save anything useful  How much hard disk space is recommend? What else is stored besides games?