firstly I cloned my own repo from github, because i wanna amend the last commit, so i type "git commit --amend" and push to github, but some errors occur. Some guys said that the operation doesn't allowed by github, unless make another commit, Is that true?  and how can i amend the last commit on github?
When I've worked a bit with my source code, I did my usual thing commit and then I pushed to a remote repository. But then I noticed I forgot to organize my imports in the source code. So I do the amend command to replace the previous commit:  &gt; git commit --amend   Unfortunately the commit can't be pushed back to the repository. It is rejected like this:  &gt; git push origin To //my.remote.repo.com/stuff.git/  ! [rejected]        master -&gt; master (non-fast forward) error: failed to push some refs to '//my.remote.repo.com/stuff.git/'   What should I do? (I can access the remote repository.)
Upper bound on the number of charts needed to cover a topological manifold If $M^n$ is a compact topological manifold (not necessarily with additional structure), is there an upper bound on the number of charts needed to cover $M$ ? Does this bound depend on the dimension of $M$ ?  Thanks in advance...  Cheers Is Angular Momentum truly fundamental? This may seem like a slightly trite question, but it is one that has long intrigued me.  Since I formally learned classical (Newtonian) mechanics, it has often struck me that angular momentum (and generally rotational dynamics) can be fully derived from normal (linear) momentum and dynamics. Simply by considering circular motion of a point mass and introducing new quantities, it seems one can describe and explain angular momentum fully without any new postulates. In this sense, I am lead to believe only ordinary momentum and dynamics are fundamental to mechanics, with rotational stuff effectively being a corollary.  Then at a later point I learned quantum mechanics. Alright, so orbital angular momentum does not really disturb my picture of the origin/fundamentality, but when we consider the concept of spin, this introduces a problem in this proposed (philosophical) understanding. Spin is apparently intrinsic angular momentum; that is, it applies to a point particle. Something can possess angular momentum that is not actually moving/rotating - a concept that does not exist in classical mechanics! Does this imply that angular momentum is in fact a fundamental quantity, intrinsic to the universe in some sense?  It somewhat bothers me that that fundamental particles such as electrons and quarks can possess their own angular momentum (spin), when otherwise angular momentum/rotational dynamics would fall out quite naturally from normal (linear) mechanics. There are of course some fringe theories that propose that even these so-called fundamental particles are composite, but at the moment physicists widely accept the concept of intrinsic angular momentum. In any case, can this dilemma be resolved, or do we simply have to extend our framework of fundamental quantities? I've got an iPhone app with icon file Icon.png.  This icon shows up properly when the app is on the phone itself, but it doesn't show up in the applications pane in iTunes.  What do I need to do to get it to show up properly? Need help disabling imessage? I recently changed from iphone to android and i have been having trouble recieving messages from my iphone friends since my iphones screen is broken i cant do anything on it. Any way to fix this problem through icloud or something? This is my first question on here. I'm trying to numerically solve the Schrödinger equation for the  and find the energy eigenvalues and eigenfunctions but I am confused about how exactly this should be done.  I've solved some initial value problems in the past using iterative methods such as Runge–Kutta. I've read that  is the way to solve Schrödinger's equation but Wikipedia also describes it as an iterative method for initial value problems.  How do I use it to solve an eigenvalue problem?  This confuses me for the following reasons:   Wouldn't iteratively solving the DE require knowledge of the energy eigenvalues to use as input to the calculation? I don't know the eigenvalues yet; they're precisely what I'm trying to calculate. If I did that, wouldn't I simply get a unique solution, instead of a family of eigenfunctions and eigenvalues?    I've seen some mention of "tridiagonal matrices" being generated somehow, but am not sure what the elements of that matrix would be or how that applies to the problem. Leandro M. mentioned that "the discretization defines a finite dimensional (matrix) eigenvalue problem". This seems like the correct road I should be going down, but I haven't been able to find anything that explicitly explains this process or how the matrix is constructed. If this is the correct procedure, how is such a matrix constructed? if G is generated by {a,b} and ab=ba, then prove G is Abelian if G is generated by {a,b} and ab=ba, then prove G is Abelian  All elements of G will be of the form $a^kb^j,\,\, k,j \in \mathbb{Z}^+$   so I need to get $a^kb^j = b^ja^k$ I have a PC with an OEM install of Win 8 updated to 8.1.  It has 3 physical hard drives in it.  The drive where Windows is installed has a LOT of partitions on it already.    Can I install Ubuntu on a different physical hard drive than Windows, and be able to dual-boot?  I am able to boot to a live USB of Ubuntu 14.04, so I think I'm about ready to proceed.  But if I can make my installation easier by using a different physical drive, I'd like to do that. In templates, where and why do I have to put typename and template on dependent names? What exactly are dependent names anyway?    I have the following code:  template &lt;typename T, typename Tail&gt; // Tail will be a UnionNode too. struct UnionNode : public Tail {     // ...     template&lt;typename U&gt; struct inUnion {         // Q: where to add typename/template here?         typedef Tail::inUnion&lt;U&gt; dummy;      };     template&lt; &gt; struct inUnion&lt;T&gt; {     }; }; template &lt;typename T&gt; // For the last node Tn. struct UnionNode&lt;T, void&gt; {     // ...     template&lt;typename U&gt; struct inUnion {         char fail[ -2 + (sizeof(U)%2) ]; // Cannot be instantiated for any U     };     template&lt; &gt; struct inUnion&lt;T&gt; {     }; };   The problem I have is in the typedef Tail::inUnion&lt;U&gt; dummy line. I'm fairly certain that inUnion is a dependent name, and VC++ is quite right in choking on it. I also know that I should be able to add template somewhere to tell the compiler that inUnion is a template-id. But where exactly? And should it then assume that inUnion is a class template, i.e. inUnion&lt;U&gt; names a type and not a function? How can I develop my Android game for different phone resolutions? Defaulting on credit cards before leaving the country I have a colleague who is going back to his country after staying for a couple of years in US. He has 3-4 credit cards plus a personal loan. His total debt would come to around $10,000. Some days ago, he told me he is going to default on the accounts. He figures, since he is not planning to come back to US, it should not matter to him.  Question is, is this a bad move on his part, and if it is, how can I convince him? The Cartesian product of a family $(A_i\mid i\in I)$ is defined as $$\prod\limits_{i\in I}A_i=\{f:I\to\bigcup A_i\mid f(i)\in A_i\}$$ Let $I_n=\{i \in \mathbb N \mid i \le n\}$ for $n\in \Bbb N$ and $A_i$ be countable for all $i\in I_n$. Then $\prod\limits_{i\in I_n}A_i$ is countable.   My attempt: Lemma 1: $(\prod\limits_{i\in I_n}A_i) \times A_{n+1}$ and $\prod\limits_{i\in I_{n+1}}A_i$ are equinumerous for all $n \in \mathbb N$. (I presented a proof ) Lemma 2: If $A$ and $B$ are countable, then $A \times B$ is countable. (I presented a proof ) I will prove the theorem by induction on $n$. The theorem is trivially true for $n=0$. Assume that the theorem is true for $n=k$, then $\prod\limits_{i\in I_k}A_i$ is countable. Since $\prod\limits_{i\in I_k}A_i$ is countable (by inductive hypothesis) and $A_{k+1}$ is countable, then by Lemma 2 $(\prod\limits_{i\in I_n}A_i) \times A_{n+1}$ is countable. Furthermore, by Lemma 1 $(\prod\limits_{i\in I_k}A_i) \times A_{k+1}$ and $\prod\limits_{i\in I_{k+1}}A_i$ are equinumerous, then $\prod\limits_{i\in I_{k+1}}A_i$ is countable too. Thus the theorem is true for $n=k+1$. This completes the proof.   Does this proof look fine or contain gaps? Do you have suggestions? Many thanks for your dedicated help! I am always confused about where to put adverbs in sentences. For example, consider the questions below:        Why did they target us specifically?   Why did they target specifically us?   Why did they specifically target us?      I believe all these sentences mean the same. Am I correct? I am always confused about where to put adverbs such as always and specifically, etc. Is there a particular grammar rule for this?  Funny, you see, I can even form the above sentence in different ways.         I always confuse where to put this kind of adverb   Always I confuse where to put this kind of adverb Proving if $d_0$ is the smallest positive integer in $S$ then $d_0 = \gcd(a,b)$ Motivation  I want to include a list of related equations, say, for a proof, in my LaTeX document. As far as I know, I have two good options, eqnarray and align.   Question  What is the difference between eqnarray and align, and how do I know which I should be using? Or does it matter at all? Bathroom vanity light with no junction box My C# application is returning 0xE0434352 to Windows Task Scheduler but it is not crashing Which command should I use for textual subscripts in math mode? Textual subscripts like in W_{total} should be typeset in an upright text font (so that code isn't good practice), as has been  in   . Now there are several ways to achieve this, and I'm somewhat confused which I should use:   W_{\rm total} is nice and short, and appears to work in all circumstances, but I expect LaTeX people will frown upon it :-) Is there any good reason against this? W_{\mathrm{total}} &ndash; is this the LaTeX equivalent of the \rm approach? W_{\textnormal{total}}  as total is text and not math&nbsp;... In , Ulrike Fischer suggests a more complicated approach. Even W_{\operatorname{total}} appears to work, but it seems inappropriate.   Note: I always assume here that amsmath is loaded.  I've already asked some questions above, but my main question is: which of these options is the best practice for textual subscripts?    Let me point out why I haven't mentioned \text, \textrm or \textup above. Those commands (mostly) keep the font of the context they're used in, e.g., in an italic context, \text and \textrm would give italic subscripts, and all three yield bold subscripts in a bold context.  Final note: This question is similar to, but not the same as all those  about the  between , , , ,  that have been asked before. Maybe it's still a duplicate&nbsp;... Prove that $Ax=0$ has infinite solutions if and only if $ \text{rank}(A)&lt;n$   Here is one way of my if proof, but I don't know how to proof the other part.  Let $r$ be the rank of $A$. Then $ r\leq  n$. If $ r&lt;n$, then there are $n-r$ linearly independent solutions. Furthermore any linear combination of these solutions will also be a solution of $Ax=0$. Hence, in this case, the equation $Ax=0$ has infinite number of solutions How about a "Vote not to close" option to counter the "Vote to close"? My request is simple: Many times, there will be a question where some people feel like it should be closed. At the same time, I'll feel like it's a perfectly legit question, and it should therefore NOT be closed. Right now, I have to wait till it gets enough close votes (which it always does for some reason, as soon as 1 or 2 people vote to close, e/o else decides to vote as well) and then vote to re-open. How about, as soon as there's one vote to close, there should be an option to counter the close vote, something like "vote not to close" or whatever. This would then bring the "Vote to close" number down by one. Only when the vote to close outnumbers the vote not to close by 5, that's when a question is indeed closed. Any thoughts? How to retrieve a module's path? I want to detect whether module has changed. Now, using inotify is simple, you just need to know the directory you want to get notifications from.  How do I retrieve a module's path in python?