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The recent user profile tab name change - from "activities" to "all actions" - was not accompanied by a hyperlink update from ...?tab=activities... to ...?tab=allactions...    Click on the "posts edited" link to see the 404-error. How to SEO a Single-Page website What is the difference between the dashed and solid attack bars? I was flipping through my Pokemon list to see which kind of attacks they had, and I notice there was a small different between the attacks. Some attacks contained a dashed blue bar where as others contained a solid blue bar.   What is the difference and significance between the two? $pq\mid pn^q+qn^p+kn$ for some $k,\,$ if $p,q$ are primes WPF DataGrid : CanContentScroll property causing odd behavior Joining elements of a list in GNU Make Increase iPhone call history Executing SSIS 2012 package that has script components from external application Could you vs would you Could you write your name? Would you write your name?   When you are asked to do this, are there any situation in which you hear weird if either is used (but the other sounds pretty natural .) Proof that the set of all possible curves is of cardinality $\aleph_2$? I am reading George Gamow's book  and a certain assertion Gamow makes seems a little startling considering what I already know of the subject of infinite cardinality.     But the number of all geometrical points, though larger than the number of integer and fractional numbers, is not the largest one known to mathematicians. In fact it was found the variety of all possible curves, including those of the most unusual shapes, has a larger membership than the collection of all geometric points, and thus has to be described by the third number in the infinite sequence. [Gamow, 22]   He later does explicitly say the number of all possible curves is $\aleph_2$. But nowhere else can I find reference to this being true, nor does he provide any sort of reasoning to its validity.  My question is how can you prove the set of all possible curves is of cardinality $\aleph_2$ and not $\aleph_1$ or $\aleph_0$? Access pictures from Pictures app in my android app Just like the iPhone has a UIImagePickerController to let the user access pictures stored on the device, do we have a similar control in the Android SDK?  Thanks. Is it possible to set the default size of the Empty Object? The problem is since I switched my blender scale to metric, the Empty's default size is kinda large for most times I need it. An "urgent" tag for questions that need answers within minutes I often find myself in a spot of trouble, and when I have minutes left to fix it, I sometimes turn to SO/SF to start the "community help process". I suppose a tag like "urgent" or "immediate-attention" could enable contributors with spare time easily find the most desperate situations, giving more attention to those issues and solving them quicker. Or could this be a special tab on the home page? How come Dropbox gets an icon in Finder sidebar? How come Dropbox gets a non-generic icon in Finder's sidebar, when other directories like Google Drive and Sites (native in OS X before Lion) all have the same generic one?    How can I customise the icons used by the folders in the sidebar? OS X used to show individual icons of all folders there — not any longer. How do I extract text that lies between parentheses (round brackets)? I have a string User name (sales) and I want to extract the text between the brackets, how would I do this?   I suspect sub-string but I can't work out how to read until the closing bracket, the length of text will vary. Negative logLikelihood Kalman filter For every set $A$, the empty set is a subset of $A$. The empty set is a set. Therefore, the empty set has a cardinality $\geq 1\ldots$ How to install Ubuntu on portable external Hard Drive? OS: Windows 7. I want install Linux Ubuntu on portable external Hard Drive USB 2.0. I read a variety of methods, but I'm confused by contradictory advices and methods. Actually, installing Ubuntu on anything other than clean PC looks much more complicated than installing Windows. I need to have Ubuntu package + Python 2.7 + C compiler installed. My external hard drive is partially filled, I need to keep all files.   Will Ubuntu run entirely on external hardrive, without writing anythinhg to Windows system folders and to registry?  Can anyone post detailed guide how install Ubuntu on external hard drive? $$\tan(\theta_1+\theta_2+\cdots+\theta_n)=\frac{S_1-S_3+S_5+\cdots}{1-S_2+S_4+\cdots}$$  where  $S_i$ denotes the sum of product of tangent of angles taken $i$ at a time.     For example,$$\tan(\theta_1+\theta_2)=\frac{S_1}{1-S_2}=\frac{\tan\theta_1+\tan\theta_2} {1-\tan\theta_1\tan\theta_2}$$   (This formula is given  in my textbook with no derivation or background)  How to derive this? Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$ There is a famous Theorem telling that:  For $n≥5$, $A_n$ is the only proper nontrivial normal subgroup of $S_n$.  For the proof, we firstly start with assuming a subgroup of $S_n$ which $1≠N⊲S_n$. We proceed until at the last part of proof's body, we assume $N∩A_n=\{1\}$. This assumption should be meet a contradiction with normality of $N$ in $S_n$. There; we get $N=\{1,\pi $} in which $\pi$ is an odd permutation of order $2$. Now for meeting desire inconsistency, I have two approaches:  (a) Since every normal subgroup, having two elements, lies in the center of $G$ so, our $N⊆ Z(S_n)=\{1\}$ for $n≥5$ and then $N=\{1\}$.  (b) Clearly, $1≠N$ acting on set $\Omega=\{1,2,...,n\}$ is intransitive wherein $|\Omega|≥5$ and according to the following Proposition $S_n$ would be imprimitive.  Proposition 7.1: If the transitive group $G$ contains an intransitive normal subgroup different from $1$, then $G$ is imprimitive (Finite Permutation Groups by H.Wielandt).  May I ask if the second approach is valid? I am fond of knowing new approach if exists. Thanks.