Inserting the "incomparability" symbol
How to look up a symbol or identify a letter from a math alphabet or other character?
Number of possible permutations of n1 1's, n2 2's, n3 3's, n4 4's such that no two adjacent elements are same? When I have Excel running and I double click an Excel file in Windows explorer, I'd like it to launch in a new window by default so that I can move documents to separate monitors. Is there any way to get this behavior? Visual Studio Editor does not underline errors anymore My Visual Studio (2008) Editor has stopped to underline Errors (this nifty wavy red lines). I can't really tell when, but it can be related to the installation of .Net Framework 3.5 SP 1 or the MVC Beta (which I guess is unlikely). Furthermore have I installed and uninstalled both CodeRush and Resharper for evaluation purposes (decided not to keep either one of them).  Does anyone know the problem and how to restore this functionality again? The first time I learnt LaTeX, I thought \newcommand properly fits for inline mode and \newenvironment for displayed mode.  Later I noticed it is not correct. So the question is   What is the rule of thumb when deciding whether we should use one over the other one? The question is as follows:      Let $A'$, $B'$ and $C'$ be the midpoint triangle of triangle $ABC$. In other words, $A'$, $B'$ and $C'$ are the midpoints of segments $BC$, $CA$ and $AB$, respectively. Show that triangles $A'B'C'$ and $ABC$ have the same centroid.    My reasoning was through the means of the Midline Theorem. After drawing the diagram, we can see, for example, $C'A'$ is a midline of $\triangle ABC$, which means that $C'A'$ is parallel to the base $AC$ and half the length of it as well. Therefore, the median $B'B$ would pass through the midpoint of $C'A'$, including the midpoint of $AC$.   Is my reasoning valid or, at least, is it on the right track? Any advice on solving this problem will be greatly appreciated. How do I resize my current ubuntu partition? I've got Ubuntu 10.10 installed to use my whole hard-disk, but would like to use the 130GB of free space I've got to create a new partition and do some development on Unity and Natty.  Can I use gparted to do this?  If so how? What are the best ways to improve a site's position in Google? What are the best ways to improve a site's position in the Google search results? How to search text throughout entire file system? I received my PhD in 2009 and my adviser will not provide a good recommendation for me. This is mostly because we have fundamentally different approaches to science, and in retrospect I see that I could have avoided a breakdown in our relationship if I had been more deferential.  At this point, I leave his name off of my list of references, but I suspect that a diligent potential employer might call him anyway. I would be willing to discuss any concerns that were brought up in such a call - indeed I think that doing so will help me to find a good fit in a new position - but I do not know if I should, or how to state this fact in my job applications.  I am currently finishing my post doc, and one recommendation has been to take another post-doc so that I at least have two supportive references from postdoc advisers - and that the additional publications will place less weight on recommendations. Still, others have told me that not having a good reference from my adviser is a kiss of death.   How can I most effectively handle this situation? Eigenvectors of real symmetric matrices are orthogonal Is "You are correct" correct? I am aware it is common practice to standardize the features for ridge and lasso regression, however, would it ever be more practical to normalize the features on a (0,1) scale as an alternative to z-score standardization for these regression methods? How do you make HDDs and partitions mount at startup on Ubuntu?  I always keep my media and data files on separate partitions - one 2tb HDD and a 400 odd gig partition.  I have been trying to swap the default folder location for the home directory to my other drives.  It works when I change the /home/user_name/.config/user-dirs.dirs file to the directories I want, but only until I reboot the system. I am only assuming that the drives not mounting is the problem with it, but it would be helpful either way.  If any one knows another reason for why the directories change back to default each time that would be good also. Proving a binomial sum identity $\sum _{k=0}^n \binom nk \frac{(-1)^k}{2k+1} = \frac{(2n)!!}{(2n+1)!!}$ How do you pull first 100 characters of a string in PHP C++, array of objects without How to analyse 'Element not Found' exceptions when working with Selenium Omission of 'for' with various quantified time intervals: influence of verb LaTeX figures side by side A star's collapse can be halted by the  due to the Pauli exclusion principle. In extreme relativistic conditions, a star will continue to collapse regardless of the degeneracy pressure to form a black hole. Does this violate the Pauli exclusion principle? If so, are theorists ok with that? And if it doesn't violate the Pauli exclusion principle, why not?