I know that making a skill legendary can allow you to level up more/faster but is there any other reason, it seems like that just takes away valuable skills. Am I wrong?
I recently got my Blacksmithing skill to 100. Now in the skills menu I can press space to make it Legendary, which will put it back to a skill level of 15 and reset my perks.  I am wondering: What benefit is there from making a skill Legendary apart from being able to level up the skill more thus having infinite levels?
Why is it so difficult to find the twitter account for a Stack Exchange site? I am not able to find a link to the twitter account of Academia SE (), for example, in the Academia SE main webpage.   Why are twitter links not included on the main site page of each Q&amp;A site in SE? Should it be /about_us or /about-us?  From usability point of view, I personally think /about-us is much better for end-user yet Google and most other websites (and javascript frameworks) use underscore naming pattern. Is it just matter of style? Are there any compatibility issues with dashes? Properly discontinuous action: equivalent definitions Let us define a properly discontinuous action of a group $G$ on a topological space $X$ as an action such that every $x \in X$ has a neighborhood $U$ such that $gU \cap U \neq \emptyset$ implies $g = e$. I would like to prove that this property is equivalent to, having given $G$ the discrete topology and in the $X$ locally compact Hausdorff case, the map $G \times X \rightarrow X \times X$ given by $(g, x) \mapsto (x, gx)$ being proper (i.e. closed and preimage of compact sets is compact) plus the action being free.  I have managed to prove one direction, that is, if the action is proper and free with $G$ having the discrete topology then it is properly discontinuous. I'm having trouble though with the other direction. Here is an attempt: let's denote by $\rho : G \times X \rightarrow X \times X$ the map $\rho(g, x) = (x, gx)$. Suppose $K \subset X \times X$ is compact. We wish to show $\rho^{-1}(K)$ is compact. Let $(g_i, x_i)$ be a net in $\rho^{-1}(K)$. Then $\rho(g_i, x_i) = (x_i, g_i x_i)$ admits a convergent subnet, so passing to it we may assume $x_i \rightarrow x$ and $g_i x_i \rightarrow y$. Essentially we must now find a way to prove $g_i$ converges, but I can't seem to do this. Any hints? What is the difference between "INNER JOIN" and "OUTER JOIN"? How do you concatenate characters in java? Concatenating strings would only require a + between the strings, but concatenating chars using + will change the value of the char into ascii and hence giving a numerical output. I want to do System.out.println(char1+char2+char3... and create a String word like this.  I could do   System.out.print(char1); System.out.print(char2); System.out.print(char3);   But, this will only get me the characters in 1 line. I need it as a string. Any help would be appreciated.  Thanks Bootstrap 3 - Why is row class is wider than its container? From axiom of regularity, how can I prove $x \notin y \lor y \notin x$ Our high-school teacher told us that the Earth pulls us with some force $F$ and we pull the Earth with the same force $F$. Within Newtonian physics this is true because of , but let’s consider . My mass is small; so I don’t warp space-time much. But Earth’s large mass warps space-time to a far greater extent.  So do I pull Earth with the same force it pulls me? If yes, how? Jump between open windows on multiple monitors in Task View on Windows 10 with keyboard I'm using two monitors with Windows 10 and I have a few windows open on each monitor. When I open the Task View (Win + Tab) I can only navigate between the main monitor's windows with keyboard (using arrow keys or the Tab key). I see the other display's windows on that display but can't figure out how to cycle through those windows with my keyboard.  Is there a way I can give focus to secondary monitor's windows in the Task View using keyboard?  To put it another way, how do I select the first item on the right monitor in the following screenshot using keyboard? How can I contribute to Ubuntu? I would like to know what kinds of contributions someone can make to Ubuntu. Such as Programmer, User, Proofreader, etc. Is there a clipboard changed or updated event that i can access through C#? Background image shows in front of 3D objects, not behind them. I've done a quick 3D track in blender and I'm trying to render my output, but the plate I used to track is showing up over my 3d objects.  I want to render the objects in the scene with an alpha channel and comp them over the plate I tracked. My renders however, are covered by the aforementioned plate.  Un-checking "Background Images" in the camera properties (only removes it from the viewport) isn't doing it for my render outputs.  Working on some production tests and am not really proficient with the software yet, my apologies in advance. This comes from a brain teaser but I'm not sure I can solve it:     You are in a rowing boat on a lake. A large heavy rock is also in the boat. You heave the rock overboard. It sinks to the bottom of the lake. What happens to the water level in the lake? Does it rise, fall or stay the same?   I'd say that the water level drops, because when you drop the stone in the lake, the water level rises according to the volume of the stone, BUT the water level decreases by a volume of water weighting the stone's weight, when you take it off the boat.  Is that correct? How to instruct Windows 8 NOT to perform a fast shutdown? I have enabled fast boot in my copy of Windows 8 but I would like to be able to specifically instruct Windows not to perform a "fast shutdown" whenever I want (without disabling fast boot altogether).  I need to be able to do this because I dual-boot Ubuntu and therefore can't mount an NTFS partition as read/write if Windows has performed a "fast shutdown". (Well okay, I can force the partition to be mounted read/write, but then I could run into data loss/corruption problems.) How can mixed content compromise an entire HTTPS session? Divisibility, LCM and GCD for fractions (rationals) how do i find lcm of two fractions?  For example:  $\frac{2}{3}$ and $\frac{5}{8}$ I am following the first volume of the course of theoretical physics by Landau. So, whatever I say below mainly talks regarding the first 2 chapters of Landau and the approach of deriving Newton's laws from Lagrangian principle supposing Hamilton's principle of extremum action. Please keep this view in mind while reading and answering my queries and kindly neglect the systems to which Action Principle is not applicable:  If we use homogeneity of space in Euler-Lagrange equations, we obtain a remarkable result i.e. the conservation of momentum for a closed system.  Now, this result, using the form of Lagrange for a closed system of particles, transforms into $ \Sigma F = 0 $ . Now, how from this can we conclude that the internal forces that particles exert come in equal and opposite pairs?  Is it because for 2 particles this comes out as $ F_{1} + F_{2} = 0 $ and we take the forces exerted by particles on one other to be independent of other particles (i.e. Superposition Principle) as an experimental fact?  I doubt it as whole of Newtonian Mechanics is derivable from Lagrangian Mechanics and supposed Symmetries. So, according to me, a fact like Newton's Third Law should be derivable from it without using an additional experimental fact.  I have an idea to prove it rigorously. Consider two particles $i$ and $j$. Let the force on $i$ by $j$ be $F_{ij}$ and on $j$ by $i$ be $k_{ij}F_{ij}$. Now the condition becomes $\Sigma (1+k_{ij})F_{ij}=0$ where the terms to be included and rejected in summation understood. As this must be true for any value of $F_{ij}$, we get $k_{ij}=-1$. I don't know if this argument or refinement of such an argument holds or not. I can see many questions arising in this argument and it's not very convincing to me.  I would like to hear from you people as to if it is an experimental result used or not? If not, then is the method given above right or wrong? If wrong, how can we prove it?  Addendum  My method of proof uses the fact of superposition of forces itself, so it is flawed. I have assumed that the coefficients $k_{ij}$ are constants and don't change in the influence of all other particles which is exactly what superposition principle says.  As the superposition of Forces can be derived by superposition of potential energies at a point in space and potential energy being more fundamental in Lagrangian Mechanics, I restate my question as follows:  Is the principle of superposition of potential energies by different sources at a point in space derivable from the inside of Lagrangian Mechanics or is it an experimental fact used in Lagrangian Mechanics?  I, now, doubt this to be derivable as the fundamental assumption about potential energy is only that it is a function of coordinates of particles and this function may or may not respect superposition. How to fix gaps between flooring planks in mid-1800s house? I live in a mid-1800s house, which I plan to sell this Spring. The original (I think) wood flooring has gaps between the planks, some pretty sizable (photos follow).  Is there any good fix for this? I've seen people use wood filler/epoxy, and it didn't seem to turn out well. Perhaps doing that and painting/dying it black might work better.  I've heard the "old" solution was to pack those spaces with rope, but I don't think that would look better than the status quo.  Any suggestions?  Photos, big gap:    Medium gap:    Small gap: Inequality: $x^2+y^2+xy\ge 0$ I want to prove that $x^2+y^2+xy\ge 0$ for all $x,y\in \mathbb{R}$.  My "proof":  Suppose wlog that $x\ge y$, so $x^2\cdot x\ge x^2\cdot y\ge y^2\cdot y=y^3$ (because $x^2\ge 0$ so we can multiply both sides by it without changing the inequality sign) giving $x^3\ge y^3$. Substracting we have $x^3-y^3\ge 0$ or $(x-y)(x^2+xy+y^2)\ge 0$. Since $x\ge y$ we can divide by $x-y$ to get $x^2+xy+y^2\ge 0$.  Is it right?  Thanks for your help! I want a green for "correct answer" and a red for "wrong answer". My current choice is rgb(144, 238, 144) for the green and rgb(250, 128, 114) for the red. (See wikilearner.net/wiki for the colours in action.)  I have been told that these colors are very close in contrast, making it difficult for a person with red-green color-blindness. What would be a better choice?