I wish to write a pure-text square root symbol, like √. The purpose is to write an instruction as it is displayed on a simple calculator, i.e. something like √(2+3). I am aware of $\sqrt{}$, but I don't want to use this because with an empty argument, the square root-sign is too low compared to the surrounding text. I could fix the position of the symbol using something like $\sqrt{\color{white}{|}}$ (provided I have xcolor loaded) but the result isn't beautiful.  Is there a command to produce the √-symbol (such as we have \$ for $)? Apparently \√ doesn't exist.  Detexify suggests   $\surd$, which is exactly a math-mode square root sign without argument. \textsurd (provided the package textcomp) comes close.   I wonder if there is an exact version of √, i.e. as one can use in other text-editors.
I know what my symbol or character looks like, but I don't know what the command is or which math alphabet it came from. How do I go about finding this out?
Suppose that $f(x)$ is continuous on $(0, \infty)$ such that for all $x > 0$,$f(x^2) = f(x)$. Prove that $f$ is a constant function. Suppose that $f(x)$ is continuous on $(0, +\infty)$ such that for all $x &gt; 0$,$f(x^2) = f(x)$. Prove that $f$ is a constant function. My attempt is to show that for any point $a \neq b$ , we have $f(a)=f(b)$. But I have no idea on how to get this. Anyone can help? I'm playing Minecraft on Xbox 360 and I can't find the . I have tried every trick I can think of, including the xray glitch, and recreating the world in Creative mode to dig out the entire stronghold and the surrounding areas. I have found nothing and I am totally lost on where it could be.  The seed is 1833758535681455132 Some common problems with displaying routes created from street data, such as bus routes, include:   Routes may overlap themselves, such as when a route takes the same road in opposite directions Routes may overlap other routes that take the same street. Routes are often overly detailed, or "noisy", owing to their derivation from street data. Indicating a route's direction unambiguously without overloading it with arrows can be a challenge.   What are some techniques for dealing with these issues in order to create a practical and usable route map, such as this ? Do you know of any such public transport maps that were produced by automatic techniques rather than manual illustration/digitization?  Specifically I am using ArcGIS 10, but solutions involving other software are welcome as well.  One technique I have had some success with for dealing with 1) is using ArcMap's  with a negative offset -- assuming the lines are oriented in the direction of travel, this will offset the lines such that the right and left-hand sides are distinct and oriented as you would expect (at least for  countries, for left-hand traffic countries one would use a positive offset). However the result tends to be a bit wonky around turns, interchanges and and U-turns, and is inflexible when dealing with multiple routes.  Another possibility that I am not very familiar with but which seems promising is  -- however, I have not had much luck in finding examples of using representations for transportation maps and whether it might fit the bill. Is it possible to learn a neural networks for a constant target? I saw a paper () where they learn L based on the following cost function: $$(D_1L(q(k-1), q(k)) + D_2L(q(k),q(k+1)))² = 0$$ Here $D$ is the derivative with respect to ith argument of L. This can be obtained via automatic differentiation and it is fully compatible with backpropagation. So the target is always zero independently of the input of L but how does the optimization method knows the real values of L for a given input? I mean as long as the cost function is satisfied with a zero value the model is learning but it can be learning wrong values for L. For instance, if the real value of $D_1L(q(k-1), q(k))$ is 10 then the real value of $D_2L(q(k),q(k+1))$ has to be -10. However the neural network may be learning wrong values for L as long as they are symmetric, for example -3 and 3. This is an ill posed problem due to the infinite possible solutions. Am I missing something or the method in that paper simply doesn't make any sense? Is it possible to learn a neural network in regression task with constant target? Edit: The goal is not to predict always that value. The goal is to learn L by predicting always zero (see the cost function). The question here is in order to learn L in such a way that it respects the cost function, there are infinite possible solutions, for instance if $D1L(q(k−1),q(k))$ = x then D2L(q(k),q(k+1))=-x and its sum gives 0 respecting the cost function. But as you can see x can assume any value as long as the cost function is respected, when in reality the goal is to learn a specific L. But the optimization doesn't know a priori value for L so I guess it should just assume a random value for x. In the paper they don't mention the ill posedness of the problem, either they solved it or not. I would like to know if what I'm thinking makes sense or if I'm just missing something. Finding the derivatives of sin(x) and cos(x) We all know that the following (hopefully):  $$\sin(x)=\sum^{\infty}_{n=0}(-1)^n \frac{x^{2n+1}}{(2n+1)!}\ , \ x\in \mathbb{R}$$  $$\cos(x)=\sum^{\infty}_{n=0}(-1)^n \frac{x^{2n}}{(2n)!}\ , \ x\in \mathbb{R}$$  But how do we find the derivates of $\sin(x)$ and $\cos(x)$ by using the definition of a derivative and the those definition above?  Like I should start by doing:  $$\lim_{h\to\infty}\frac{\sin(x+h)-\sin(x)}{h}$$  But after that no clue at all.  Help appreciated! Using a foreign driver's license in California when staying with a J-1 visa I'm planning to attend a Californian university as a visiting scholar (not paid by the university) on a J-1 visa, for a total of four weeks; a colleague of mine will do the same, but for 12 weeks. I've been told (personally, ie. no citable sources) that, if you're staying on a J-1, you're effectively a California resident for the time you're there, and, therefore, need a Californian driver's license.  I've read up on this and found  that states:     If you are a visitor in California over 18 and have a valid driver   license from your home state or country, you may drive in this state   without getting a California driver license as long as your home state   license remains valid.      If you become a California resident, you must get a California driver   license within 10 days. Residency is established by voting in a   California election, paying resident tuition, filing for a homeowner's   property tax exemption, or any other privilege or benefit not   ordinarily extended to nonresidents.   I'm not planning to vote in any elections, nor will I own a home there, but I'm not sure what would constitute "privileges or benefits not ordinarily extended to nonresidents".  Do we need to get driver's licenses in California, or can we use our foreign licenses? How about day trips to Arizona or Nevada?  Note: this seems to be related to , but my question is specifically about staying there on a J-1. I'm trying to amass a list of physics books with open-source licenses, like Creative Commons, GPL, etc. The books can be about a particular field in physics or about physics  in general.  What are some freely available great physics books on the Internet? edit: I'm aware that there are tons of freely available lecture notes online. Still, it'd be nice to be able to know the best available free resources around.  As a starter:         Table of contents sorted by field (in alphabetical order): Unable to change payment information to NONE in iOS Appstore Need advice on flavoring/sweetening my homebrew cider I've just finished my primary fermentation and have produced a cider that is coming in at 5.2%. I am about to bottle my cider and add some priming sugar to give it a bit of a fizz. I would like to try and flavor some of the ciders with a fruit coulis. am I correct in thinking that the natural sugar in the fruit should give the cider a natural fizz and I don't need to add any sugar? Also, I am a fan of a sweeter cider, I have been advise not to add more than a teaspoon of priming sugar, and to use a sugar substitute at the same stage if i wish to sweeten it. I have purchased Xylitol, I plan on trying a few combinations with the priming sugar/Xylitol &amp; no additive fruit coulis. Does this all sound like it makes sense or am I just going to ruin my cider. Is there a way I can share the 3.42 GB download of Windows 8.1 from Windows Store? \bar vs. \overline - when to use what, semantically? Following the question "" which is simply about the lengths of both, I'd like to know when to use \bar and when to use \overline from a semantically viewpoint.  I always used \bar, because up until now I only had single letter mean values to type. But now I came to a problem where I needed a wider "bar".  Then I just tried  \documentclass{article}  \begin{document}   \[ \bar{a} \overline{a} \]   \[ \bar{abc} \overline{abc} \] \end{document}   where one can see that they also differ in position (\overline is lower), and also in thickness (\overline is thicker).  So, the question here is:  What does \bar represent semantically? And when to choose it over \overline and vice versa? What does this notation mean? $f(x) \equiv A$? If $\lim_{x\rightarrow\infty}f(x) = A$, prove that $f(x)\equiv A$.  Any help would be appreciated! I just don't even understand the question. Proving a function is Lipschitz continuous Show that the following function is Lipschitz continuous and find a Lipschitz constant  $$y\mapsto f(x,y)\\ f(x,y)=\frac{y}{x}\ln(\frac{y}{x})\text{  , } |x-1|\leq\frac{1}{2}\text{  , } |y-e|\leq\frac{e}{2} $$  I have no clue on where to begin to prove this.   My first question is how I should interpret this function, is $x$ a sort of constant? Unbiased estimator for geometric distribution parameter p What are the meaning and possible origin of "word!" and "word up"? I would like to parse a string such as p1=6&amp;p2=7&amp;p3=8 into a NameValueCollection.  What is the most elegant way of doing this when you don't have access to the Page.Request object? If there are injective homomorphisms between two groups in both directions, are they isomorphic? If I have two groups, $G$ and $H$ and two injective homomorphisms $\phi:G \to H$ and $\psi: H \to G$, then by the first isomorphism theorem applied to $\phi$, we have that $G \cong \mathrm{Im} (\phi)$, a subgroup of $H$. Similarly, $H$ is isomorphic to a subgroup of $G$. For finite groups, this guarantees that $G \cong H$ but does this hold for infinite groups?  Weird things can happen for infinite groups, e.g $n\mathbb Z \subsetneq \mathbb Z$ but $n \mathbb Z \cong \mathbb Z$. I'm wondering if this kind of thing stops an isomorphism from occurring.  I think this question generalises to rings, modules, fields and so on. Can this be answered for all of these structures? Why can't a single photon produce an electron-positron pair? In reading through old course material, I found the assignment (my translation):     Show that a single photon cannot produce an electron-positron pair, but needs additional matter or light quanta.   My idea was to calculate the wavelength required to contain the required energy ($1.02$ MeV), which turned out to be $1.2\times 10^{-3}$ nm, but I don't know about any minimum wavelength of electromagnetic waves. I can't motivate it with the conservation laws for momentum or energy either.  How to solve this task? I was wondering how to add plugins to my Minecraft server. I am using Bukkit, and the things I would like to be able to do is spawn stuff, teleport to other players, set home locations, have an in-game currency/shop and be able to teleport to homes. Expected Value of Local Maxima and Local Minima Recently I came across this question:  Given a random permutation of integers 1, 2, 3, …, n with a discrete, uniform distribution, find the expected number of local maxima. (A number is a local maxima if it is greater than the number before and after it.) For example, if n=4 and our permutation was 1, 4, 2, 3, then the # of local maxima would be 2 (both 4 and 3 are maxima). I know the answer will be (n+1)/3 .I wanted to know what will be the answer when we have to consider the local maxima as well as the local minima i.e Finding out the expected number of local maxima and local minima.