Let $f$ and $g$ be functions, and suppose $f$ and $g$ are continuous (in particular, this means $D(f)=\mathbb{R}\; D(g)=\mathbb {R}$). Suppose that for every rational number $x\in\mathbb{Q}$, we have $f(x)=g(x).$ Prove that $f(x)=g(x)$ for ${every}$ number $x\in\mathbb{R}$.  Any suggestions on how I am supposed to even begin to approach this problem would help.
Suppose $f,g$: $\Bbb R$ → $\Bbb R$ are continuous functions such that $f(r) = g(r)$ for all $r$ in $\Bbb Q$. That is to say, $f$ and $g$ are equal on the rational numbers.   Prove that  $f(x) = g(x)$  for all $x$ in $\Bbb R$
Are there any rules for adjudicating a ranged attack fired at a target engaged in melee combat with an ally? While running a session recently, one of the players chose to "assist" his companion who was in melee with a goblin, by firing an arrow at the pair of them. I couldn't find any particular rules for this scenario so just had him roll at a disadvantage, counting a miss as a hit on his companion (damage to be ascertained by a second roll).   This seemed to work okay, and became a running joke for the night as the arrow bounced off the companions back, but are there specific rules for this scenario? What's the best way to protect your house from Endermen stealing your walls? How to influence the position of float environments like figure and table in LaTeX? How to influence the position of float environments like figure and table in LaTeX?   This is a general question and should collect useful answers for all users. I hope we can use this as a reference The only thing I need is an exact copy of an existing shapefile in the same directory with a different name.  I have tried:   arcpy.CopyFeatures_management (ORLinks, MyLinks) #ORLinks: old links, MyLinks: new links   but for some reason, I cant make it a feature layer using:  arcpy.MakeFeatureLayer_management(MyLinks, 'MyLinks')   Error Encountered:  Error: Failed to execute. Parameters are not valid. ERROR 000732: Input Features: Dataset  M:\RAIL\Rail2.0.shp does not exist or is not supported Failed to execute (MakeFeatureLayer). HTML text input allow only numeric input Is there a quick way to set an HTML text input (&lt;input type=text /&gt;) to only allow numeric keystrokes (plus '.')? I want to put some symbols in green color with lstdefinelanguage in latex, but it seems that symbols are not recognized.  The symbols I need to be colored are =, > and &lt;. Is it possible? How can I do this?  The main file:  \documentclass{article}   \usepackage{graphicx,color} \usepackage{booktabs} \usepackage{listings}   \lstdefinelanguage{NeoIDL}{   sensitive = true,   keywords = [1]{module, resource, enum, annotation, for, import, entity, path,   @get, @post, @put, @delete, require, ensure, otherwise, call},   %ndkeywords={int, \char{}  },   %ndkeywordstyle=\color{blue}\bfseries,   morekeywords=[2]{&gt;, &lt;, ==},   keywordstyle=[2]\color{green},   numbers=left,   numberstyle=\scriptsize,   stepnumber=1,   numbersep=8pt,   showstringspaces=false,   breaklines=true,   frame=top,   comment=[l]{//},   morecomment=[s]{/*}{*/},   commentstyle=\color{purple}\ttfamily,   stringstyle=\color{red}\ttfamily,   morestring=[b]',   morestring=[b]"   }  \begin{document}  \begin{figure}[htb] \begin{small} \lstinputlisting[language=NeoIDL,firstnumber=1]{store_pos_servico.neo} \end{small} \caption{Service 1} \end{figure}   \end{document}   The file to be formatted:  module store {    (...)     resource order  {      path = "/order/{id}";       @post   int postOrder (Order order)     require (call store.getOrder(id) == "NotFound"),     otherwise "InvalidPrecondition"    }; } Disable ClearType (blurry fonts) in Internet Explorer 10 on windows 7 I've installed recently the latest Internet Explorer 10 and found out again what was my issue with the previous upgrade -- blurry fonts aka ClearType! Unfortunately there are some apps that use IE engine and thus all content there is blurry too :/  I know about  but unfortunately it seems that it is only for IE9. Is there any other solution to disable CT in IE10?  (and for clarity - I don't like CT, I've tried tweaking it but for me it's just blurry and case pain in my eyes no matter what I do... it's probably related to the low dpi of my monitor) How to find normal and lognormal moments, given partial information? $Y=\ln(X)$. $X$ is lognormal and $Y$ is normal. If all I know is the arithmetic mean of $Y$ and the standard deviation of $X$. What is the formula to calculate the arithmetic mean of $X$ and the standard deviation of $Y$? Find out which process is locking a file or folder in Windows Why can't an electric field line suddenly break? My book has the following question in it as an exercise:  An electrostatic field line is a continuous curve i.e. a field line cannot have sudden breaks. Why not?  I cannot seem to be able to reason for or against this statement.  Can somebody please tell me why they can't suddenly break and if that were to happen then what will be its outcome? Script access to tangent and bitangent, per face: how? Suppose you have a mesh; you go into Edit mode,  set Transform Orientation to Normal,  show 3D manipulator widget, Pivot Point = Active Element, face select mode, and then you select any one face: immediately you will see a blue arrow representing the face normal, and also a red and a green arrow representing the face's tangent and bitangent.  What is the most straightforward way to refer  to said tangent and bitangent vectors from a Python script? The API documentation confuses me with loops and uv's, yet, clearly, Blender assigns a tangent and bitangent to each face without hesitation! Prove $\binom{n}{a}\binom{n-a}{b-a} = \binom{n}{b}\binom{b}{a}$ I want to prove this equation, $$ \binom{n}{a}\binom{n-a}{b-a} = \binom{n}{b}\binom{b}{a} $$ I thought of proving this equation by prove that you are using different ways to count the same set of balls and get the same result. But I'm stuck. Help me please.   (Presumptive) Source: Theoretical Exercise 1.14(a), P19, A First Course in Pr, 8th Ed, by S Ross. Is there a way to access QGIS plugins in Python?   I'd like to write a script to do some geoprocessing, and I'd like to use the clip, regular points and convex hull tools in fTools, as well as the Road graph plugin. The latter is probably a different can of worms because it is a C++ rather than Python plugin. $(U\cap W)^0 = U^0 + W^0$ Let $V$ be a finite dimensional vector space and $U^0$ and $W^0$ denote the annihilators of subspaces $U$ and $W$, respectively.  Then I need to show that $(U\cap W)^0 = U^0 + W^0$.  I can show that $U^0 + W^0 \subseteq (U\cap W)^0$ like so: Let $f\in U^0$ and $g\in W^0$.  Then, because $U^0, W^0 \subseteq (U\cap W)^0$, we see that if $f\in U^0$ and $g\in W^0$, then for any $v\in U\cap W$ and $a,b \in \Bbb F$, $(af+bg)(v) = af(v) + bg(v) = 0$.  Thus $af+bg\in (U\cap W)^0$.  But because $f$ and $g$ were arbitrary, this implies that any linear combination of elements of $U^0$ and $W^0$ is an element of $(U\cap W)^0$.  I.e. $U^0+W^0 \subseteq (U\cap W)^0$.  But I haven't had any luck proving the other direction.  Obviously I should start with $f\in (U\cap W)^0$.  But then it looks like I need to somehow break that function into two to show its in $U^0 + W^0$.  That's throwing me off. Is there a safe way to run a diff on two zip compressed files? Seems this would not be a deterministic thing, or is there a way to do this reliably? Retrieving the last record in each group - MySQL Question Prove that for every integer k≥1, exists a self-complementary graph with 4k vertices half of which are of degree 2k-1 and the other half of degree 2k.  My approach So, I think the easiest way to prove what is asked is by induction. I can prove the base case for k=1, but as far as the inductive step is concerned, I cannot seem to reach a conclusion as to why if the statement holds for n, then it holds for n+1.  Any help would be appreciated. Is this statement true?      In a metric spase $(E,d)$, a sequence $(x_n)$ is Cauchy if and only if $  \forall k\in \mathbb{N}, \lim_{n\rightarrow+\infty}d(x_{n+k},x_n)=0$   I proved that $\Rightarrow$ is true,indeed if $(x_n)$ is Cauchy then for all $\varepsilon&gt;0,\exists n_0\in\mathbb{N}, \forall p,q\geq n, d(x_p,x_q)&lt;\varepsilon$ it still right for all $ n\geq n_0$ and $m=n+k&gt;n\geq n_0$   But I don't know if $\Leftarrow$ is true ? Is it OK to add [Solved] to the title of a question? I was confused when I saw this Question with [Solved] in its title where I couldn't find a solution: .  Then I found out that the "[Solved]" part was put there by someone else through editing like these:       I was feeling that this was not how it's supposed to be done and searched meta to find, that it is indeed discouraged to do so:        But on the other hand, the user who did the edits has a whole lot of reputation so I might me missing something here. So what's the correct thing to do? Should those edits be reverted? As of today, a  has been found affecting versions 1.0.1 through 1.0.1f (inclusive) and 1.0.2-beta.  Since Ubuntu 12.04, we are all vulnerable to this bug. In order to patch this vulnerability, affected users should update to OpenSSL 1.0.1g.  How can every affected user apply this update now?