Dumbledore explains to Harry in Order of the Phoenix that he is protected so long as he returns once a year to the Dursleys’ home:     While you can still call home the place where your mother's blood dwells, there you cannot be touched or harmed by Voldemort. He shed her blood, but it lives on in you and her sister. Her blood became your refuge. You need return there only once a year, but as long as you can still call it home, there he cannot hurt you.   If Voldemort, or one of his Death Eaters, had killed the Dursleys (perhaps while Harry was away from Hogwarts), then Privet Drive would not be “the place where your mother’s blood dwells”. There are no other relatives of his mother that he could stay with, which would mean that nowhere else would qualify for that magic.   Wouldn’t that mean that the following year, Harry would have nowhere to go and the protection would not renew, thus he would be vulnerable to Voldemort?
Voldemort couldn't kill Harry as long as he called the Dursleys home. Why didn't he just murder the Dursleys? This would prevent Harry from being able to live there.
Some icons are correct, and some are whack. Turns out it's not just the hot questions list, but the whole icon set. Linux network troubleshooting and debugging From time to time Linux and Unix users faced with various network problems. Many of these problems are presented here and at some others troubleshooting forums, but they are very concrete and contains a lot of additional technical information, and sometimes it's rather difficult to understand the main point and the real reason of buggy system behavior.   By asking this question, my intention is to start a community wiki page which allows generalizing our network troubleshooting and debugging experience. I hope the Linux and Unix users could easier recognize and solve("divide and conquer") their network problems using this page.   The parent of this page should be  . But here we should focus on troubleshooting the network problems from user- and kernel-space.  I suppose, if you:    Share the information about using some great network diagnostic tool with concrete usage examples and examples of network bugs, which they help to catch. Share the link to the great network tutorial connected with this subject Tell about a general method or recipe which allows to tackle some class of network problems Share information about your tool-set for network debugging and troubleshooting   it would perfectly fits for this topic.    I'll begin from sharing the link to varios  and . Also  seem to have actual information about our subject. And for diving into linux networking we definetely need to visit . Homotopy equivalence of universal cover As part of am exam question (Q21F ), I'm trying to prove that if $X$ and $Y$ are path-connected, locally path-connected spaces with universal covers $\widetilde{X}$ and $\widetilde{Y}$, respectively, then if $X \simeq Y$ then $\widetilde{X} \simeq \widetilde{Y}$.  My attempt might be correct, but it seems too complicated and amongst the jumble I may have made some incorrect assumptions. So what I'm looking for is (a) verification or correction; and (b) ideas as to how I could simplify my argument.    My argument:  Let $p:\widetilde{X} \to X$ and $q:\widetilde{Y} \to Y$ be the covering maps, and let $X \overset{f}{\underset{g}{\leftrightarrows}} Y$ be a homotopy equivalence.  Fix a point $\widetilde{x} \in \widetilde{X}$, let $x=p(x) \in X$ and $y=f(x) \in Y$, and fix $\widetilde{y} \in q^{-1}(\{y\}) \subseteq \widetilde{Y}$. Also let $x' = g(y) \in X$ and fix $\widetilde{x'} \in p^{-1}(\{x'\}) \subseteq \widetilde{X}$.  Define a map $\widetilde{f} : \widetilde{X} \to \widetilde{Y}$ as follows. For $\widetilde{z} \in \widetilde{X}$ let $\widetilde{u}:[0,1] \to \widetilde{X}$ be a path from $\widetilde{x}$ to $\widetilde{z}$. Let $z=p(z)$ so that $u=p\widetilde{u}$ is a path in $X$ from $x$ to $z$. Let $v=fu$, so that $v$ is a path in $Y$ from $y$ to $f(z)$. Lift $v$ to a path $\widetilde{v}$ in $\widetilde{Y}$ with $\widetilde{v}(0) = \widetilde{y}$. Define $\widetilde{f}(\widetilde{z}) = \widetilde{v}(1)$.  Notice that $q\widetilde{v}=v$ so that $q\widetilde{f} = fp$.  Define $\widetilde{g}:Y \to X$ analogously: For $\widetilde{z} \in \widetilde{Y}$ let $\widetilde{a}:[0,1] \to \widetilde{Y}$ be a path from $\widetilde{y}$ to $\widetilde{z}$. Let $z=q(z)$ so that $a=q\widetilde{a}$ is a path in $Y$ from $y$ to $z$. Let $b=fa$, so that $b$ is a path in $X$ from $x'$ to $g(z)$. Lift $b$ to a path $\widetilde{b}$ in $\widetilde{X}$ with $\widetilde{b}(0) = \widetilde{x'}$. Define $\widetilde{g}(\widetilde{z}) = \widetilde{b}(1)$.  Likewise, notice that $p\widetilde{g}=gq$.  Claim: $\widetilde{X} \overset{\widetilde{f}}{\underset{\widetilde{g}}{\leftrightarrows}} \widetilde{Y}$ is a homotopy equivalence.  We have $p\widetilde{g}\widetilde{f} = gq\widetilde{f}=gfp \simeq p$ and $q\widetilde{f}\widetilde{g} = fp\widetilde{g} = fgq \simeq q$.  This shows that $\widetilde{g}\widetilde{f}$ and $\widetilde{f}\widetilde{g}$ are covering translations (deck transformations) and are therefore homotopic to the respective identity maps. So we have a homotopy equivalence.    Any comments would be appreciated. I'd like to write an N-body simulation in which I collide two disk galaxies. To give you an idea of the accuracy I'm trying to achieve, I'm aiming to make this my screensaver at 30fps on my work desktop. Think Euler's method, large epsilons in denominators to prevent blow up, all that lazy stuff.   One place I don't want to be lazy, however, is in the initial construction of the galaxies I'm trying to collide. I want to design a galaxy that will at least sort of hold together by its own gravity until it smash it into another one.   How might I go about selecting the orbital velocities for each of the bodies composing the galaxy? Fixing geometry validity errors in QGIS 2? Call native javascript function that has been "erased" by the web page Mathematician learning theoretical physics I need to save/compile a few times and a bunch of weird files (like foo.tex.Ak6664) appear in my Dropbox folder each time I need to compile between two and four times before I see changes I make in the editor (TeXstudio) and each time I compile, a new .tex file is created with random letters and numbers at the end.   For example, If I create the file hello.tex and compile two to four times I'll get the file,   hello.tex.QU6664      then I make some small changes in the editor and compile two to four times I'll get the additional file,   hello.tex.Ak6664   After continuing to do this (each time compiling between two to four times before I see the changes I made), I now have many files that look like  hello.tex.QU6664, hello.tex.Ak6664, hello.tex.YX6664, hello.tex.sN6664, hello.tex.Ss6664, ...   A little bit of additional information (in case it's relevant): Everything was working fine up until a few days ago, i.e. only needed to compile once and only the file hello.tex was created. I still only get one .aux,  .synctex and .pdf files. I use TeXstudio to write and compile. I don't think it has anything to do with the bibliography (I tried removing bibliography altogether and still having the same problem).  How do I prevent these additional files from appearing and only compiling once like I used to? Has anyone had a similar problem? I know we can use both Present Simple and Present Continuous to describe future actions. But I don't know when to use the correct form.   For example:  We fly to Paris next week.  We are flying to Paris next week.   These sentences both seem correct to me.  Can anyone explain me how to correctly use these tenses? Finitely generated monoids- axiomatization- compactness theorem. If every element of set A ia an element of set B then we say that A is subset of B. A is said to be proper subset if A does not equal B.  My question is - whether the symbol we use to show subset is  same as that for proper subset? I have seen that A is subset of A itself is shown by the same symbol as that for the subset while when we write improper subset, we usually write equal to sign with symbol of subset. So, please help me to know this. Matlab arrays operation Evaluation of OptionValue[] C# List Sort by x then y Similar to , we want to sort by one element, then another.  we want to achieve the functional equivalent of   SELECT * from Table ORDER BY x, y     We have a class that contains a number of sorting functions, and we have no issues sorting by one element. For example:    public class MyClass {     public int x;     public int y; }    List&lt;MyClass&gt; MyList;  public void SortList() {     MyList.Sort( MySortingFunction ); }   And we have the following in the list:    Unsorted     Sorted(x)     Desired ---------    ---------    --------- ID   x  y    ID   x  y    ID   x  y [0]  0  1    [2]  0  2    [0]  0  1 [1]  1  1    [0]  0  1    [2]  0  2 [2]  0  2    [1]  1  1    [1]  1  1 [3]  1  2    [3]  1  2    [3]  1  2   Stable sort would be preferable, but not required. Solution that works for .Net 2.0 is welcome. Intuitive Explanation of Tippe Top Effect? This is a canonical question that will hopefully encompass all of the questions we get asking us to determine what year a bicycle was manufactured (how old is my bike, how old is my frame, etc.). Each "answer" should address a different way to determine the manufacturing year of a bicycle. To some extent, these will also help you narrow down the model as well as it will tell you what distinguishing features to look at.  The span of answers would include things such as:      Skiptooth cranks Cartridge bottom brackets (BB30/90 etc) Elliptical chainring Quick releases versus contemporary through-axles How the steerer attaches to the fork (quill vs. threadless)  Braking system (especially with mountain bikes: v-brake, direct pull, etc.)   Shifting ramps and pins on cassettes/sprockets and chainrings (versus flat sprockets) Frame material (e.g., shift from tubular steel to use of CF and hydroformed aluminium)  Frame tubing type (e.g. Reynolds 531 tubing introduced around 1934, still used today; Reynolds 501 tubing introduced around 1983). So a frame with an original 501 decal can't be from the 70', 531 decal doesn't help as much because of the range of years produced. Also, see Decals.   *Decals: style/design, amount, placement, color, etc. can help not only determine models, but also year of manufacture. Many changed decal design for the same model bike often yearly, with special/limited editions even more specific. This applies only if decals are original or have been replaced with the identical design. Tubing decals (Reynolds, Columbus, etc.) also changed designs for same tubing made in different years, although the changes aren't made as often, and manufacturers didn't always put tubing Brand decals on every model. Earlier bikes tended to have less fancy, less colorful, less quantity of decals.   Headbadges: most early bikes had actual "badges", often quite detailed and fancy, made of metal, then plastic, and finally just using decals on the headtube. Most bikes lost their metal badges in the 60's and early 70's, although some brands still have actual badges to this day, but in general a real badge indicates an earlier model bike. Dropout style (including the later inclusion of lawyers lips) Presence or absence of CPSC reflectors (USA only) Manufacturing method (shift from lugs to TIG welding, for example)  Number of gears (shift from 2x5 ten-speed to 3x8, 2x9, 1x11, etc.)  Inspection of lug design: pantographs, cut-out, stampings, custom brazing/filing, chrome, fork crow n sweep, etc. Frame/Fork Braze-ons. Race bikes tended have less braze-ons the earlier the year of manufacture. Most 60's racers and earlier had few or none with cable guides/stops, shifters, bidons, etc. being clamp-on. By the 80's if it was clamp-on, it was a sign of very cheap models and most frames had braze-ons for all cables, with multiple bottle and accessory bosses depending on style and use.   and so forth. Please edit this question if you have an answer that isn't in the index above.   A couple of caveats:   A previous owner could have replaced or upgraded components on a bicycle, so this guide only applies to original equipment There is a delay between the introduction of a technology (such as indexed shifting) and when manufacturers start selling products that use it. Low-end manufacturers may continue using technology that is severely outdated (such as one-piece cranks, freewheels, or quill stems) because it is cheaper to do so. A number of bikes are built in a Retro style, but with modern components.  Dutch bikes, trendy coffee cruisers, and beach cruisers may be modern but appear to be 1950s styling.  These tend to have modern rims and brakes as a giveaway.     Note that bicycles.stackexchange does not do valuations of bicycles. How much your bicycle is worth depends on the location of the buyer and seller, how much the buyer wants the bike, etc. etc. etc. Merging two files, one column at a time I am a software engineer but try to keep up with maths as I really enjoyed the subject at school. I just saw a great TED talk:   The talk states that the current largest known prime is $2^{57885161}-1$  This got me thinking - how does one actually prove whether a number this large is prime or not?  Is it just done by brute force via a computer algorithm or are there any well known mathematical techniques for doing so?  I would be really grateful for any pointers as I am eager to learn about these techniques (if they exist). Assuming $f:\mathbb R\to\mathbb R $ be an uniform continuous function, how to prove $$\exists a,b\in \mathbb R^+ \quad \text{such that}\quad |f(x)|\le a|x|+b.$$ Past Subjunctive vs Future Subjunctive form