$(X,d)$ is  a compact metric space  and  $$f\ :\ X\rightarrow X $$  be  such  that $$d(x,y)=d(f(x),f(y))$$ Show that  $f$  is  onto .  I  have  to  show  that for  any  $y\in X$  there  exist $x\in X$  such that  $$f(x)=y.$$ How  to  begin$?$
Possible Duplicate:          Let $X$ be a compact metric space and $f$ be an isometric map from $X$ to $X$. Prove $f$ is a surjective map.
A few months ago I was introduced to the new  type and was glad 's flaws with regard to time zones were finally taken care of.  However, I was left wondering if there were any overhead or problems that could occur from using this new type.  I work on a multi-locale web application. Does anyone know of anything that could sway me from just using it for all my date/time work? Is there a window for abuse here?  Reference: What is the difference between the dashed and solid attack bars? I was flipping through my Pokemon list to see which kind of attacks they had, and I notice there was a small different between the attacks. Some attacks contained a dashed blue bar where as others contained a solid blue bar.   What is the difference and significance between the two? This is a followup to my question  . StrongBad, in a comment replying to one of my comments, suggested that I go ahead and ask something along these lines. This question is directed at those who have experienced unwelcoming behavior. I'm so confused over the nature of the unwelcoming behavior that others have alluded to. If I can't figure out what is happening because it gets deleted quickly, there's little I can do to work toward preventing future occurrences. What, specifically, can individuals in the community do to support those who have experienced gender bias? I'm asking you -- those of you who have experienced bias related to being LGBTQ or some other sort of gender bias. What do you want or need us to do so that you feel welcomed?  Are you looking primarily for greater awareness of the issues you commonly face? That is, there is nothing really that specific for us to do except to attend sensitivity training, show greater empathy, etc. Do you want us to be more vigilant in voting down and flagging unwelcoming content so that it gets deleted quicker? Are there a few specific users that you want to be &quot;taught a lesson&quot;, and the rest of us are caught up in the crossfire? Do you want us to proactively ask you for your pronouns or other biographical or identity details before we engage with you? (I apologize for accidentally misgendering Aza in my previous question, but there's nothing on her profile to indicate her gender or that she wants people to be particularly sensitive in this regard towards her. Perhaps I could have sent her a note &quot;Hey Aza, I'm going to reference you in an upcoming post, what are your pronouns?&quot;, but that seems so awkward.) Do you want help with lobbying Stack Exchange into making changes to the existing system such as adding support for adding pronouns, sexual orientation, etc. to user profiles? In what format does piped output get sent and received from one command/program to another? Alignment issue in 'Your Sites' section in the Android app Unexpected behavior of rule matching a pattern Its a .vbproj and looks like this  &lt;Project DefaultTargets="Build" xmlns="http://schemas.microsoft.com/developer/msbuild/2003"&gt;     &lt;PropertyGroup&gt;         &lt;ProjectGuid&gt;15a7ee82-9020-4fda-a7fb-85a61664692d&lt;/ProjectGuid&gt;   all i want to get is the ProjectGuid but it does not work when a namespace is there...   Dim xmlDoc As New XmlDocument()  Dim filePath As String = Path.Combine(mDirectory, name + "\" + name + ".vbproj")  xmlDoc.Load(filePath)  Dim value As Object = xmlDoc.SelectNodes("/Project/PropertyGroup/ProjectGuid")   what can i do to fix this? I love admin-ajax.php. But I hate having to localize in order to point frontend scripts to it, and I wish there was an equivalent, easy-to-find file for themes. (It also just bothers me to see frontend requests go through "/wp-admin/". No practical reason, just looks ugly IMO.)  So I've simply copied admin-ajax.php to the root dir at "/ajax.php", adjusted the include paths and removed the WP_ADMIN constant definition. Seems to work like gangbusters (I can now just direct all my frontend AJAX requests to /ajax.php! And I can still use the normal wp_ajax hooks in my plugins!).  But is this safe? What might go wrong? Since this isn't built into core, I assume there's a good reason as to why not. But looking through the code, I can't see any immediate problems.   You're smart--tell me if this approach is crazy. Or if there's a simpler method that I'm overlooking. How do get my sitelinks to appear on Google search results? Predicting the number of decimal digits needed to express a rational number The number $1/6$ can be expressed with only two digits (and a repeat sign denoted as $^\overline{}$), $$ \frac{1}{6} = \,.1\overline{6}$$  Meanwhile, it takes 49 digits to express the number $1/221$, since a string of 49 digits repeats: $$\frac{1}{221} = .\overline{004524886877828054298642533936651583710407239819}$$ Yet for $1/223$, 222 digits repeat, giving a total of 224 digits needed to express the number.  If $f:\mathbb{Q}\rightarrow\mathbb{N}$ is a function that gives the smallest number of digits needed to express a rational number in decimal notation, what can we say about $f$?  For example, if we do not consider the negative sign to be a digit, then $f$ is an odd function.  Other than that, is there any pattern to it at all? Can I insert elements to the beginning of an element using .appendChild()? If the user selects an option in a dropdown box, there must be added a label and a textbox. Using appendChild, these elements get added to the end of the container.  var newFreeformLabel = document.createElement('label'); newFreeformLabel.innerHTML = 'Omschrijving:';  var newFreeformField = document.createElement('input'); newFreeformField.className = 'textfield'; newFreeformField.name = 'factuur_orderregel[]';  var newFreeformSpacer = document.createElement('div'); newFreeformSpacer.className = 'spacer';  container.appendChild(newFreeformLabel); container.appendChild(newFreeformField); container.appendChild(newFreeformSpacer);   The issue is that these elements should be inserted at the beginning of container, not at the end.  Is there a solution to this in PrototypeJS? The identification of an electron as a particle and the positron as an antiparticle is a matter of convention. We see lots of electrons around us so they become the normal particle and the rare and unusual positrons become the .  My question is, when you have made the choice of the electron and positron as particle and anti-particle does this automatically identify every other particle (every other fermion?) as normal or anti?  For example the proton is a particle, or rather the quarks inside are. By considering the interactions of an electron with a quark inside a proton can we find something, e.g. a conserved quantity, that naturally identifies that quark as a particle rather than an antiparticle? Or do we also just have to extend our convention so say that a proton is a particle rather than an antiparticle? To complete the family I guess the same question would apply to the neutrinos. Batch normalize audio volume on .ogg-files Are there any simple tools to normalize an .ogg-library of 10'000+ songs so that the volume is the same throughout all songs?  Terminal or GUI doesn't matter, it only need to be simple.  One caveat though, I don't want soft interludes/intermissions and ballads blown out of proportion.  Preferably the process should find the overall gain of the album (I have all my CD's ripped into separate folders) and normalize the level thereafter. I'd like to estimate the correlation between:  An ordinal variable: subjects are asked to rate their preference for 6 types of fruit on a 1-5 scale (ranging from very disgusting to very tasty) On average subjects use only 3 points of the scale.  A continuous variable: the same subjects are asked to quickly identify these fruits, which results in an mean accuracy for the 6 fruits.   Is Spearman rho the best method to analyze these data and/or are there other good methods I could consider? How to install Chrome browser properly via command line? I am trying to install chrome browser via command line.  I tried this:  $ apt-cache search chrome browser   The results show that the proper term is "chrome-browser," so I tried that:  $ sudo apt-get install chrome-browser   And then "Y" for the Y/n question.  But the installation threw errors.  Does someone see anything wrong with the commands I issued? Ierator and for-each loop both we use for traverse no of items, I have used for-each many times but I am not clear about iterator, means when we should use ierator. I am studying salesforce workbook example..  global class CustomIterable implements iterator&lt;Account&gt;{    public List&lt;Account&gt; accs {get; set;}   public Integer i {get; set;}    public CustomIterable(){      accs =[SELECT Name fROM Account limit 5];      i = 0;              }   global boolean hasNext(){          if(i &gt;= accs.size()) {          return false;         } else {          return true;         }    }    global Account next(){          if(i == 8){return null;}          i++;          return accs[i-1];     } }   //------------  @isTest(seealldata=true) global class IteratorClass{     public static testmethod void main(){          IteratorClass obj = new IteratorClass();         Iterator&lt;Account&gt; acs =  obj.Iterator();         system.debug(acs);      }     global Iterator&lt;Account&gt; Iterator(){             return new CustomIterable();          }  } Derive a formula to find the number of trailing zeroes in $n!$ Possible Duplicate:          I know that I have to find the number of factors of $5$'s, $25$'s, $125$'s etc. in order to do this. But how can you derive such a formula for any number $n$? How do I remove code duplication between similar const and non-const member functions? Let's say I have the following class X where I want to return access to an internal member:  class Z {     // details };  class X {     std::vector&lt;Z&gt; vecZ;  public:     Z&amp; Z(size_t index)     {         // massive amounts of code for validating index          Z&amp; ret = vecZ[index];          // even more code for determining that the Z instance         // at index is *exactly* the right sort of Z (a process         // which involves calculating leap years in which         // religious holidays fall on Tuesdays for         // the next thousand years or so)          return ret;     }     const Z&amp; Z(size_t index) const     {         // identical to non-const X::Z(), except printed in         // a lighter shade of gray since         // we're running low on toner by this point     } };   The two member functions X::Z() and X::Z() const have identical code inside the braces.  This is duplicate code and can cause maintenance problems for long functions with complex logic.    Is there a way to avoid this code duplication? Why is the mol a fundamental physical quantity? I am starting to study physics in detail and as I read about physical quantities, I was puzzled why mol (amount of substance) is taken as a physical quantity.  A physical quantity is any quantity which we can measure and has a unit associated with it. But a mol represents the amount of substance by telling the number of particles (atoms, molecules, ions, etc.) present. So it is a pure number and numbers are dimensionless. So mol should not be considered a physical quantity.  Also, fundamental physical quantities should be independent of each other. I am wondering whether mass and mol are independent. This is so as they surely affect each other as we can evidently see while calculating the number of moles and using the mass of that sample for calculation.  So how is the mol a fundamental physical quantity and independent of mass? There's something wrong with the vertical alignment on the :   (click to enlarge)  On the , which uses a similar list but without the Favorite column, the vertical alignment is correct.  (Tested in the latest Firefox, Safari and Chrome on macOS Catalina.)