is it possible to leave out the relative pronoun "where"?
When it's OK to omit "where?"
Infinite metric space has open set $U$ which is infinite and its complement is infinite Let $(X,d)$ be a metric space where $X$ is an infinite set. Prove that the space has an open set $U$ such that both $U$ and its complement are infinite sets.   I have considered if $d$ is the discrete metric, then one such $U$ exists. But if $d$ is not discrete, how do we find such $U$? Parsing an Int from a string in javascript In javascript, what is the best way to parse an INT from a string which starts with a letter (such as "test[123]")?  I need something that will work for the example below.  My JS:  $(document).ready(function() {      $(':input').change( function() {         id = parseInt($(this).attr("id"));  //fails for the data below         alert(id);     }); }   My generated HTML:  &lt;select id="attribute[123]"&gt; &lt;!-- various options --&gt; &lt;/select&gt; &lt;select id="attribute[456]"&gt; &lt;!-- various options --&gt; &lt;/select&gt;   Thank you! I have a shell script with this code:  var=`hg st -R "$path"` if [ -n "$var" ]; then     echo $var fi   But the conditional code always executes, because hg st always prints at least one newline character.   Is there a simple way to strip whitespace from $var (like trim() in )?   or   Is there a standard way of dealing with this issue?   I could use  or , but I'd like to think there is a more elegant solution to this problem. Finding the distribution of the sum of three independent uniform random variables What is the best way to handle a lot of misused tags? So today I noticed a question that had the  tag. As the question was not about JSFiddle, and only included a link to the site, I thought somebody has just created this for the sake of it. So I decided the best action would be to remove it, and try to stop it from getting out of control.  But then I searched (clicked the tag) for other questions that used it and I was amayonaised to see over 500 questions had the very same tag! Most of which were incorrectly tagged. So I cleaned up a couple and then quickly got bored.  So I am wondering, aside from going through them all by myself, is there a more efficient way?  I think it would be a great idea if there was some feature (probably an admin feature) that allowed a new tag queue to be added to the review list. I think this could work well as follows:   Somebody brings up the problematic tag in question (e.g. Me on here) An admin reviews my concern, and decides that the tag is very misused That admin adds the tag for review in a (temporary) new review queue. All users that can review can then go through existing tags, and vote for "No action" or "Remove tag" The world becomes a slightly better place   ...or not?    By the way, I tried to add some new tags to this post but I don't have the rep. So if someone could create them for me that would be swell: "musefan", "today", "sunny-spells", "pointless-tags" Will my Chinese visa still be valid if I renew my passport? Will my Chinese visa still be valid if I renew my passport? If so how does that work?  I have heard that you can travel with your new passport and just show the old passport with the valid visa when entering China. Has anyone done that? Recently?   I have also been told that you have to get a new visa, which seems somewhat logical but frustrating, especially when my Chinese visa is only a few months old.  My Chinese visa was issued in late Nov 2014 and I heard the rules changed between the US and China. My visa says it's good for 10 years and my US passport expires in 5. How to redirect output to a file and stdout In bash, calling foo would display any output from that command on the stdout.  Calling foo &gt; output would redirect any output from that command to the file specified (in this case 'output').  Is there a way to redirect output to a file and have it display on stdout? I am designing the layout for a touchscreen for outside use, What are some good color combination to use that will be visible under the sun light for outside use? Maybe bright neon colors? I am trying to identify the general case algorithm for counting the different ways dice can add to a given number.  For instance, there are  with two 6-dice.  I've spent quite a bit of time working on this (for a while my friend and I were using Figurate numbers, as the early items in the series match up) but at this point I'm tired and stumped, and would love some assistance.  So far we've got something to this effect (apologies for the feeble attempt at mathematical notation - I usually reside on StackOverflow):  count(x):    x = min(x,n*m-x+n)    if x = n       1    else       some sort of (recursive?) operation   The first line simplifies the problem to just the lower numbers - where the count is increasing.  Then, if we're looking for the count of the minimum possible (which is also now the max because of the previous line) there is only one way to do that so it is 1, no matter the n or m. I think that all the zeros of the Riemann-Zeta function ${\zeta}( z ) = \frac{1}{1-2^{1-z}} \sum_{n = 0}^{\infty} \frac{1}{2^{n+1}} \sum_{k = 0}^{n} (-1)^k \binom{n}{k} (k+1)^{-z}$  have real part smaller than 1, but I don't know how to prove it. If Re(z) > 1 than  ${\zeta}( z ) = \sum_{n = 1}^{\infty} \left( \frac{1}{n} \right)^z$ Capturing emoticons using regular expression in python The Crumple-Horned Snorkack is one of various weird and wacky things which Luna Lovegood believes in and most people (especially the ever-rational Hermione) don't. Now we know that Luna is a bit ... odd, and believes in a lot of nonsense; but on the other hand, Hermione's pooh-poohing isn't always to be believed either - Divination, for instance, is a real thing in the Potterverse.  Is it ever established for sure, in canon, in-universe, whether or not Crumple-Horned Snorkacks exist? $\mathbb Z[1/2]$ is not finitely generated ?   Maybe I misunderstood, what finitely generated means.  it says, we need finitely many elements and I think $1$ and $1/2$ suffices as generators.  But , at the end of Proposition $5.1.4$, from the fact that $\mathbb Z[1/2]$ is not finitely generated it is concluded that $1/2$ is not integral. How to write permutations as product of disjoint cycles and transpositions $$\sigma=\begin{pmatrix} 1 &amp; 2 &amp;3 &amp; 4&amp; 5&amp; 6&amp;7 &amp;8 &amp;9 &amp;10 &amp; 11 \\ 4&amp;2&amp;9&amp;10&amp;6&amp;5&amp;11&amp;7&amp;8&amp;1&amp;3    \end{pmatrix}$$  (1) I am asked to write this permutation in $S_{11}$ as a product of disjoint cycles and also as a product of transpositions.   (2) Also find the order of the element. Is this permutation even or odd?  I think these are the disjoint cycles  $E_{1}=(1,4,10)$, $\;\operatorname{order}E_1 =3$  $E_{2}= (3,9,8,7,11),\;$ $\operatorname{order}E_{2} =5$  $E_{3}=(5,6),\;$ $\operatorname{order}E_{3} =2$  $S_{11}$=  $E_{1} \cdot E_{2}\cdot  E_{3}$  The order of $\operatorname{order}E_{3}$ is even so the order of the permutation is even. Why are they asking this? And what is the significance of it being even or odd?  Transpositions – I have read this a couple times but the one example in my textbook is rather unclear, I am not sure what this means?  I think the transposition for $E_{1}$ is $(1,4)(1,10)$ but I'm not sure what this means. How to move a visible file to a hidden folder? I've only been using Ubuntu for two weeks and have been able to find answers to any problem I had, however this one defies my searches.  I want to move a visible programme file (wallch) to a hidden directory ./config/autostart.  I have been able to enter this directory and the subject file is not there and I want to have this program start at bootup.  Can anyone assist?  Thanking you Trying to identify a short sci-fi story about a human that is "resurrected" by malignant aliens Solve the recurrence $T(n) = 2T(n-1) + n$ Performing test for homogeneity of variance without samples I'd like to perform a test for homogeneity of variance in r, but I don't have samples available to test.    I have the sample mean of each group, the sample deviation of each group, and the sample size of each group(100).  Brand    ybar_i  s_i    n_i --------------------------- LowTar   9.64    .291   100 A        10.22   .478   100 B        10.77   .372   100 C        11.57   .352   100 D        13.59   .469   100   I'm thinking I should use the Levene test from Lawstat package, but that requires samples to test.  Or I think I could use the Fmax test. but that also requires samples. How to Toggle Selected Objects Visibility with H shortcut as in Maya I want to be able to toggle the visibility of selected objects with a shortcut (H) the way you can do in Maya and XSI, shown in the GIF. I'm guessing scrippting is needed. I've tried to do it my self but I'm new to Python and Blender and as soon as the objects are hidden they seem to no longer be in a selection state/list. Eg if I manually select the hidden object/s in the Outliner and try to print the selected object to the console, none seem to be selected. Is this possible to do with the current state of Blender 2.8? Schrödinger Equation for Two Electrons? I'm having trouble finding a simple answer to this question (maybe because there isn't one), but I'm just confused about how the Schrödinger Equation would look for two electrons. I understand that it would exist in 6 dimensional configuration space, but how does the potential look? It's confusing that the potential would be different for each electron depending on where the other one is.