Is it possible to put pairwise disjoint open 3d-balls with radii $\frac{1}{2},\frac{1}{3},\frac{1}{4},\dots$ inside a unit ball?    not an original question,  I found it somewhere in the internet once, but without any answer.
This problem occurred to me when I came across a similar problem where the radii were taken over only the primes. That question was unanswered, but it seems to me infinitely many circles of radius $1/2, 1/3, 1/4...$ can fit into a unit disk. The area of all those circles would be $\pi \sum_2^\infty 1/n^2 = \pi^3/6 -\pi$, which is less than the area of the unit disk $\pi$. But can the circles actually be packed with no overlaps?
How check with SOQL if a picklist value is available or not for a specified record type How check if a picklist value is available or not for a specified record type ( through SOQL)? Thanks in advance What is the difference between "I've been to China" and "I've gone to China"? Both are in the present perfect, but one uses the verb 'to go' and the other 'to be'. Is there a rule for this?  Is there any chance that the differences between "I have been" vs. "I have gone", are differences in English dialect (I don't know if this is the right word).  Edit Could I say that North American English speakers use "I have gone", and maybe U.K speakers say "I've been"? Or vice versa. How to programmatically bind a (dependency) property of a control that's inside a DataTemplate? Understanding DNA match of 1,723 cM I have a DNA match of 1,723 cM with a male 6 years younger than me. His father is one of a twin, could my match be not my half-sibling but my 1st cousin. pgfplots fillbetween with multiple curves I have a TikZ picture like this:  \begin{tikzpicture}   \begin{axis}[     axis lines=middle,     xmin=-0.5,xmax=3.5,ymin=-0.5,ymax=3.5   ]   \addplot[very thick,blue, samples=300, domain=0:3, name path=A] {sqrt(x)};    \addplot[very thick,yellow!70!red, samples=300, domain=0:3, name path=B] {9-3*x};    \addplot[very thick,red!90!teal, samples=300, domain=0:3, name path=C] {3};    \addplot[very thick,green!70!magenta, samples=300, domain=0:3, name path=D] coordinates{(1/9,-6) (1/9,6)};   \end{axis} \end{tikzpicture}     I’d like to fill the area enclosed by these four curves.  Similar questions have been answered using pgfplots’s fillbetween package, but it only seems to support filling between two curves. What are my options? How to cite own unpublished work in text and reference? What are the best SEO practices when changing domain names? I'm using the Yoast SEO plugin on a WordPress site on a new, more memorable domain to replace an old static HTML site with no SEO. I've followed , set up 301 redirects from the old domain to the new one, and filed a change of address in the Google Search Console. However, after a few days, the old site still shows in search results, and is ranked higher than the new one if you google our company name.   And, if I try to set the preferred domain in the Google Search Console Site Settings for the new site, I see this in place of the options to prefer www/non-www/http/https:     Not all options are available because of a Change of Address request   related to this site.   I've read of some cases where this condition has lasted for .  Is there anything more I can do to fix this? Have I done something wrong, or do I just need to wait, and for how long? How can I easily encrypt a file? My table doesn't fit; what are my options? I have a table that I want to insert on a page, but at least one (perhaps both) of the following conditions are met:   The table is too wide to fit within the text block or page. That is, I'm exceeding some horizontal restriction. The table is too tall to fit within the text block or page. That is, I'm exceeding some vertical restriction.   What are my options to make this table fit? If it doesn't fit, regardless of my attempts, what other options exist? Uninstalling Ubuntu from dual boot / changing bootloader Can I sync bookmarks between Firefox and Chromium? So, Firefox has turned so resource intensive that my netbook can't run it without making me want to pull my hair out. Thus, I have been trying Chromium with quite some success (I have managed to find proper equivalents for my firefox plugins), the only thing I'm lacking is my bookmarks, which are stored in my Firefox Sync account. Point is I don't want to use Google Bookmarks, mostly because of the whole thing with encryption.  Is there any way to use Firefox Sync with Chromium?, or is there any secure alternative? Disabling IPv6 on Mint and Debian How does one disable IPv6 completely (for all interfaces, resp. for the whole machine?  Keep in mind, I don't want any kind of GUI solution.    OS in question:   Linux Mint 18.x Cinnamon 64-bit GNU/Linux Debian 9.x Cinnamon 64-bit No internet after 16.04 LTS 18.04.01 upgrade This may seem like a duplicate, but many solutions have been unsuccessfully tried. Currently I have no internet, WIFI or Ethernet. Sometimes: "no wifi adapter found".  The device is HP dm4, dual boot with Windows 7.    Here is the  The issue started 3 weeks ago as no GUI after 16.04 LTS to 18.04.01 upgrade.  At that time, I was able to use the terminal to connect to the Internet and run "fixes" in   Then mysteriously, the GUI ran after restarting several times.  But since then, I am unable to connect to the Internet in the terminal or GUI.    There is a chatroom  about my issues.  sudo nmcli c up &lt;saved WIFI connection&gt;   only appears to connect.   sudo nmcli d wifi list   shows strong signal strength, but ping to google and nyt fails.   The phone I use as a hotspot shows a successful connection.    In the GUI Network Tools show the phone/hotspot recently used minutes ago, the Available Networks list shows the phone/hotspot as available with a check mark, but the "connect" button is grayed out and unfunctional.    REGDOMAIN=00 and attempts to change this has failed as others describe. I have a similar set up to the one described by cipricus in  and the situation described in Calculating Statistics Based on Expression in QGIS? Is it possible to calculate the sum of polygon areas based on whether or not it has a value in another column?   For example:  In column 2 I have the area of polygons. I want to calculate the area of all polygons that contain 'AG' in column 1 or all polygons that are IN column 1. But calculate them separately so I can get the total area of each type in column 1. I need to cast single figures (1 to 9) to (01 to 09). I can think of a way but its big and ugly and cumbersome. I'm sure there must be some concise way. Any Suggestions First let me explain what I mean by "transitive" Suppose that the price of product A and the price of product B has a correlation of .5 Suppose also that the price of product B and product C has a correlation of .5  One might thing that if correlation(A,B) = .5 and correlation(B,C) = .5 then correlation(A,C) > 0, but with an intuitive example we can see why this is not the case:  Suppose that A is a fruit salad made of papaya and banana, suppose also that B is a fruit salad made of banana and strawberry and, finally, suppose that C is strawberries and cream. Clearly, when the price of banana goes up, both the price of A and B will go up; when the price of strawberry goes up the price of B and C will go up; but since A and C have no ingredients in common, their price isn't correlated.  My question is which statistical concept captures this intuitive idea. Is it the concept of dimensions?  What do I mean by transitive? Let me define the binary operator X corr? Y as 1 if correlation(X,Y) != 0 and 0 otherwise, so:   A corr? B = 1, B corr? C = 1, but  A corr? C could be = 0   If corr? was transitive, then A corr? C = 1 Biliniear form to inner product Let $f:V\times V\rightarrow F$ be a bilinear form in a finite inner product space V.  If $F=R$, how can I prove that there exists a single linear transformation $T:V \rightarrow V$ so that for each $v,u\in V$, $f(u,v) = (Tu, v)$ ?  Would that sill be the case if $F=C$? How to find max of amount of opportunity related to account? I have a below requirement : I need to find maximum amount on related opportunities and to display on account. Ex: suppose I have account A1 and A1 have 5 opportunities with amount o1=>100 o2=>500 o3=>300 o4=>1000 o5=>50 on my account i should have max_opportunity_amount =1000.  I have written below trigger ,but  I am not sure what to do further  trigger maxOppAmountonAcc on Opportunity(after insert){      map&lt;id,Opportunity&gt; oppMap = new map&lt;id,Opportunity&gt; ();     set&lt;Id&gt; oppId = new set&lt;Id&gt;();     for(Opportunity o : Trigger.new)     {         oppMap.put(o.accountId,o);         oppId.add(o.id);     }       List&lt;Account&gt; accList = new List&lt;Account&gt;();      for(Account a : [Select id ,MaxOppAmount__c,(select id,max(amount)  from opportunities) from Account where id in : oppMap.keyset()])     {      }  } Let, $X$ be a countable set. Which of the following are true?   There exists metric $d$ on $X$ so that $(X,d)$ is complete. There exists metric $d$ on $X$ so that $(X,d)$ is not complete. There exists metric $d$ on $X$ so that $(X,d)$ is compact. There exists metric $d$ on $X$ so that $(X,d)$ is not compact.   4 is true as we can take discrete metric. Then $\{\{x\}:x \in X\}$ is an open cover containing no finite subcover.  If there exists a compact metric then it would automatically become complete also. Hence if 3 is true, so is 1.  What about 2? Any other comment? Splitting a string into words and punctuation I'm trying to split a string up into words and punctuation, adding the punctuation to the list produced by the split.  For instance:  &gt;&gt;&gt; c = "help, me" &gt;&gt;&gt; print c.split() ['help,', 'me']   What I really want the list to look like is:  ['help', ',', 'me']   So, I want the string split at whitespace with the punctuation split from the words.  I've tried to parse the string first and then run the split:  &gt;&gt;&gt; for character in c: ...     if character in ".,;!?": ...             outputCharacter = " %s" % character ...     else: ...             outputCharacter = character ...     separatedPunctuation += outputCharacter &gt;&gt;&gt; print separatedPunctuation help , me &gt;&gt;&gt; print separatedPunctuation.split() ['help', ',', 'me']   This produces the result I want, but is painfully slow on large files.  Is there a way to do this more efficiently?