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Every subsequence of $x_n$ has a further subsequence which converges to $x$. Then the sequence $x_n$ converges to $x$. During the beta of Windows 10 it was hard know what version you were running unless it had it posted to the desktop. Once that wasn't there - how do you tell what version / build you are running?   This will become more of an issue as Microsoft starts releasing more builds with the new update mechanism. Evaluate  $$\lim_{n\to\infty} \left(\frac{1^p+2^p+3^p + \cdots + n^p}{n^p} - \frac{n}{p+1}\right)$$ Is there a notification mechanism for when a dependency property has changed? Change \headheight for a \pagestyle I have a document class that auto generates header from some user input. The problem is the first page should have a different page header than the others and the headline can be multi line. So \headheight is too small. Here is a demonstration of the problem:  \documentclass[twoside]{scrartcl} \newcommand{\longfirstpagehead}{% \begin{minipage}{10cm} some\\long\\text\\text\\text\\text\\text\\text \end{minipage}} \newcommand{\normalhead}{normal} \usepackage{scrpage2}  \newpagestyle{firstpage}{%     {\longfirstpagehead\hfill} %twoside links     {\longfirstpagehead\hfill} %twoside rechts     {\longfirstpagehead\hfill} %oneside     (\textwidth,1pt) }{%     {\pagemark\hfill} %twoside links     {\hfill\pagemark} %twoside rechts     {\hfill\pagemark} %oneside } %  \newpagestyle{normal}{%     {\normalhead\hfill} %twoside links     {\normalhead\hfill} %twoside rechts     {\normalhead\hfill} %oneside     (\textwidth,1pt) }{%     {\pagemark\hfill} %twoside links     {\hfill\pagemark} %twoside rechts     {\hfill\pagemark} %oneside } %    \pagestyle{normal} \AtBeginDocument{     \thispagestyle{firstpage}}  \usepackage{blindtext} \begin{document}     %\vspace*{1cm}     \blindtext      \blindtext     \pagebreak \end{document}   I tried to read the height with \settototalheight and:   add a \vspace at beginning of document (unnice hack):  still the bad box warning (of cause) first section has different alignment  manually change \headheight in pagestyle  text height and page foot is wrong (can't change this because some scoping?)  use Komascript in pagestyle  \recalctypearea warning  geometry in pagestyle  pretty much the same problem like the manual attemp    So I would like to change the \headheight for the pagestyle firstpage, but the page should still have the same page margins, etc. The problem is that this has to work with \thispagestyle. (Better Ideas are also welcome) Something like \thispagegeometry in geometry would be great. ;) Short story about a group of sci-fi writers sitting around discussing their profession Why are properties lost in the Cayley–Dickson construction? Motivating question:    I'm aware that one can construct a hierarchy of number systems via the Cayley–Dickson process:  $$\mathbb{R} \subset \mathbb{C} \subset \mathbb{H} \subset \mathbb{O} \subset \mathbb{S} \subset \ldots $$  "Reals" $\subset$ "Complex" $\subset$ "Quaternions" $\subset$ "Octonions" $\subset$ "Sedenions" $\subset$ $\ldots$  and that at each step you're given a multiplication table that tell how the elements interact. As you move up the ladder, certain "nice" properties are lost: ordering,  commutativity, associativity, multiplicative normedness, etc... Given the multiplication table, you can show that these properties don't hold.   Eric Naslund noted that "the first 4 are very special as they are the unique 4 normed division algebras over ℝ", no surprise then that these $2^n$-ions have found quite a bit of use. I'm interested in the sequence itself however, irrespective of how useful a $2^{256}$-ion might be (ducenti-quinquaginta-sex-ion?).   I feel like something deeper is going on here though that I don't understand. Why are these particular properties lost at each step? Is it possible to quantify the process such that, at the $2^n$-ion you can say something about the symmetry of the multiplication table*?  * I'm making an ansatz that there is a connection between the symmetry of the multiplication table and these "nice" properties. A term for when people insist on giving you help you didn't ask for? People love to tell other people what to do. It may not be control, so much as trying to help, especially when you've asked for help directly. However, there's a difference between answering someone's question and answering while piling on recommendations the person didn't ask about, and this is what I'm seeking a term for. Advertising and marketing feel similar to me in this vein. In the worst cases this can be overzealous religious followers professing your damnation if you don't follow with them (I think in Christianity they call it "witnessing"). Any which way, it comes across to me as a form of unsolicited advice: I didn't ask for it, so I don't want it; I want to stay focused.  Is there a better term for this than "unsolicited advice"? Also, is there a term for a person who exhibits this kind of behavior frequently? How to copy a file to multiple directories using the gnu cp command Drush PHP syntax error when running I am following the instructions to install Drush that are listed on this page:   I seem to be getting a syntax error within the code:  [user@localhost ~]$ wget https://github.com/drush-ops/drush/releases/download/8.0.0-rc4/drush.phar --2015-11-16 16:23:02--  https://github.com/drush-ops/drush/releases/download/8.0.0-rc4/drush.phar Resolving github.com (github.com)... 192.30.252.131 Connecting to github.com (github.com)|192.30.252.131|:443... connected. HTTP request sent, awaiting response... 302 Found 2015-11-16 16:23:05 (1.47 MB/s) - drush.phar saved [3496991/3496991]  [user@localhost ~]$ php drush.phar core-status  Parse error: syntax error, unexpected '[' in phar:///home/user/drush.phar/includes/output.inc on line 188   I am not seeing this error on Google. Any idea how to fix it? How does editing work? multiple prints on the same line in Python For example:  $ sudo apt-get install curl Reading package lists... Done Building dependency tree Reading state information... Done You might want to run 'apt-get -f install' to correct these: The following packages have unmet dependencies: bsh : Depends: libjline-java but it is not going to be installed groovy : Depends: libjline-java but it is not going to be installed rhino : Depends: libjline-java but it is not going to be installed E: Unmet dependencies.   Try 'apt-get -f install' with no packages (or specify a solution).   I get the same or similar errors when I attempt to install clojure1.3, leiningen, and several other packages.   When I try the suggestion made in the error message, this is what happens:  $ sudo apt-get -f install  Reading package lists... Done Building dependency tree        Reading state information... Done Correcting dependencies... Done The following packages were automatically installed and are no longer required:   diffstat linux-headers-3.2.0-26-generic linux-headers-3.2.0-26 dh-apparmor dkms html2text libmail-sendmail-perl libsys-hostname-long-perl Use 'apt-get autoremove' to remove them. The following extra packages will be installed:   libjline-java Suggested packages:   libjline-java-doc The following NEW packages will be installed:   libjline-java 0 upgraded, 1 newly installed, 0 to remove and 0 not upgraded. 23 not fully installed or removed. Need to get 0 B/72.0 kB of archives. After this operation, 129 kB of additional disk space will be used. Do you want to continue [Y/n]? Y (Reading database ... 226243 files and directories currently installed.) Unpacking libjline-java (from .../libjline-java_1.0-1_all.deb) ... dpkg: error processing /var/cache/apt/archives/libjline-java_1.0-1_all.deb (--unpack):  trying to overwrite '/usr/share/java/jline.jar', which is also in package scala 2.9.2-400 Errors were encountered while processing:  /var/cache/apt/archives/libjline-java_1.0-1_all.deb E: Sub-process /usr/bin/dpkg returned an error code (1)  $ sudo apt-get upgrade Reading package lists... Done Building dependency tree        Reading state information... Done You might want to run 'apt-get -f install' to correct these. The following packages have unmet dependencies:  bsh : Depends: libjline-java but it is not installed  groovy : Depends: libjline-java but it is not installed  rhino : Depends: libjline-java but it is not installed E: Unmet dependencies. Try using -f. So, to explain the title, I'm referring to the necessity of the axiom of choice in the existence of a well ordering on reals, or any uncountable set.  Now, while tweaking some sets, I came across this :  We start with the natural numbers, $N$. We take the power set of the naturals, $P(N)$.  Then we remove all the finite subsets of $N$ from $P(N)$. Let us call this new set $S$. This set is the set of all infinite subsets of $N$.  It is easy to show that $S$ has uncountable cardinality, same as that of real numbers. This is because the removal of finite subsets only removes a countable number of elements. (Haven't posted this deduction, for it is very easy, but I may post it if it is not so evident)  Now, we seek to find an ordering on the set $S$. Every set in this set is an infinite subset of natural numbers, so each of these sets are well ordered by the natural ordering of $N$.  Taking any two sets in $S$, say $A$, and $B$, we seek to order them by checking their elements lexicographically. We compare the first two elements in $A$, and $B$. Let them be $a_1$, and $b_1$ respectively. If $a_1 = b_1$, then we move on to the second elements in the sets, $a_2$, and $b_2$, and so on. If, at any point, $a_n &lt; b_n$, then $A &lt; B$, or if $b_n &lt; a_n$, then $B &lt; A$.  This order seems to be a well ordering of the uncountable infinity of reals. I don't seem to have invoked the axiom of choice anywhere in the construction of this set $S$.  So, why isn't this a well ordering on the uncountable of reals? Complete classification of the groups for which converse of Lagrange's Theorem holds OS: Ubuntu 12.04  Accidentally deleted dpkg. Now, packages can't be installed. So, needs an dpkg installer which installs packages. Prove that if $A$ is transitive, then $\mathcal{P}(A)$ is transitive too. My book on set theory says     Prove that is a set $A$ is transitive, then $\mathcal{P}(A)$ is also transitive, where $\mathcal{P}(A)$ is the power set of $A$.   I don't know understand how. Let $A=\{a,b\}$. Clearly it is transitive. Now $\mathcal{P}(A)=\{\{a\},\{b\},\{a,b\},\emptyset\}$. This is clearly not transitive. Showing $\sum\limits_{p \in P} \frac{1}{p}$ where $P$ is the set of all primes is divergent I'm playing around, trying to write some code to use the  APIs to shorten a URL.  After reading , I tried:     TRIM_API_URL = 'http://api.tr.im/api'    auth_handler = urllib2.HTTPBasicAuthHandler()    auth_handler.add_password(realm='tr.im',                              uri=TRIM_API_URL,                              user=USERNAME,                              passwd=PASSWORD)    opener = urllib2.build_opener(auth_handler)    urllib2.install_opener(opener)    response = urllib2.urlopen('%s/trim_simple?url=%s'                               % (TRIM_API_URL, url_to_trim))    url = response.read().strip()   response.code is 200 (I think it should be 202).  url is valid, but the basic HTTP authentication doesn't seem to have worked, because the shortened URL isn't in my list of URLs (at ).  After reading  I also tried:     TRIM_API_URL = 'api.tr.im/api'    password_mgr = urllib2.HTTPPasswordMgrWithDefaultRealm()    password_mgr.add_password(None, TRIM_API_URL, USERNAME, PASSWORD)    auth_handler = urllib2.HTTPBasicAuthHandler(password_mgr)    opener = urllib2.build_opener(auth_handler)    urllib2.install_opener(opener)    response = urllib2.urlopen('http://%s/trim_simple?url=%s'                               % (TRIM_API_URL, url_to_trim))    url = response.read().strip()   But I get the same results.  (response.code is 200 and url is valid, but not recorded in my account at .)  If I use query string parameters instead of basic HTTP authentication, like this:     TRIM_API_URL = 'http://api.tr.im/api'    response = urllib2.urlopen('%s/trim_simple?url=%s&amp;username=%s&amp;password=%s'                               % (TRIM_API_URL,                                  url_to_trim,                                  USERNAME,                                  PASSWORD))    url = response.read().strip()   ...then not only is url valid but it's recorded in my tr.im account. (Though response.code is still 200.)  There must be something wrong with my code though (and not tr.im's API), because  $ curl -u yacitus:xxxx http://api.tr.im/api/trim_url.json?url=http://www.google.co.uk   ...returns:  {"trimpath":"hfhb","reference":"nH45bftZDWOX0QpVojeDbOvPDnaRaJ","trimmed":"11\/03\/2009","destination":"http:\/\/www.google.co.uk\/","trim_path":"hfhb","domain":"google.co.uk","url":"http:\/\/tr.im\/hfhb","visits":0,"status":{"result":"OK","code":"200","message":"tr.im URL Added."},"date_time":"2009-03-11T10:15:35-04:00"}   ...and the URL does appear in my list of URLs on .  And if I run:  $ curl -u yacitus:xxxx http://api.tr.im/api/trim_url.json?url=http://www.google.co.uk   ...again, I get:  {"trimpath":"hfhb","reference":"nH45bftZDWOX0QpVojeDbOvPDnaRaJ","trimmed":"11\/03\/2009","destination":"http:\/\/www.google.co.uk\/","trim_path":"hfhb","domain":"google.co.uk","url":"http:\/\/tr.im\/hfhb","visits":0,"status":{"result":"OK","code":"201","message":"tr.im URL Already Created [yacitus]."},"date_time":"2009-03-11T10:15:35-04:00"}   Note code is 201, and message is "tr.im URL Already Created [yacitus]."  I must not be doing the basic HTTP authentication correctly (in either attempt).  Can you spot my problem?  Perhaps I should look and see what's being sent over the wire?  I've never done that before.  Are there Python APIs I can use (perhaps in pdb)?  Or is there another tool (preferably for Mac OS X) I can use? Am I correct to say the difference between a signed and unsigned integer is:  Unsigned can hold a larger positive value and no negative value. Unsigned uses the leading bit as a part of the value, while the signed version uses the left-most-bit to identify if the number is positive or negative. Signed integers can hold both positive and negative numbers.  Any other differences?