Knowing $$\lim_{n\to\infty}x_ny_n = 0$$try to prove $$\lim_{n\to\infty}x_n = 0$$or$$\lim_{n\to\infty}y_n = 0$$
Assume   $$\lim_{n\to \infty}{x_ny_n}=0$$  then  $$\lim_{n\to \infty}{x_n}=0$$ or $$\lim_{n\to \infty}{y_n}=0$$  I couldnt find two series who disprove that.. just hint please thanks
Matryoshka words Since it's Friday and others are playing games, here's another one to take us into the weekend.  Everyone knows about those Russian nesting dolls (called matryoshka dolls, I believe). A small doll nests inside a larger, which itself is inside a larger doll, and so on.   This game does the same with words. You start with a three-letter word, add a letter to make another word, and so on. Longest word wins. The catch? Each additional letter has to form a legitimate word.  Here's one to start you off:     bur   burr   burro   burrow   burrows     Good luck. Excel How to make Text Qualifier editable or add a new entry in the existing list? Is there an elegant way to have performant, natural sorting in a MySQL database?  For example if I have this data set:   Final Fantasy Final Fantasy 4 Final Fantasy 10 Final Fantasy 12 Final Fantasy 12: Chains of Promathia Final Fantasy Adventure Final Fantasy Origins Final Fantasy Tactics   Any other elegant solution than to split up the games' names into their components    Title: "Final Fantasy" Number: "12" Subtitle: "Chains of Promathia"   to make sure that they come out in the right order? (10 after 4, not before 2).  Doing so is a pain in the a** because every now and then there's another game that breaks that mechanism of parsing the game title (e.g. "Warhammer 40,000", "James Bond 007") I have the following pieces of hardware I would like to network mostly for file sharing (media primarily): 1 gaming laptop, 1 i7 (2.3Tb storage) desktop, 1 P4 desktop (500g storage), and 1 250gig PS3.  I am looking to setup a linux host (with a PS3 media server) with the i7 desktop but am concerned about leaving it on all the time. What stripped down, low energy usage distro can I couple with which windows &amp; PS3 friendly software?  Also, how should i reformat my i7 (in terms of partitions, RAID options, whatever)? It has 2 1Tb drives (likely adding a third), and 1 320 gig. Can I make my Ubuntu make sounds when I press Caps Lock etc.? What are alternatives to ExtJS? So what I'm looking for is a javascript framework I can use that has several UI controls. I have taken a look at  but those controls are very basic compared to ExtJS. Are there any other competitive alternatives?     This question exists because it has historical significance, but it is not considered a good, on-topic question for this site, so please do not use it as evidence that you can ask similar questions here. More info: . How does gravity work on Star Wars ships? Inspired by the question , how does gravity work on the Millennium Falcon and other ships its size? The passengers are not strapped in and regularly move around just easily as they would on a planet with Earth's gravity.   The answer for the Death Star refers to gravity often being "coreward" (presumably taking advantage of the natural gravity an object of such substantial mass would have), but that doesn't apply for a small ship. So how is gravity accomplished? How to remove \n from a list element? Does tourist visa (90 days) apply after a long-term visa ends in Schengen countries? I want the figures and tables to be numbered 1, 2, 3, ... until the end of the document instead of 1.1, 1.2, ... in chapter I, 2.1, 2.2, ... in chapter II and so on.  I know how to convert the "chapter" part of figure/table numbers from Roman to arabic:  \renewcommand \thefigure     {\ifnum \c@chapter&gt;\z@ \@arabic\c@chapter.\fi \@arabic\c@figure} \renewcommand \thetable     {\ifnum \c@chapter&gt;\z@ \@arabic\c@chapter.\fi \@arabic\c@table}   One could modify the above code in order to remove the "chapter" part, but the figure/table counters would still be reset to 0 at the start of new chapters. How do I reset a lost password (using recovery mode requires me to type the password)? I need to reset my password. I have followed these steps:    However, then I go to "root" or "netroot" recovery options, it tells me:  Give root password for maintenance (or type Control-D to continue)   Clearly, I do not know the root password. If I type CTRL+D, I return to the list of options. From  I read:  Under chapter 'The Other Way':  4. Highlight the line that begins kernel and press 'e' to edit`   But in the grub configuration file I have no line that starts with kernel. Only:  setparams 'Ubuntu...' recordfail set gxfpayload... insmod part_msdos insmod ext2 set root=... search --no-floppy... linux /boot/vmlinuz-2.6.38... initrd /boot/initrd.img-2.6....   Those are all lines in my GRUB. Which line should I edit? Or is there another way to reset my password? Show that there is no epimorphism from ($\mathbb{Q}$, +) to ($\mathbb{Z}$, +) What's the meaning of "be blowed"? I would like to know what's the meaning of "be blowed" in the following text:     'I'm going to smoke' Jenkins said; 'be blowed to Bertie dear.' (Mrs. Smythe had once addressed her husband in the office as 'Bertie dear', and thereforth that had been his name among the staff.) Richard made no answer. When a minute later Jenkins, discreetly directing his puffs to the open window, asked him for the titles of one or two of Zola's novels in English, and their price, he gave the required information without turning round and in a preoccupied tone.   , Arnold Bennett, 1911. just after the Big Bang and before inflation the currently observable universe was the size of a coin. One millionth of a second later the universe was the size of the Solar System, which is an expansion much much faster than speed of light. Can space expand with unlimited speed? MySQL Syntax error message "Operand should contain 1 column(s)" I tried running the following statement:  INSERT INTO VOUCHER (VOUCHER_NUMBER, BOOK_ID, DENOMINATION) SELECT (a.number, b.ID, b.DENOMINATION)  FROM temp_cheques a, BOOK b WHERE a.number BETWEEN b.START_NUMBER AND b.START_NUMBER+b.UNITS-1;   which, as I understand it, should insert into VOUCHER each record from temp_cheques with the ID and DENOMINATION fields corresponding to entries in the BOOK table (temp_cheques comes from a database backup, which I'm trying to recreate in a different format). However, when I run it, I get an error:  Error: Operand should contain 1 column(s) SQLState:  21000 ErrorCode: 1241   I'm running this in SQuirrel and have not had issues with any other queries. Is there something wrong with the syntax of my query?  EDIT:  The structure of BOOK is:  ID  int(11) START_NUMBER    int(11) UNITS   int(11) DENOMINATION    double(5,2)   The structure of temp_cheques is:  ID  int(11) number  varchar(20) I'm working in C, and I have to concatenate a few things.  Right now I have this:  message = strcat("TEXT ", var);  message2 = strcat(strcat("TEXT ", foo), strcat(" TEXT ", bar));   Now if you have experience in C I'm sure you realize that this gives you a segmentation fault when you try to run it. So how do I work around that? Does the following limit exist? $$\lim_{x \to 0} x\sin\left(\frac{1}{x}\right)$$  If yes, then I have to find it; if no, then I need to give reason why. I couldn’t figure out how to prove this formally, can someone please help me out. Improving Review Queues - Design overview II: Changing review bans and other new features Show that $x^{n-1}+\cdots +x+1$ is irreducible over $\mathbb Z$ if and only if $n$ is a prime. How do I remove XFCE from my computer? My computer is overheating because I got too many desktop environments installed like: MATE, Cinnamon and XFCE.  I uninstalled them, but XFCE failed to uninstall. I get this error.   sudo apt-get purge xfce4     Reading package lists... Error!     E: Problem syncing the file - sync (5: Input/output error)     E: The package lists or status file could not be parsed or opened.