Is the union of a chain of topologies a topology?
Union of ascending chain of Topologies
Getting server name during servlet initialization Is normal extension of normal extension always normal? Usage of :- (colon dash) in bash Execute script after specific delay using JavaScript Showing a compact metric space has a countable dense subset Reference for the subgroup structure of $\rm{PSL}_2(q)$ A cardinal $\kappa$ such that $2^{\lambda}<\kappa$ for all $\lambda<\kappa$ is regular? A cardinal $\kappa$ such that $2^{\lambda}&lt;\kappa$ for all $\lambda&lt;\kappa$ is regular?  I would appreciate very much an answer I was trying to install Lightworks 11.5.1 (amd64) on Ubuntu 14.04(amd64) but there's a notice: Dependency is not satisfiable: libtiff4. Is there anyway to solve this dependency issue?  Thanks in advance. What would happen if two wizards made each other a Horcrux? Would they be invincible? How would you kill one of them? What's the recommended max width for the main container and for the main column, for large screens? Based on this question,  and its comments and answers, I did some research, but I didn't find a complete answer.   For me it is obvious that it is a good decision to limit the width of the main container, but what is the recommended max-width for the main container for large screens, in 2017, when the screens become larger and larger? What variables should be considered in this decision?  Also, let's say a website has multiple columns in the main container, what is the max-width for the main column?  Update: I have now a related question. I recommended to one client to reduce the width of the main container on the homepage, but I can't convince him. It is a website with photos, like pexels.com. It is in this case important to limit the width if the elements are not one more important than other? Make program first read from pipe, then from keyboard Can I pay two different costs with the same payment? How to solve $y^2=3x^4+3x^2+1$ for integers. If $x,y \in \mathbb Z$ , then find all the solutions of   $$y^2=3x^4+3x^2+1$$       I was asked this question by my friend who said that he encountered this while solving another problem. I have tried several things but am unable to solve this question. Moreover, this has to be done using elementary methods only. So far, I have tried to factorize and use Pell's equation. At the end, I'm getting $$2y_{n} + (2x^2_{n}+1)\sqrt{3}=(2+\sqrt{3})^{n}$$   where $n \in \mathbb Z^{+}$    But I'm not able to figure out how to show a contradiction from here. Can anyone please help me out? Thanks. bash script – for i in {x..y} i am writing a script in bash and I would like to give the two numbers in the brackets, x and y to be precise, as variables.  I wrote the script this way:  echo "x?" read x echo "y" read y  for i in {$x..$y}   but it does not work.  How could I set it up to make it function?  Thanks a lot in advance. how to launch Bluez on Lubuntu Trying to launch a BT adapter/manager(default installed on Lubu)a little window informs me that it cannot because there's no Bluez launched.  In terminal: sudo apt install bluez, it answers: Bluez is already the new version (5.46-0ubuntu3) Then invites me to remove a couple of obsolete packages.  So where's Bluez Daemon to launch?  Writing:systemctl status bluetooth.service ; hcitool dev  Answer:   bluetooth.service - Bluetooth service    Loaded: loaded (/lib/systemd/system/bluetooth.service; enabled; vendor preset    Active: inactive (dead)      Docs: man:bluetoothd(8)   Command:lspci -k | grep -A3 -i "wireless\|network\|bluetooth" Answer: 04:00.0 Ethernet controller: Qualcomm Atheros AR242x / AR542x Wireless Network Adapter (PCI-Express) (rev 01)     Subsystem: Quanta Microsystems, Inc AR242x / AR542x Wireless Network Adapter (PCI-Express)     Kernel driver in use: ath5k     Kernel modules: ath5k 0f:06.0 CardBus bridge: Texas Instruments PCIxx12 Cardbus Controller oem@oem-Extensa-5220:~$ Find $\int \frac{x^3}{x^2-1} \:\mathrm{d}x$ Find $\displaystyle \int \dfrac{x^3}{x^2-1} \:\mathrm{d}x$.   I think there are a few ways to do this. We could just break this up using long division or break it up into partial fractions then use long division. My homework says to break this up into its roots so that's why I brought up partial fractions. Is that the best way to do it here? Show that all horses are of the same color. Im trying to understand the solution about this, and all the other solutions are.. a bit weird for me and dont answer all my questions!  Reference :   Im using the answer there as reference, but my understanding is a bit different!     Find the error in the following proof that all horses are the same   color. CLAIM: In any set of h horses, all horses are the same color.      PROOF: By induction on h.      Basis: For h = 1. In any set containing just one horse, all horses   clearly are the same color. Induction step: For k > I assume that the   claim is true for h = k and prove that it is true for h = k + 1. Take   any set H of k + 1 horses. We show that all the horses in this set are   the same color. Remove one horse from this set to obtain the set H1   with just k horses. By the induction hypothesis, all the horses in H,   are the same color. Now replace the removed horse and remove a   different one to obtain the set H2 . By the same argument, all the   horses in H2 are the same color. Therefore all the horses in H must be   the same color, and the proof is complete.   Here's what i have come up with :  Suppose a set of 1 horse. $H_a = { horse_{1} }$  Obviously, all the horses in set $H_a$ are the same, since theres just 1 horse.  So using that as the Basis of the induction we can proceed and try to prove its true for $N$ horses.  -- I dont fully understand the part below   As an example : set $H_0$ :   $H_0 = { horse_{1}, horse_{2}, horse_{3}... horse_{n} }$  In my understanding, its because, I can make a subset  formed by 1 horse :  $K_1  = {horse_{1}}$ $K_2  = {horse_{2}}$ ...  I don't get it. I clearly know that this proof is a lie.  And for me, its because you cant claim theres a relation on a set with size $&gt;= 2$ , since :  $H_1 = { horse_{1}, horse_{2}}$  Theres nothing that says $horse_{1}$ equals $horse_{2}$. The basis was for one horse. But that alone is not a proof.  So what should I do ? How do I start DMing a new game after the Red Box? Unparsed HTML shows on search result page When you search on any of the SE network sites, with a tag (so that a description is shown); it shows the tag info content box, with the highlight-search-term span elements.  For eg. I searched ; ; and the results are as shown:                  Notice the &lt;span class='search-highlight'&gt; boxes around searched tag terms. I am trying get an unused server up and running, it booted fine but i was greeted with the login window and none of the known passwords seem to work. The server I am trying to get to work is not a Domain Controller and has not been used in a long time.  OS: Windows 2003 Server R2 Enterprise Edition  I tried Ophcrack XP (there is no WinServer version of Ophcrack) - it couldn't locate the partitions with hashes. I tried mounting the partitions myself (#mount /dev/hda*x* /mnt/ntfs), but it gave me an error saying /dev/hda*x* didn't exist.  Next I tried booting into a Ubuntu 10.04.3 LiveCD so that I could install and use chntpw - no go, Ubuntu Live wouldn't boot.  Based on what I've read up the following tools may be of help:   Windows Password recovery Petter Nordahl-Hagen's Offline NT Password &amp; Registry Editor Openwall's John the Ripper EBCD – Emergency Boot CD - Bootable CD (R)ecovery (I)s (P)ossible Linux rescue system   I am hoping that someone here has prior experience with Win2k3 Administrator password resets so that I don't end up having to try all of the above to find out which one works.