Can I play D&amp;D 4e without reading the Red Box, as I already have the Player's Handbook, Monster Manual, and Dungeon Master's Guide?
I've asked several questions about 4th Edition D&amp;D because I may be able to start a game. However, I'd need to purchase (some) materials. I am aware of the 4 book set (core) and the expected Essentials Red Box.  So now I need to know: presumably buying either the 4 book set or essentials will be enough to get my game on. Would there be something 'lacking' though? Would I be missing character types, for instance, as I've seen that the splatbook strategy is still in effect?  I'm an experienced player and GM and plenty creative, so many holes I'd be able to fill in myself. I just don't want to get sucked into too much financial impact.
Consider the group $\mathbb{Q}$ under addition of rational numbers. If $H$ is a subgroup of $\mathbb{Q}$ with finite index, then $H = \mathbb{Q}$.  I just saw this on our exam earlier and was stumped on how to show this. Any ideas? Consider the following snippet:  $$\text{d}_{H}(A,B)  = \max\left\{ \sup_{a\in A} \inf_{b\in B} \text{d}(a,b),\sup_{b\in B} \inf_{a\in A}\text{d}(a,b)\right\}$$     In the output, the text under the inf's is significantly smaller then the one under the sup's. The same happens when I have it in an align environment.  You can see the same problem in the wiki definition of the . How can I have the typeset under the inf's and sup's in the same size? Reputation graph not interactable with a touch screen I am having an issue with wifi; it seems when I'm trying Ubuntu without installing, it only detects connection via the ethernet cable.  I can't connect and none of the available wifi networks are detected.  $ lspci 00:00.0 Host bridge: Intel Corporation Device 5904 (rev 02) 00:02.0 VGA compatible controller: Intel Corporation Device 5916 (rev 02) 00:04.0 Signal processing controller: Intel Corporation Skylake Processor Thermal Subsystem (rev 02) 00:08.0 System peripheral: Intel Corporation Sky Lake Gaussian Mixture Model 00:14.0 USB controller: Intel Corporation Sunrise Point-LP USB 3.0 xHCI Controller (rev 21) 00:14.2 Signal processing controller: Intel Corporation Sunrise Point-LP Thermal subsystem (rev 21) 00:16.0 Communication controller: Intel Corporation Sunrise Point-LP CSME HECI (rev 21) 00:17.0 SATA controller: Intel Corporation Sunrise Point-LP SATA Controller [AHCI mode] (rev 21) 00:1c.0 PCI bridge: Intel Corporation Device 9d10 (rev f1) 00:1c.4 PCI bridge: Intel Corporation Sunrise Point-LP PCI Express Root Port (rev f1) 00:1c.5 PCI bridge: Intel Corporation Sunrise Point-LP PCI Express Root Port (rev f1) 00:1f.0 ISA bridge: Intel Corporation Device 9d4e (rev 21) 00:1f.2 Memory controller: Intel Corporation Sunrise Point-LP PMC (rev 21) 00:1f.3 Audio device: Intel Corporation Device 9d71 (rev 21) 00:1f.4 SMBus: Intel Corporation Sunrise Point-LP SMBus (rev 21) 01:00.0 Display controller: Advanced Micro Devices, Inc. [AMD/ATI] Sun XT [Radeon HD 8670A/8670M/8690M / R5 M330] (rev 83) 02:00.0 Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller (rev 15) 03:00.0 Network controller: Realtek Semiconductor Co., Ltd. Device d723     $ lspci -knn | grep Net -A3 03:00.0 Network controller [0280]: Realtek Semiconductor Co., Ltd. Device [10ec:d723]     DeviceName: Hanksville Gbe Lan Connection     Subsystem: Hewlett-Packard Company Device [103c:8319] How to find creation date of file? I want to find out the creation date of particular file, not modification date or access date.  I have tried with ls -ltrh and stat filename. Is it OK to call a professor by his first name when he/she signs emails by only first name? If a professor in a North American country presents his- or herself by his/her first name in email messages, does this mean that students can refer to him/her by his/her first name? Or is this generally not a good idea, unless the professor has explicitly mentioned that he/she can be referred to by first name? I've noticed that most professors, who prefer to be referred to more formally, do not sign their emails with just their first names, but usually initials or first and last name. Transit Visa in Hong Kong for 15 hour layover between India and USA? We are (2) Indian nation and travelling from India to USA via Hong Kong airport and about 15 hours layover in Hong Kong airport. Do we need a transit visa even if only changing planes? And can we apply in Hong Kong Airport? Problem with sudo apt get update: The repository cdrom... does not have a Release file Every time I try update (using sudo apt-get update) my Ubuntu I get this problem:  W: The repository 'cdrom://Ubuntu 16.04 LTS _Xenial Xerus_ - Release amd64 (20160420.1) xenial Release' does not have a Release file. N: Data from such a repository can't be authenticated and is therefore potentially dangerous to use. N: See apt-secure(8) manpage for repository creation and user configuration details. W: The repository 'ppa.launchpad.net/kirillshkrogalev/ffmpeg-next/ubuntu xenial Release' does not have a Release file. N: Data from such a repository can't be authenticated and is therefore potentially dangerous to use. N: See apt-secure(8) manpage for repository creation and user configuration details. E: Failed to fetch cdrom://Ubuntu 16.04 LTS _Xenial Xerus_ - Release amd64 (20160420.1)/dists/xenial/main/binary-amd64/Packages  Please use apt-cdrom to make this CD-ROM recognized by APT. apt-get update cannot be used to add new CD-ROMs E: Failed to fetch cdrom://Ubuntu 16.04 LTS _Xenial Xerus_ - Release amd64 (20160420.1)/dists/xenial/main/binary-i386/Packages  Please use apt-cdrom to make this CD-ROM recognized by APT. apt-get update cannot be used to add new CD-ROMs E: Failed to fetch ppa.launchpad.net/kirillshkrogalev/ffmpeg-next/ubuntu/dists/xenial/main/binary-amd64/Packages  404  Not Found E: Failed to fetch ppa.launchpad.net/kirillshkrogalev/ffmpeg-next/ubuntu/dists/xenial/main/binary-i386/Packages  404  Not Found E: Some index files failed to download. They have been ignored, or old ones used instead.   How can I fix it? I use Ubuntu 16.04 LTS Effect of switching response and explanatory variable in simple linear regression How do I summon a baby mob? In Minecraft Java Edition, one can summon baby zombies and drowned using the IsBaby NBT tag: /summon zombie X Y Z {IsBaby:1b}  Likewise, one can summon baby breedable mobs (Pigs, Cows, etc.) by giving them a negative Age NBT tag (the number of ticks until the mob grows up): /summon cow X Y Z {Age:-100000}  Since NBT is inaccessible from commands in Bedrock Edition, the above commands will not work there. How do I summon baby mobs in Minecraft Bedrock Edition? Prove that a subset of a separable set is itself separable Stack Overflow is not getting refreshed automatically Stack&nbsp;Overflow is not getting refreshed automatically. I have to press F5 explicitly to refresh the website. What might be the issue? Covariance of Poisson and Conditional Binomial RV's Problem Statement  Let $X$ and $Y$ be random variables such that $X \sim \text{Poisson}(\lambda)$ and $Y|X \sim \text{Binomial}(x+1,p)$. Find $\text{Cov(X,Y)}$.  Attempt at a Solution  I would like to be able to write $Y$ as $X + Z$ where $Z$ is Poisson and independent of $X$, since then by  the variance is easy to compute. To this end, write $Y|X$ as a sum of independent binomials: $ Y|X = Z_1|X + Z_2|X, $ where  $Z_1|X \sim \text{Binomial}(1,p)=\text{Bernoulli}(p)$ and $Z_2 | X \sim \text{Binomial}(x,p).$ Then $Z_2 \sim \text{Poisson}(\lambda p)$, which we can obtain by directly computing the pdf: \begin{aligned} P(Z_2 = z) &amp;= \sum_x P(Z_2=z, X=x)\\ &amp;= \sum_x P(Z_2=z\mid X=x)P(X=x) \\ &amp;= \sum_{x=y}^\infty \frac{e^{-\lambda} \lambda^x}{x!}\frac{x!}{z!(x-z)!}p^z(1-p)^{x-z} \\ &amp;= \frac{(\lambda p)^z}{z!}e^{-\lambda p} \sum_{x=z}^\infty \frac{[\lambda(1-p)]^{x-z} e^{-\lambda(1-p)}}{(x-z)!} \\ &amp;= \frac{(\lambda p)^z}{z!}e^{-\lambda p}. \end{aligned} However, I cannot get the same approach to simplify for $Z_1|X$, which instead involves the CDF of $X$. I also tried this approach on $Y|X$ directly, hoping to obtain a sum in the form of the expectation of $X$, but I can't seem to reduce it. Even if I could, I'd still need to compute $E[XY]$ for the covariance. I suspect there may be a better approach than grinding through several more sums. 2-10x Slower Deployments with Winter '15? I am looking to identify a story that I read around 2001 (it is probably much older).  Someone showed me the story on pages printed from the internet, and it was attributed to Isaac Asimov (although I cannot state that is the true author).    The story is told in glimpses at different points of time in the future.  In each glimpse, humans are asking a more and more "intelligent" computer how to prevent the universe from collapsing into a singularity in the future, and the computer states it needs more computational power and resources to solve this problem.  At some point, man becomes one with the computer, and the computer exists in hyperspace (or subspace?).    In the final glimpse, it is the end of time and the universe is collapsing into a singularity.  At the instant the universe reaches the singularity, the computer figures out how to prevent it and says "Let there be light" and the universe begins to expand again.  Is anyone familiar with this story? Some items in Terraria drop only very rarely from certain enemies. It's a pain having to farm so many enemies to try to get these rare items. Is there any way to make them drop more often? Notify more frequently than once a day? Is there a way to subscribe to a question and be notified more frequently than once a day?  I'd like to be notified immediately on any posts to a question. First chapter appearing before first line in table of contents I have the CKeditor plugin installed by itself (i.e. not using WYSIWYG module.) Then, it uses a CKEditor library located in sites/all/libraries/ckeditor. This works fine. I'd like to add more plugins to it; namely, the footnotes plugin. (For the moment, please refrain from "just download a new library from ckeditor.com and replace it"; there were other issues/considerations involved.)  Now, I see this everywhere when I try to look for a solution  config.extraPlugins = 'footnotes';   I tried adding that to admin/config/content/ckeditor/edit// -> Advanced Options -> Custom JavaScript configuration, but it white screens the editor.  I tried adding it to the config.js in sites/all/libraries/ckeditor like below, but it had no effect.  CKEDITOR.editorConfig = function( config ) {   config.extraPlugins = 'footnotes'; };   I can't really add it to a ckeditor.config.js file, dump that file in my theme, and choose "Yes" for "Load ckeditor.config.js from the theme path", since (for content creation/editing) it uses the admin theme which is different from the theme we're developing.  So, I'm at a loss. The only other thing I can think of is to use a hook in the module we have for the site, but I'm not sure if that's write/what hook would be called.  Is it just me, or does it seem like clear documentation on how to manage CKEditor in Drupal is severely lacking? Any help would be appreciated.  UPDATE: After some testing, it looks like the "Custom JavaScript configuration" is supposed to work, but it is possibly broken for CKEditor 4.4+ I read something (can't seem to find it now) that suggested the plugin/widget import was broken on 4.4+, so I changed to 4.3 and the extraPlugins worked. Now, I wasn't able to get footnotes working (which is what kicked this whole thing off), but some other plugins that previously failed during the same steps now work on 4.3. So, there's that. I'm wondering now if it's something with footnotes itself. Can you attach a UIGestureRecognizer to multiple views?