I was reading some lore from the Forgotten Realms and saw something about higher level spell slots (10, 11 and 12) and them being sealed off for mortal beings.  So I was wondering if PCs know about spell levels as we know them, being able to sort them into tables based on spell level, knowing a fireball is a level 3 spell and magic missile a level 1.  I'm asking this because I want to make a character that is obsessed with 9+ level spells. But this would kinda fall flat without them being able to know the difference between a level 9 and level 10 spell.
Is there anything in RAW that supports spell level as a character concept, or alternatively that supports it as solely a player concept?  On the one hand, I see nothing that explicitly states that a character knows that there are spell levels. On the other hand, I don't see how a spellcaster could manage spell slots without knowing about spell levels.
A student of mine has been self-studying some elementary number theory. She came by my office today and asked if I had any hints on how to prove the statement      If $m$ is odd then $\gcd(2^m-1,2^n+1)=1$.    It's been a while since I took number theory and I'm not sure what to do. She said she is learning about congruences, primitive roots, and power residues.  She has not taken any group theory. JavaScript closure inside loops – simple practical example If virtual particles sometimes add more mass/energy to a system then was inputed or comes out in the output, how do they not violate conservation of mass/energy. Calculate battery life I would like to know how to calculate battery life when using an LED strip. The LED strip is powered by 8 AA batteries in series. LED Current Draw = 260 mA. LED power consumption: 3.1 W. LED Operating Voltage range: 9-14.8 VDC. Please see attached images for battery datasheet.  This is my calculation, but I'm not sure if it's correct:     Battery Life = (Battery Capacity)/(Load Current) = 2000 mAh /260 mA = 7.7 Hours   This is for one battery, and the lights are powered by 8 batteries, so is the total battery life = (7.7)x(8) = 61.6 hours ? Buying from Play store using a credit card with foreign billing address Is it possible to use a credit card with a foreign billing address to buy items from a local Play store? I have a Visa credit card from a German bank with a billing address in Germany registered in my Google Wallet. I have successfully used my Wallet to pay for online purchases from several online service providers in different foreign currencies so I am sure the credit card is correctly registered in my Wallet account. However, while physically located in the UK, I cannot complete any purchase from the UK Play store. At the point when I need to select my preferred payment method from my Wallet account, it shows my registered credit card greyed out with the text "Unsupported Payment method" next to it. How did half of Darth Maul survive? Filter subscription email is not being delivered (June 2019 - Feb 2020) I have created a custom filter in  and specified that I would like to get email updates:  However, I never got a confirmation mail nor any notifications based on my filter. I tried the &quot;resent confirmation mail&quot; button on the right hand sidebar:  But again nothing happens. The mail address should be fine  I used it for all kinds of notifications from Stack Exchange. For example the rep recalculation email arrived just fine on this address.  I retyped it several times to make sure there really isn't any typo  I double checked that it did not end up in the spam filter  I don't think it is a problem with my particular email provider, users with other mail providers seem to have the same problem, see     This is possibly related to , but this claims to be &quot;status complete&quot;.   EDIT: Although the &quot;status-completed&quot; tag was added, the problem still persists  EDIT 2: As of Feb 2020, it finally works I have created a 'control' using jQuery and used jQuery.extend to assist in making it as OO as possible.  During the initialisation of my control I wire up various click events like so  jQuery('#available input',              this.controlDiv).bind('click', this, this.availableCategoryClick);   Notice that I am pasing 'this' as the data argument in the bind method. I do this so that I can get at data attached to the control instance rather from the element that fires the click event.   This works perfectly, however i suspect there is a better way  Having used Prototype in the past, I remember a bind syntax that allowed you to control what the value of 'this' was in the event.  What is the jQuery way? Unable to find minimized terminal I just installed 11.10 and found that once I minimize the terminal window, I can't bring it back. All other Windows are getting minimized to the Unity launcher and I can relaunch them from there. If I go to the launcher and click on terminal a new terminal session is created and the old one is lost completely. This is the first time I am facing such a problem and all my previous installations of 11. 10 didn't throw up any such behaviors. Any suggestions? I am a beginner of ordinals and I don't know any powerful techniques in it. I come across with a problem about the first uncountable ordinal like this.  Let $X$ be a set of uncountable cardinality. Using the Principle of Well Order we have a well ordering $\le$ on X(and $&lt;$ means $\le$ but not euqual). By adding an element, which we denote by $∞$, and introducing the convention that $x &lt; ∞$ for all $x ∈ X$, we will assume that X has a maximum with respect to $\le$.   We define $ω_1 = \text{min} \{ x ∈ X : \{y ∈ X : y &lt; x \} \  \text{is uncountable}\} $  Clearly such a $ω_1$ exists. we define $0 = \text{min} \ X$ and intervels $[0,x], [x,y), (a,b]$ etc. in the usual sense.  Here are my questions:  (1)For any countable $A ⊂ [0, ω_1)$ there is an $x &lt; ω_1$ so that $A ⊂ [0, x]$.(I don't know how to make use of the countability and uncountablity here)   (2)Equipped with the topology generated by open intervals,  $[0, ω_1]$ is compact.   (3)A famous application of the first uncountable ordinal is to find an example of a Borel measure (with respect to the topology in (2)) that is not Radon. So how to construct a finite Borel measure $µ$ on $[0, ω_1]$ which is not a Radon measure?  Any solutions or elementary references will be appreciated! Make a div fill the height of the remaining screen space Can't SSH in as root I'm using the default installation of openssh-server for my Ubuntu 14.04 server. I can connect through the console as root like normal, with my username and password. When I try to SSH with the same username/password, however, I repeatedly get Access Denied errors. /var/log/auth.log reports Failed password for root from &lt;ip address&gt; port &lt;port&gt; ssh2, but I'm entering the correct password.  Why can't I connect to the server via SSH, even though the username and password ARE correct? Why are neural networks becoming deeper, but not wider? In recent years, convolutional neural networks (or perhaps deep neural networks in general) have become deeper and deeper, with state-of-the-art networks going from 7 layers () to 1000 layers ( in the space of 4 years. The reason behind the boost in performance from a deeper network, is that a more complex, non-linear function can be learned. Given sufficient training data, this enables the networks to more easily discriminate between different classes.  However, the trend seems to not have followed with the number of parameters in each layer. For example, the number of feature maps in the convolutional layers, or the number of nodes in the fully-connected layers, has remained roughly the same and is still relatively small in magnitude, despite the large increase in the number of layers. From my intuition though, it would seem that increasing the number of parameters per layer would give each layer a richer source of data from which to learn its non-linear function; but this idea seems to have been overlooked in favour of simply adding more layers, each with a small number of parameters.  So whilst networks have become "deeper", they have not become "wider". Why is this? How do I sort a vector of pairs based on the second element of the pair? If I have a vector of pairs: std::vector&lt;std::pair&lt;int, int&gt; &gt; vec;  Is there and easy way to sort the list in increasing order based on the second element of the pair? I know I can write a little function object that will do the work, but is there a way to use existing parts of the STL and std::less to do the work directly? EDIT:  I understand that I can write a separate function or class to pass to the third argument to sort.  The question is whether or not I can build it out of standard stuff.  I'd really something that looks like: std::sort(vec.begin(), vec.end(), std::something_magic&lt;int, int, std::less&gt;()); How do you use the Dungeon Defender's Portal Gun? The topic pretty much sums up my question. I have not yet figured out how the gun operates aside from the fact that it creates Portal portals. The weapon description indicates that it deals 250+ base damage, but how is that damage applied to the monsters? How do I safely investigate a USB stick found in the parking lot at work? I work at an embedded software company. This morning I found a USB stick in the parking lot in front of the building. With all the stories of "dropped USB stick attacks" in mind, I'm obviously not going to just plug it into my laptop. OTOH, I'm curious to know whether this was actually an attempt to compromise our systems, or it's really just an innocent case of somebody accidentally losing a USB stick. How do I safely inspect the USB stick without risking exposure?  I'm worried not just about malware and crafted file system images; there's also stuff like power surge attacks:.  EDIT: Many of the answers seem to assume I want to keep the drive and use it afterwards. I have no interest in that at all, I know USB sticks are cheap, and that it wouldn't be mine to keep anyway. I only want to know whether this was indeed a semi-targeted attack, partly out of curiosity whether this actually happens in real life and not just in security papers, but also so that I could warn my coworkers.  I want to know how I would figure out whether the stick contains malware. And that's not just a matter of looking at the drive contents and seeing a suspicious autorun.inf or a carefully crafted corrupt file system - I very much also want a way to inspect the firmware. I sort-of expected that there were tools for extracting that and comparing to known-good or known-bad binaries. Mod shows up with OP background when viewing deleted comments Skate shoes vs mtb shoes? It's an old argue on forums, still cant get it. What is the (real, that worth the money and time for ordering from abroad, in my case) difference, let's say between  shoes and some kind of old school skate shoes (the fat ones, like )?  P.S as far as I know most dirt BMXers are quite happy with regular skate shoes. How to update Android Studio in Ubuntu? I am trying to update from version 2.0.0 to version 2.1.2 in Ubuntu 64bit/14.04LTS but when I click "update and restart" it says "Downloading patches" and it closes.   It does not start again and if I try to open it, the version is still 2.0.0.   Is there any tutorial to manually update android studio? (keep all settings and etc). Properties possessed by $H , G/H$ but not G i) Does there exist a group $G$ with a normal subgroup $H$ such that $H , G/H$ are abelian but $G$ is not ?   ii) Does there exist a group $G$ with a normal subgroup $H$ such that $H , G/H$ are cyclic but $G$ is not ?