In D&amp;D 5e, I am wondering how mechanically using +1 bows and arrows (or crossbow and bolts) work, specifically:   If a character uses a +1 bow but mundane arrows, do they get +1 to both the attack roll and the damage roll? If a character uses a +1 arrow but a mundane bow do they get +1 to both the attack roll and the damage toll? If they use both a +1 bow and a +1 arrow do the effects stack so that the character gets +2 to attack and damage rolls?   The way I have been working it is that a +1 bow grants the bonus to attack rolls, and the +1 arrow grands the bonus to damage rolls. Is this correct?
One of my players has a +1 shortbow, and recently found some +1 arrows. If he fires a +1 arrow from a +1 bow, will the bonus to attack and damage be +1, or +2?
What are tag synonyms and merged tags? How do they work? I need to refer to a model described elsewhere, from a section title, like  \section{Analysis of model X}    One way of referring to a model is to create a new counter, and then write  \section{Analysis of \cref{grandmodelofeverything}}   But now hyperref will complain because of invalid token, and it does not look good in the TOC either, especially since the titles of the sections the describe the models are more descriptive than  \section{Model 1}   They are currently like  \section{Adding the effect from Y processes}   Do I need to invent semi-descriptive long names like "The model by Authors with this modification" or can I live with these quirks? Prove that $ S=\{0\}\cup\left(\bigcup_{n=0}^{\infty} \{\frac{1}{n}\}\right)$ is a compact set in $\mathbb{R}$, but $\bigcup_{n=0}^{\infty} \{\frac{1}{n}\}$ is not a compact set.   (Can we use definition of compact set for this problem? ) I'm looking for a phrase that describes trying to fix problems caused by underlying issues, with the result of compounding the issue. I usually call this "targeting surface problems rather than root problems", but my terminology is verbose.  Example 1: A government bans buying and selling bananas in the state. Later, it passes a clause allowing citizens to purchase imported bananas.  Example 2: A divided highway is erected with two lanes going in each direction but, since it gets lots of traffic, the shoulders are widened into new lanes. This leaves no shoulder room.  What would be a more concise phrase? How do I install the Cinnamon Desktop? I have read that there is a new Gnome-2 like interface called Cinnamon produced by the Linux Mint developers.  Is this available for Ubuntu users - and if so how do I install it? When should a supervisor be an author? A Light is shone out the side window of a spaceship ( moving close to light speed ), will the light still travel at the speed of light in the B axis? I have installed GCC compiler by installing the build-essential package.  After the installation I wrote a simple C program. I tried to run it with the following command:  gcc First.c ./a.out   but I'm getting a bash: ./a.out: Permission denied message. I don't know what to do now. Stack Overflow is getting a Meta of its own Train passport control from London to Paris I'm a non-EU citizen, I will be travelling from London to Paris next month, so I was wondering since most countries track entry and leave dates, if I use the train to switch these countries and they don't control it, my UK visa will seem like entry YES but no leaving. Same for the Schengen, I wouldn't have an entry date but I'll be leaving,  Will it be trouble later? Are they controlling this on trains? If not is there anything I should do before? Parameter evaluation order before a function calling in C Can it be assumed a evaluation order of the function parameters when calling it in C ? According to the following program, it seems that there is not a particular order when I executed it.   #include &lt;stdio.h&gt;  int main() {    int a[] = {1, 2, 3};    int * pa;      pa = &amp;a[0];    printf("a[0] = %d\ta[1] = %d\ta[2] = %d\n",*(pa), *(pa++),*(++pa));    /* Result: a[0] = 3  a[1] = 2    a[2] = 2 */     pa = &amp;a[0];    printf("a[0] = %d\ta[1] = %d\ta[2] = %d\n",*(pa++),*(pa),*(++pa));    /* Result: a[0] = 2  a[1] = 2     a[2] = 2 */     pa = &amp;a[0];    printf("a[0] = %d\ta[1] = %d\ta[2] = %d\n",*(pa++),*(++pa), *(pa));    /* a[0] = 2  a[1] = 2 a[2] = 1 */  } Meaning of the word "axiom" Thus, axioms are propositions we assume to be true and we use them in an axiomatic theory as premises to infer conclusions, which are called "theorems" of this theory.  For example, we can use the  to prove theorems of arithmetic.  This is one meaning of the word "axiom". But I recognized that the word "axiom" is also used in quite different contexts.  For example, a group is defined to be an algebraic structure consisting of a set $G$, an operation $G\times G\to G: (a, b)\mapsto ab$, an element $1\in G$ and a mapping $G\to G: a\mapsto a^{-1}$ such that the following conditions, the so-called group axioms, are satisfied:   $\forall a, b, c\in G.\ (ab)c=a(bc)$, $\forall a\in G.\ 1a=a=a1$ and $\forall a\in G.\ aa^{-1}=1=a^{-1}a$.      Why are these conditions (that an algebraic structure has to satisfy to be called a group) called axioms? What have these conditions to do with the word "axiom" in the sense specified above? I am really asking about this modern use of the word "axiom" in mathematical jargon. It would be very interesting to see how the modern use of the word "axiom" historically developed from the original meaning.   Now, let me give more details why it appears to me that the word is being used in two different meanings:  As peter.petrov did, one can argue that group theory is about the conclusions one can draw from the group axioms just as arithmetic is about the conclusions one can draw from the Peano axioms. But in my opinion there is a big difference: while arithmetic is really about natural numbers, the successor operation, addition, multiplication and the "less than" relation, group theory is not just about group elements, the group operation, the identity element and the inverse function. Group theory is rather about models of the group axioms. Thus: The axioms of group theory are not the group axioms, the axioms of group theory are the axioms of set theory.  Theorems of arithmetic can be formalized as sentences over the signature (a. k. a. language) $\{0, s, +, \cdot\}$, while theorems of group theory cannot always be formalized as sentences over the signature $\{\cdot, 1, ^{-1}\}$. Let me give an example: A typical theorem of arithmetic is the case $n=4$ of Fermat's last theorem. It can be formalized as follows over the signature $\{0, s, +, \cdot\}$: $$\neg\exists x\exists y\exists z(x\not = 0\land y\not = 0\land z\not = 0\quad\land\quad x\cdot x\cdot x\cdot x + y\cdot y\cdot y\cdot y = z\cdot z\cdot z\cdot z).$$ A typical theorem of group theory is  which states that for any finite group G, the order of every subgroup H of G divides the order of G. I think that one cannot formalize this theorem as a sentence over the "group theoretic" signature $\{\cdot, 1, ^{-1}\}$; or can one? To be clear on this, I know what is the definition of an inner product space and some properties and theorems about them. What I am asking for is an intuition for this definition in the complex case. In the real case, the intuition (or at least one of them) is  geometric: The inner product of two vectors is the length of the projection of the first to the second scaled by the norms of both vectors so that it is symmetric (modulo some details). In particular I (and everybody else) think of "inner product zero" as geometric orthogonality and of orthonormal bases as, well, orthonormal bases and so on. The question is, what should I think about when working with complex (or should I say hermitian?) inner product spaces? what is the "meaning" of the complex number associated to two vectors called their inner product?  I will be happy to hear all kinds of answers. For example, what physical phenomena does it model or in what mathematical situations does in "naturally" appear. Answers that stress the "nice structure" resulting are also welcome, yet I feel that by itself  it is a bit unsatisfying. Proving that if $A$ is a $8\times 8$ matrix over $\mathbb{R}$ and $A^3=A$, then $A$ is diagonalizable. Is it possible for an iPad to get a virus? A google search gives number of methods to hide ALL tabs in chrome , but I want to hide 1 particular tab / change the display name of that tab.   Reason: I have an online music playing website open, which keeps showing tracks in the tab name and I just want to remove it from view of my work. Trying to run , embedded Tomcat instance fails.  Error seems to appear here:    Apr 17, 2015 2:13:47 AM org.apache.catalina.startup.HostConfig deployDescriptor  INFO: Deploying configuration descriptor /opt/OpenForisCalc/calc-server/tomcat/conf/Catalina/localhost/calc.xml  Apr 17, 2015 2:13:58 AM org.apache.catalina.core.StandardContext startInternal   SEVERE: Error listenerStart   Then if messes up with the rest (this repeats a lot):  Apr 17, 2015 2:13:58 AM org.apache.catalina.core.StandardContext startInternal  SEVERE: Context [/calc] startup failed due to previous errors Why are my PHP sessions dying? And why can't I restore them? I have an app using PHP and the PayPal API. The basic way it works to get a payment is that you do a web service call to PayPal to get a token and then do a browser redirect to PayPal with that token for the user to pay. After the payment details have been confirmed, PayPal redirects back to the URL you originally set in the service call.  This all works, millions of people use it every day, et cetera.  Strange thing is, when PayPal redirects back, the PHP session is gone. It's a .  First question: why is this happening? Both pages are on the same domain, both use HTTPS. The session works for all requests up until the PayPal redirect back.  The linked forum thread suggests a workaround, to persist the session ID in the PayPal request and then to retrieve it later and restore the session. Great, except it doesn't seem to work.  I can add some log statements:  log(session_id());   before and after the various redirects. When coming back from PayPal, I log some more.  log("session id is " . session_id()); $session_id = get_session_id_from_paypal(); log("setting it back to " . $session_id); session_id($session_id); session_start(); log("session id is now " . session_id());   The result is not at all what I'd expect:     session_id is fc8f459a186a3f4695ff9ac71b563825   setting it back to 82460dcf8c8ddd538466e7cb89712e72   session_id is now 360ba3fd99d233e0735397278d2b2e55     Second question: why is the session id not at all what I set it to? What am I doing wrong? Or, at least, why do none of the session variables come back? Find four groups of order 20 not isomorphic to each other. Changing console font on Ubuntu 10.04 Server How can I change local console font on Ubuntu 10.04 Server to Inconsolata?