Could you wish for an ability score of 30 in D&amp;D?
Are there any drawbacks to using a wish spell to increase ability scores? If not then what would stop players from just using wish repeatedly and raising their ability scores to 30?  I'm just getting back into RPGs with D&amp;D 5e after not playing for years, and I seem to remember this being covered in the editions we played back then.
Let $p\in[1,\infty]$, $a\in\ell^\infty$ and $$T:\ell^p\to\ell^p\;,\;\;\;x\mapsto ax.$$ Note that $\left\|T\right\|=\left\|a\right\|_{\ell^\infty}$. It's easy to see that if $a\in\ell^1$, then $T$ is nuclear and hence compact.  Can we more generally conclude that $T$ is compact?  Assume $p&lt;\infty$. The intuitive approach would be to define $$T_n:\ell^p\to\ell^p\;,\;\;\;x\mapsto(a_1x_1,\ldots,a_nx_n,0,\ldots)$$ for $n\in\mathbb N$ and to show that $\left\|T_n-T\right\|\to0$. Now, $$\left\|(T_n-T)x\right\|^p=\sum_{i=n+1}^\infty|a_ix_i|^p\tag1$$ for all $x\in\ell^p$ and $n\in\mathbb N$. The right-hand side of $(1)$ clearly converges to $0$ as $n\to\infty$, but this only yields convergence in the strong operator topology. On the other hand, if $(a_n)_{n\in\mathbb N}$ would be nonincreasing and $a_n\to0$ (e.g. $a_n=\frac1n$), then $$\left\|(T_n-T)x\right\|^p\le|a_{n+1}|^p\left\|x\right\|_{\ell^p}^p\tag2$$ for all $x\in\ell^p$ and $n\in\mathbb N$ and we could immediately conclude $\left\|T_n-T\right\|\to0$. EDIT: Maybe the general result can be obtained from the convergence in strong operator topology (which holds by $(1)$) by noting that $\ell^p$ has the approximation property; but I'm not sure whether this is true. How to restore a system after accidentally removing all kernels? I was trying to delete old kernels, but I must have deleted all of the kernels on my Ubuntu 11.04 laptop. Is there any way to fix this via USB boot or mounting hard drive on another system? How to monitor USB power consumption? I'm looking for a way to monitor the power being drawn from the USB ports on my Mac.  System Profiler doesn't appear to display this and I haven't been able to find any applications or tools to do the job either.  Can anyone suggest anything (preferably software based)? How do I show that $\ln(x) = \lim_{n\to\infty} n (x^{1/n} - 1)$?  I ran into this identity on . I haven't been able to find any proof online and my efforts to get from $\ln(x) := \int_1^x \frac{\mathrm dt}t$ to that limit have been a failure. Finding out NSArray/NSMutableArray changes' indices What is the difference between max, min and sup, inf? Is there a way to make Git mark a file as conflicted? How to remove version and thank you message from the admin footer How do I call legacy PHP files? I am unable to call PHP files inside the Drupal directory. My task is maintaining staff's old pages on the new platform. With pages written on clear HTML, there is no problem: I place files in a folder I created (domain.org/sites/default/files/share/staff_folder).  In sites/default/files/.htaccess I added DirectoryIndex share and now the link to the domain.org/sites/default/files/share/staff_folder/index.html can be used. When I import pages written in PHP, e.g. calling domain.org/sites/default/files/share/staff2_folder/index.php, I get a 403 error:     Forbidden      You don't have permission to access /sites/default/files/share/staff2_folder/index.php on this server.   While /sites/default/files/share/staff2_folder/index.html still works. How to prove that $\frac{(mn)!}{m!(n!)^m}$ is an integer? $\forall m,n\in\mathbb Z$ , $m\ge1$ and $n\ge1$ how to prove that  $$\frac{(mn)!}{m!(n!)^m}$$ is an integer?  Thanks in advance. Deduction of $\forall y \exists x (x=y)$ Give a deduction of $\forall y \exists x (x=y)$  My thinking is I can prove $\exists x(x=y)$ then use generalization theorem， which is equivalent to prove $\neg \forall x \neg (x=y)$ but I got stuck proving this... thanks in advance  Sorry that I did not specify what deduction system that I want to use here, it is the deduction sequence  where ai is either Axiom or original hypothesis or obtained from MP curl in Mathematica, google link-shortener How do I get list of all tables in a database using TSQL? I'm reading  and I'm trying to understand the proof under "Degeneracy in One Dimension".  Here's what it says:     Considering a one-dimensional quantum system in a potential $V(x)$ with degenerate states $|\psi_1\rangle$ and $|\psi_2\rangle$ corresponding to the same energy eigenvalue $E$, writing the time-independent Schrödinger equation for the system:       $$-\frac{\hbar^2}{2m}\frac{ \partial^2\psi_1}{ \partial x^2} + V\psi_1 =E\psi_1$$       $$-\frac{\hbar^2}{2m}\frac{ \partial^2\psi_2}{ \partial x^2} + V\psi_2 =E\psi_2$$   Multiplying the first equation by $\psi_2$ and the second by $\psi_1$ and subtracting one from the other, we get:       $$\psi_1\frac{d^2}{d x^2}\psi_2-\psi_2\frac{d^2}{d x^2}\psi_1=0$$   Integrating both sides       $$\psi_1\frac{\partial \psi_2}{\partial x}-\psi_2\frac{\partial \psi_1}{\partial x}=constant$$   In case of well-defined and normalizable wave functions, the above constant vanishes, provided both the wave functions vanish at at least one point, and we find: $\psi_1(x)=c\psi_2(x)$ where $c$ is, in general, a complex constant. So, the two degenerate wave functions are not linearly independent. For bound state eigenfunctions, the wave function approaches zero in the limit $x\to\infty$ or $x\to-\infty$, so that the above constant is zero and we have no degeneracy.   Here are the parts I don't understand:   How does integrating $\psi_1\frac{d^2}{d x^2}\psi_2-\psi_2\frac{d^2}{d x^2}\psi_1=0$ yield $\psi_1\frac{\partial \psi_2}{\partial x}-\psi_2\frac{\partial \psi_1}{\partial x}=constant$.  Without having explicit formulas for $\psi_1(x)$ and $\psi_2(x)$, how do we just apparently pull them both out of the integral? I don't understand how the constant in the last equation vanishes just because $\psi_1$ and $\psi_2$ vanish at infinity. Even if it does vanish, how does that imply $\psi_1=c\psi_2$? Prove : $p$(n│even number of ODD parts)=$p$(n│distinct parts ,number of ODD parts is even ) I'm trying to prove the following Integer Partition claim :   $p$(n│even number of ODD parts) = $p$(n│distinct parts ,number of ODD parts is even) .  So I tried to prove a stronger claim :   $p$(n│number of odd parts) = $p$(n│number of distinct parts) :  Using generating functions :   DISTINCT PARTS =  $$(1+x)\cdot(1+x^2 )\cdot(1+x^3 )\cdot(1+x^4 )\cdot\cdot\cdot\cdot$$  = $$\frac {1-x^2} {1-x} \cdot \frac {1-x^4} {1-x^2} \cdot \frac {1-x^6} {1-x^3} \cdot \frac {1-x^8} {1-x^4}\cdot\cdot\cdot\cdot$$  $$ \frac {1} {1-x} \cdot \frac {1} {1-x^3} \cdot \frac {1} {1-x^5} \cdot \frac {1} {1-x^7} \cdot\cdot\cdot\cdot $$  = ODD PARTS  But I'm not sure regarding the proof , does it really prove that even number of odd parts equals distinct parts ,where number of ODD parts is even ?   Thanks Please tutor the usage of patchcmd and xpatch I understand that the  package provides a command \patchcommand that can be used to add material at the beginning and/or end of the replacement text of an existing macro. It works for macros with any number of normal arguments but has limitations for macros with optional arguments.   was introduced to take care of the above limitations as well as provide some additional functionality.   Now, when I try to comprehend the usage of the above packages by reading the user documentations (, ), I get the feeling that they move to implementation details a little too quickly compared to other package documentations. There are not enough explanations or examples.  I also tried to grasp the concepts by reading the  and more or less understood whatever is presented there. However, that is not enough.  So, do you think we can ask for a complete tutorial on the usage of patchcmd and xpatch? Explaining the usage of the relevant commands like \patchcmd, \pretocmd and \apptocmd as well as, \xpatchcmd, \xpretocmd and \xapptocmd with sufficient examples should suffice. Prepend 0 to sublists How can I bump other users' unanswered questions? I'm looking around for answers to my questions on several Stack Exchange sites and the good boy that I am I don't want to ask duplicate questions.  Often I find that there are other people who asked the same questions, sometimes years earlier, but still don't have an answer. I'd figure I could bump these back to top, but if I don't have enough rep for a edit (or comment), how would I do that?  Or, in that case, I should just post a 'newer' version of the same question? I am looping through a text file, using 'while read'. I read three variables from each line - two filenames and a decimal number. I know that this works in a vanilla setup (loop, read line, echo line, extract variables, nothing else), because I have tested it on my input file.  I am getting an odd result, though, once I add in the meat of my routine - which is a call to ffmpeg to merge the audio and video streams represented by the filenames. Successive 'read' operations omit leading characters from the line. I read  that calls for 'read' input within a 'while read' loop can cause problems, and wonder if the ffmpeg call is doing something that confuses bash, but this seems unlikely and bizarre! NB: I don't really understand the ffmpeg call - I got it from an answer to another question.  Any help would be appreciated!  The first 'read' works as expected (and the ffmpeg command completes):  LINE  1 vidsNeedingSound/448£generic@06_10_16-09_30_47.mp4 soundToAdd/448£generic@06_10_16-12_11_54.wav 6.988354 V: vidsNeedingSound/448£generic@06_10_16-09_30_47.mp4   A: soundToAdd/448£generic@06_10_16-12_11_54.wav   D: 6.988354   The second 'read' loses 36 characters from the beginning of the line (and the ffmpeg command fails because the file represented by the variable V which takes the first item of the line doesn't point at a file):  LINE  2 6-09_30_47.mp4 soundToAdd/452£generic@06_10_16-12_11_54.wav 9.64663 V: 6-09_30_47.mp4   A: soundToAdd/452...   The third 'read' works as expected (and the ffmpeg command completes):  LINE  3 vidsNeedingSound/452£left@06_10_16-09_30_47.mp4 soundToAdd/452£left@06_10_16-12_11_54.wav 9.862118 V: vidsNeedingSound/452£left@06_10_16-09_30_47.mp4   A: soundToAdd/452...   The fourth 'read' loses 37 character (one more than the last fail) from the beginning of the line (and the ffmpeg command fails):  LINE  4 09_30_47.mp4 soundToAdd/452£right@06_10_16-12_11_54.wav 9.431392 V: 09_30_47.mp4   A: soundToAdd/452....   That's the pattern. When not preceded by a successful call to ffmpeg, the 'read' works as expected. After each successive successful ffmpeg call, characters are omitted from the beginning of the line: 36 characters to begin with, then 37, 38, 39...  The clincher is that when ffmpeg fails after a 'successful' read (due to another problem), the following 'read' works as expected.  CONCLUSION: a successful ffmpeg call results in a read fail on the next iteration through the loop.  Why does this happen, and how can I stop it?  Here's my code: ...  # Loop through lines in the merge file IT_COUNT=1 while read MERGE_LINE                do              echo "LINE " $IT_COUNT     ((IT_COUNT+=1))     echo $MERGE_LINE   # testing use     read VID_FILE AUD_FILE DURATION &lt;&lt;&lt; "$MERGE_LINE" # Get the data from each line     echo "V: $VID_FILE   A: $AUD_FILE   D: $DURATION"         # testing use ....     # add audio to video     ffmpeg -i $VID_FILE -i $AUD_FILE -filter_complex "aevalsrc=0:d=$AUD_SHIFT[s1];[s1][1:a]concat=n=2:v=0:a=1[aout]" -c:v copy -map 0:v -map [aout] $FILE_OUT -hide_banner  done &lt;$MERGE_FILE     Thanks for looking! We have a group of three characters: The lawful good paladin (acolyte), the lawful good fighter (soldier) and the chaotic good druid (criminal). All try to help NPCs in need, won't fight between themselves, but of course have different alignments and personalities. The druid is greedy, but otherwise a good guy. This brought up the question for our group whether greed can be considered a contradiction to having a chaotic good alignment? I understand it as "acting upon what is good, but having your own understanding of 'good'". But I am not sure if the PC being is played 'wrong'.   How do you determine if a given action is in line with a PC's alignment? And should the GM intervene if a PC is played differently that his/her alignment indicates?  Example: There is a Chaotic Good druid with a criminal background. The druid attacked caravans who destroyed his homeland, which he was protecting as his druidic duty, to make way for faster trade routes. Thus he made a name of himself and soon had quite a pile of goods in his territory. The thieves guild caught wind of that and made a deal with him to smuggle wares through his territory as long as they won't hurt the wildlife. So far, seems like a reasonable match between criminal and CG.  Upon opening a chest in a dungeon the druid found a magic chainmail and a bag filled with 420gp. As he was the only one next to the chest, he turned around and told his two comrades there were 360gp in the chest, keeping an extra 60gp to himself without them knowing. Later after finishing a task for the mayor the druid and the paladin persuaded him to give them 550 instead of 500gp, while the fighter was drunk outside. The druid told the paladin to keep his share of those 10% extra, as a gift for always being successful on those charismatic tasks. This was done to check out the personality of the paladin. He accepted without a second of doubt and didn't even contradict when the druid told him not to tell the fighter anything about the extra.   I am now confused about whether this is just unlawful or also not good, and if so what should I as DM do about it?