It's clear that in the game of D&amp;D, 'good' and 'evil' are objective. The 5th edition Player's Handbook gives a few small examples of alignment behaviour on page 122, such as:     Lawful Good (LG) creatures can be counted on to do the right thing as expected by society.   or     Neutral Evil (NE) is the alignment of those who do whatever they can get away with, without compassion or qualms.   These and other examples in the PHB suggest that helping others or 'following your conscience' are good acts, whereas theft and violence are evil acts. Thus, it seems 'good' is somewhat open to interpretation - it involves having a moral or civil 'conscience'.  Alignment gets another short mention in the chapter on spellcasting, in the sidebar on page 203:     Creating the undead through the use of necromancy spells such as animate dead is not a good act, and only evil casters use such spells frequently.   This is again a little unclear - by describing it as 'not good' it leaves both 'neutral' and 'evil' available, but goes on to say it's only used frequently by evil casters.  My question is, are there any other references, in particular more specific ones, to what constitutes a good or evil act in D&amp;D 5th edition?
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?
How to initialize all members of an array to the same value? On a fresh install of TL 2018, on Linux, no tikz graph drawing libraries can be found.  The files, e.g. texlive/2018/texmf-dist/tex/generic/pgf/graphdrawing/tex/pgflibrarygraphdrawing.trees.code.tex are there.  \documentclass{scrartcl}   \usepackage{tikz} \usetikzlibrary{graphdrawing} \usegdlibrary{trees}    \begin{document}  Hello World  \end{document}   Compiling with lualatex yields   ! Package pgf Error: Graph drawing library 'trees' not found. Cardinal number subtraction We all know that $|\mathbb{N}| = \aleph_0$. Since $|\{-1\} \cup \mathbb{N}| = \aleph_0$ as well, I guess you could say that $\aleph_0 + 1 = \aleph_0$.  You can go on to derive that $\aleph_0 + \aleph_0 = \aleph_0$, and by induction $n \times \aleph_0 = \aleph_0$ (assuming that $n$ is finite, anyway).  Now, here's a thing: What is $\aleph_0 - \aleph_0$?  Well, $|\mathbb{P}| = \aleph_0$, and $|\mathbb{P} \backslash \mathbb{N}| = \aleph_0$, so perhaps $\aleph_0 - \aleph_0 = \aleph_0$?  No, wait. Consider the set $S = \{n \in \mathbb{N}: n &gt; 5\}$. Now we have $|S| = \aleph_0$, and yet $|\mathbb{N} \backslash S| = 5$. So maybe $\aleph_0 - \aleph_0 = 5$?  But that is absurd, since we can redefine $S$ to make the result any finite number we wish. Or we can define $S$ such that the result is countably infinite.  Does this mean that the notion of $\aleph_0 - \aleph_0$ simply has no definite answer? Or am I just being too simplistic here? How to understand the Ubuntu file system layout? I am looking for a pipe symbol that can be made to vary in height automatically.  One of the common ways of writing "such that" in mathematics is with the pipe symbol (|). The pipe can be represented in LaTeX directly as the character | or as \vert, but neither of these expands vertically in math presentation mode. I can adjust it manually this way:  \[\mathcal{H}=\left\lbrace h(x)=\sum_{i=0}^{k-1}a_{i}x_{i}\mod m\ \Bigg\vert      \ a_{i}\in\mathbb{Z}_{m^{k}}\right\rbrace\]     but I am looking for a true variable-sized option, parallel to \lbrace etc.  The amsmath package provides \lvert and \rvert, but I do not find them expanding as expected, and the amsmath documentation specifies that they should be used as binary delimiters (one on each side of something else), rather than alone. System Settings icons missing in 14.04 If I roll two fair dice, the probability that I would get at least one 6 would be.... Determining application path in a Python EXE generated by pyInstaller I have an application that resides in a single .py file.  I've been able to get pyInstaller to bundle it successfully into an EXE for Windows.  The problem is, the application requires a .cfg file that always sits directly beside the application in the same directory.  Normally, I build the path using the following code:  import os config_name = 'myapp.cfg' config_path = os.path.join(sys.path[0], config_name)   However, it seems the sys.path is blank when its called from an EXE generated by pyInstaller.  This same behaviour occurs when you run the python interactive command line and try to fetch sys.path[0].  Is there a more concrete way of getting the path of the currently running application so that I can find files that are relative to it? I was wondering why binary crossentropy can be used as the loss function in autoencoders trained on (normalized) images, e.g.  or ? I know that binary crossentropy can be used in binray classification problems where the ground-truth labels (i.e. $y$) are either 0 or 1 and therefore when predictions (i.e. $p$) are correct, in both cases, the loss value would be zero:  $$ BCE(y,p) = -y.log(p) - (1-y).\log{(1-p)} $$  $$ BCE(0,0) = 0, BCE(1,1) = 0 $$  However, binary crossentropy does not have a value of zero when neither of its arguments are both zero or one, which is the case for an autoencoder with ground-truth labels in range $[0,1]$ (i.e. assuming the input data has been normalized in this range). I thought a regression loss function such as mean squared error or mean absolute error must be used instead, which have a value of zero when labels and predictions are the same. What am I missing here? Here is the problem setup  \begin{equation} \begin{array}{c} \text{min} \hspace{4mm}  \mathbf{b}^{T}_{}\mathbf{A}^{}_{}\mathbf{b}^{}_{} \\ s.t \hspace{5mm} \mathbf{b} \in \mathbb{R}^{N} \\ \hspace{9mm}b_0=1\\ \hspace{62mm}b_i=b_{i-2}b_{i-1} \hspace{5mm} \forall \hspace{5mm} 2&lt;i\leq N-1 \end{array} \end{equation}  where $\mathbf{A}$ is a $N\times N$ positive semi-definite matrix  To handle $b_0=1$ constrain, I know I can introduce Lagrange multiplier in objective function  \begin{equation} \begin{array}{c} \text{min} \hspace{4mm}  \mathbf{b}^{T}_{}\mathbf{A}^{}_{}\mathbf{b}^{}_{} + \lambda(\mathbf{b}^{T}_{}\mathbf{u}^{}_{}-1) \end{array} \end{equation}  where $\mathbf{u}_{}^{}$ is a $N\times 1$ column vector and $u_0=1$ and $u_i=0 \forall 1&lt;i\leq N-1$.  But I dont know how to handle second set of constraints?   EDIT: Example  Let $N=4$. Therefore I am looking for $\mathbf{b}=[b_0 \quad b_1 \quad b_2 \quad b_3]^T = [1 \quad b_1 \quad b_2 \quad b_1b_2]^T$. How do I include $b_3=b_1b_2$ constraint in objective function can I use same functions with the different type of argument inputs The problem:  Consider the smooth quadric $Q=V(X_{0}X_{1}+X_{2}X_{3}+X_{4}^{2})\subset\mathbb{P}^{4}$ and the line $L=V(X_{0},X_{2},X_{4})$ contained in it. Prove that there exists a vector bundle $F$ on $Q$ with a section vanishing exactly at $L$.  The hardest thing is to get the transition matrices. Any help is appreciated. Natural number solutions to $\frac{xy}{x+y}=n$ (equivalent to $\frac 1x+\frac 1y=\frac 1n$) I have a question about the following problem from a Putnam review:  Let $n\in \mathbb{N}$. Find how many pairs of natural numbers $(x, y)\in \mathbb{N}\times \mathbb{N}$ solve $$ \frac{xy}{x+y}=n. $$  I have found some solutions for all $n$, such as $(2n, 2n)$ and $(n+1, n(n+1))$, but I feel as though this is the wrong approach, as the question is only asking for the number of solutions to the equation.  I don't really want a complete solution, but any hints would be greatly appreciated. Audits bug in the filtered review queue Just recently the . I've got  this morning which seems to be out of scope for my filtered list. I have filtered my list to only review VBA and Excel-VBA tags while the audit is tagged with perl http pipes which have nothing in common with VBA. I see a problem with the way the system currently works  Since I have a filtered list of tags, once I see a differently tagged question I already know it's an audit. Come on, that's too easy!  Can this please be fixed? update I have ran into  which I decided to edit - the question was tagged VBA and I thought it had nothing to do with VBA so I selected Edit which was the correct action. Now, once the first audit was clearly one to close - nothing to do with VBA and really easy to know that it actually was an audit - the second one was a very good audit. I am just thinking now if this is a proper bug or just a matter of malfunction in the system. I think the first one may have been made an audit for the wrong reason. Let's turn this into a discussion as I can't clearly work the system out. Do stars remain electrically neutral? Set of branch points isn't discrete, but branch points are isolated? I refer to , which I understand says that the branch points of a nonconstant holomorphic map $F: X \to Y$ between Riemann surfaces $X$ and $Y$, both of which are not necessarily compact, form a discrete subset of range $Y$ of the map $F$. (Not sure if 'connected' is part of the definition of Riemann surfaces in other textbooks, but it is here.) Question 1: Do I understand correctly, and is this indeed true? What else I understand:  $A$ is a discrete subspace/subset (I just assume everything here is the usual subspace topology) of $B$ if and only if every singleton subset of $A$ is open in $A$ if and only if every point of $A$ is isolated.  This overflow question () seems to suggest this is not true but is true if $F$ is proper. However, I'm not sure the definitions of Riemann surface are the same (maybe some answers use definitions where Riemann surfaces are not necessarily connected or something).  2.1. I know $F$ is 'discrete' (meaning that its fibres are discrete; here, i refer to a ): see definition before Lemma 3.1, on p. 7), by Proposition II.3.12, and open, by open mapping theorem, which is Proposition II.3.8, but I'm not sure these help show $F$ is proper or are otherwise helpful. Ostensibly 'discrete' maps don't map discrete subsets to discrete subsets.   This stackexchange question () seems to suggest this is true.  I think this is true if $F$ is injective or at least something like locally injective. (Please don't make me type up all the stuff I did for this part.) However based on the question in (3) and based on the , which I think uses the term 'branch points' to mean the same thing as what Miranda means by 'ramification points' (and thus is different from Miranda's 'branch points'), it seems that no neighbourhood $U$ of a ramification point $p \in U \subseteq X$ of $F$ is such that the restriction $F|_U$ is injective.  Kinda related:    This page () says    Now, the ramification and branch points must form a discrete set  I don't think the page assumes anything like $F$ is proper.  The  text in (2.1) actually seems to assume proper based on the '3.7. Proper holomorphic maps' part, but said part refers to 'Lemma 3.17', so I think proper can be replaced with closed. Maybe $F$ is closed or something.  Kinda related (see Question 2 below):     says    If $F$ is proper then the image $\Delta = F(R)$ is discrete in $Y$.   This seems to have all the same assumptions as with Miranda. Ostensibly, either Miranda is wrong or there's some higher level machinery that allows us to omit $F$ proper.  Question 2: To possibly generalise this, what are the minimum requirements on $F, X$ and $Y$ to make $F$ map discrete subsets to discrete subsets? I mean, I'm not sure we really need 'holomorphic' here. I have a feeling this applies perhaps to maps that are just open/closed, continuous and discrete and spaces that are just Hausdorff and locally compact or something.  (again) Kinda related: Is there a command to delete all the files in a directory that haven't been modified in N days?  I need to clean up some old logs. How to display Trash and Home folder icons? I've googled quite a bit but nothing I've found works. I just want to display the Trash, Home folder, Computer etc icons on my Desktop in Ubuntu.  The closest I've come is installing dconf-tools, running it, going to org -&gt; gnome -&gt; desktop -&gt; background and checking show-desktop-icons then org -&gt; gnome -&gt; nautilus -&gt; desktop and checking the icons I want to show.  Nothing happens.  I've also tried looking in compizconfig-settings-manager and gconf-editor but can't find anything there.  Ideas? Status-* tags - moderator only? Round function in Excel, worksheet function vs VBA I had an application for returning closest matches to certain values in a large  cluster of values( as in my earlier )   and I chose a VBA solution. While in the course of using the said application, I observed that the results for the value of 0.5 were not correct. I had been using the VBA Round function which I found to be returning 0 for 0.5 rounded to integer whereas the worksheet round function returns 1. Strangely, the VBA round function returns 2 for 1.5. I had to substitute the worksheet function in place of the VBA one.  Am I missing something?