Why did R.A.B even use the fake locket at all? Sirius's brother Regulus took Kreacher to the cave, drank the potion, and swapped the real locket for a fake one.  Inside the fake one was a note telling whoever happened to find the locket--most likely Voldemort--his initials and exactly what he'd done. Voldemort is pretty smart, he would probably figure out everything, kill Kreacher, and take the locket back.  So why did Regulus even bother making a fake locket?  And once he had, why did he put the note in the locket?  It just seems stupid to me.
Why did R.A.B. put the locket back in the basin? led me to asking this one. R.A.B. takes the "real" locket out and asks Kreacher to destroy it, then puts the "fake" locket back in the basin. Why would he feel the need to do this? He knows already that Voldemort has used someone else to drink the potion (Kreacher). In fact Kreacher's story to him about his mistreatment on the island seems to push him over the edge to act.   Instead of assuring that someone else (most likely innocent like Kreacher) would have to drink from the basin, why not just leave the note outside the basin for someone to find? If Voldemort finds it then so be it, at least then no presumably innocent person would have to drink again.
Prove that if $B$ is the set of rationals in $[0,1]$ with a finite subcover, then: $1 \leq \sum_{k=1}^n m^*(I_k)$ I have the following homework problem:  Let $B$ be the set of rational numbers in the interval $[0,1]$, and let $\{I_k\}_{k=1}^n$ be a finite collection of open intervals that covers $B$. Prove that $\sum_{k=1}^n m^*(I_k) \geq 1$.    This is my approach, First we have that $B = \mathbb{Q}\cap [0,1]$. Now, $B \subset \bigcup_{k=1}^nI_k$, where $I_k$ are open intervals.In particular $0 \in B \wedge 1 \in B$.Now, since $B \subset \bigcup_{k=1}^nI_k$ then there exist positive numbers, $\epsilon_0, \epsilon_1$ such that: $$(0-\epsilon_0,0+\epsilon_0)\subset \bigcup_{k=1}^nI_k$$ $$(1-\epsilon_0,1+\epsilon_0)\subset \bigcup_{k=1}^nI_k.$$   Clearly, $-e_0 \notin [0,1]$ and $e_1 \notin [0,1]$.I am not sure, if so far I am in the right track. How to show this property of $\mathbb{RP}^{n}$. To prove that: The $n$-dimensional projective space can be presented as:  $\mathbb{RP}^n=\bigcup_{i=0}^{n} A^{i}$.  (The intersection of each two $A^{i}$ is empty)، $A^{i}$ is isomorphic to $\mathbb R^{i}$ ($A^{0}$ includes only one point). The definition of $\mathbb{RP}^n$ is: $\mathbb{RP}^n= (\mathbb R^{n+1} \setminus \{0\})/ \sim$ , $\sim$ is defined as: $x \sim \lambda x$for all $\lambda\in \mathbb R^\times$ and $x\in \mathbb R^{n+1} \setminus \{0\}$. $\mathbb R^\times $ is the productive group of scalars $\ne0$ in the field $\mathbb R$. I'm just a beginner in this field so any help would be appreciated. cin>> not work with getline() Are there any examples of $\frac{a}{b}+\frac{c}{d}=\frac{a+c}{b+d}$? I am writing a short discussion of Farey numbers and was wondering if there are any examples of when the mediant function is ever actually equal to the sum of the two fractions in the usual sense? (Not to produce Farey numbers, I just thought it might be an amusing way to introduce Farey addition).   Explicitly: Are there any examples of fractions $\frac{a}{b}$ and $\frac{c}{d}$ where  $$\frac{a}{b}+\frac{c}{d}=\frac{a+c}{b+d}$$ for positive integers?   Currently I have found the example  $$\frac{1}{1}+\frac{1}{i} =\frac{1+1}{1+i}$$ if we remove the integers requirement but it would be nice to find a case that didn't involve complex numbers though! ${!FOO} and zsh ${!FOO} performs a double substitution in bash, meaning it takes the (string) value of FOO and uses it as a variable name. zsh doesn’t support this feature.  Is there a way to make this work the same in bash and zsh?  Background:  I’ve got a list of environment variables, like  PATH MAIL EDITOR   and want to first print the variable names and afterwards their values.  This works in bash but not zsh:    for VAR in LIST do         echo $VAR         echo ${!VAR} done   It should be somehow possible “the old way” with eval, but I can’t get it to work:  for VAR in LIST do         echo $VAR         echo `eval \$$VAR` done   I’m never going to understand why I can’t simply do arbitrary deep substitutions like ${${VAR}} or even ${${${VAR}}} if need be, so an explanation for that would be nice, too. When traveling to a country with a different currency, how should you take your money? What does $(command) & do? Why is "ask" sometimes pronounced "aks"? We've recently moved from New Zealand to New York City, and have noticed that many people (most of whom have good English) pronounce "ask" as "aks". For example:     Could you please go aks her tomorrow?   Sure, I'll ax her! :-)  What's the origin/etymology of "aks"? It seems to be more common among African Americans, but it's definitely used by others too. equivalent norms in Banach spaces of infinite dimension Has it been practically proven that quantum superposition exists ? If yes, how does it even work? give a variable to an operator For a workflow tool I made a panel in which it displays each separate library that is linked in my file. For each library I want to add some buttons that does stuff to the library in question.  So in this example I have my panel which shows for example 2 libraries and for each one it creates a "reload" button.  Now my question is.. How do I make it so the reload button only reloads the library I want to reload? I would probably have to give the button an id or something so it knows for which library it was created...  my code so far:  import bpy  libs = bpy.data.libraries  class Reloadlib(bpy.types.Operator):     """Reloads the current Library"""     bl_idname = "my.reload_lib"     bl_label = "Reload"      def execute(self, context):         libs[?????].reload()         self.report({'INFO'}, 'Reloading ' + libs[?????].name)         return {'FINISHED'}  class LibPanel(bpy.types.Panel):     """Creates a Panel in the scene context of the properties editor"""     bl_label = "Scene Libraries"     bl_idname = "SCENE_PT_layout"     bl_space_type = 'PROPERTIES'     bl_region_type = 'WINDOW'     bl_context = "scene"      def draw(self, context):         layout = self.layout         scene = context.scene         layout.label(text="Libraries:")          for i in libs:             layout.label(text= i.name.replace(".blend",""))             row = layout.row()             sub = row.row()             sub.operator("my.reload_xref", icon = "FILE_REFRESH")  def register():     bpy.utils.register_class(Reloadlib)     bpy.utils.register_class(LibPanel)  def unregister():     bpy.utils.unregister_class(Reloadlib)     bpy.utils.unregister_class(LibPanel)  if __name__ == "__main__":     register()   Where the question marks are is where I should be able to make the difference between the first [0] or second [1] library in the libs[] array.  In future I would also like to ad an 'open' and an 'unlink' button for each library so I can make changes to the other file. But this works by the same principle as the reload button. Any Video formats that render with Alpha Channel? Does anyone know if there are any video formats (besides the HUGE uncompressed avis) that you can render in that maintain the alpha channel? (i.e. for after FX etc.)   I used to use quicktime, but that's no longer an option.  I know you can render in png. or other image formats, but video is significantly smaller, and I often work on machines with less space &amp; resources. How to replace forward slash with backward slash Possible to lock focal length on zoom lens? (SELP1650) (This could turn out to be a bone, practical, product-specific query, but this is the internet so the worst that could happen is a 0 rather than a 1.)  Anyhoo: is it possible to lock a zoomable lens to a certain focal length? Is this a typical feature for a lens?  I want to keep my SELP1650 at X mm to help with some creative experiments, but the thing shifts whenever I move my hand against the lens ring. Does SELP1650 (or the body, Sony A6000) specifically have this option?  Or... is there a reasonably non-goofy DIY trick I could pull off, without bricking the thing? (anticipating a sarky 'duct tape' suggestion) Is it possible to walk between all three terminals in Dubai Airport without leaving airside? We are arriving into Terminal 2 on the 28th December and want to go to the business lounge in Terminal 1 before getting a flight from Terminal 3 eight hours later. The minimum system requirements for 18.04 are "2 GHz dual core processor or better"; would a quad-core at 1.8 GHz meet (or approximate) this requirement? What color codes can I use in my PS1 prompt? I used several colors in my PS1 prompt such as   \033]01;31\] # pink \033]00m\]   # white \033]01;36\] # bold green \033]02;36\] # green \033]01;34\] # blue \033]01;33\] # bold yellow   Where can I find a list of the color codes I can use?  I looked at  but it didn't answer my question about a list of the actual codes.  It would be nice if there was a more readable form also.  See also I'm trying to create an annotated bibliography. Here's my .tex document:  \documentclass[12pt]{article} \title{Annotated Bibliography}  \begin{document}  \nocite{*}  \bibliography{annotatedbib}  \end{document}   And here is the associated .bib document:  @Misc{hacker,     AUTHOR = `{Andrew Hacker'},     TITLE = {Is Algebra Necessary?},     HOWPUBLISHED = {New York Times},     MONTH = {July 31},     YEAR = {2012},     ANNOTE = {This article was published in the New York Times.}, }   No matter into which format I compile my .tex document, the annotation will not show up! Is there something that I'm missing? Product norm on infinite product space I wonder whether it is possible to perform within R a clustering of data having mixed data variables. In other words I have a data set containing both numerical and categorical variables within and I'm finding the best way to cluster them. In SPSS I would use two - step cluster. I wonder whether in R can I find a similar techniques. I was told about poLCA package, but I'm not sure ...