Use of "have/has" when you don't know if the subject will be singular or plural
When a sentence uses a parenthetical plural, should the rest of the sentence treat it as singular or plural?
Why "a user" instead of "an user"? I am getting confused while using an article an. Because an is used while referring to vowels (a,e,i,o,u).  But today I read an article where for user they used a user.  My question is, why was an not used?  Could someone explain this with an example? Wild Magic Surge - What does "You cast ..." mean for your spell slots? In response to  question, I started to think about what it means when a Wild Magic Surge results in a "You cast spell-X".  So, "specific beats general" gives:   You can cast a second spell when you would not normally be allowed to You can cast a spell you don't know If the surge forces you to cast a concentration spell you would lose any concentration spell that you currently had active Subject to what the specific entry says you can target it how you like Unless the specific entry prohibits it you could use metamagic on the spell   I am pretty confident in all of the above but if anyone disagrees please address in an answer.  Here comes the question.  How does this impact on your available spell slots?  "You cast ..." to me suggests that if you have an applicable slot available then you have to use it to cast the spell because that is the general rule for casting spells but if you don't then "specific beats general" and it is cast anyway.  Specific examples:     You cast fireball as a 3rd-level spell centered on   yourself   This must be a 3rd level spell:   if you have a 3rd level slot available you have to use it? if you don't, if you have 5 sorcery points and a bonus action available must you use these to get that slot? if you don't have any of that then the spell goes off anyway?      You cast confusion centered on yourself.   No level specified and confusion is a 4th level spell:   if you have a 4th level slot available you have to use it? if you have a 4th, a 6th and an 8th level slot you can choose which one to use? if you have only a 5th level slot but also 6 sorcery points and a bonus action, you could choose to use the 5th level slot or use the points to create a 4th level slot? if you don't have any 4th level or higher slots but you have 6 sorcery points and a bonus action available must you use these to get that slot? if you don't have any of that then the spell goes off anyway?   And so on ... Today I was thinking about composition of functions.  It has nice properties, its always associative, there is an identity, and if we restrict to bijective functions then we have an inverse.  But then I thought about commutativity.  My first intuition was that bijective self maps of a space should commute but then I saw some counter-examples. The symmetric group is only abelian if $n \le 2$ so clearly there need to be more restrictions on functions than bijectivity for them to commute.  The only examples I could think of were boring things like multiplying by a constant or maximal tori of groups like $O(n)$ (maybe less boring).  My question: In a euclidean space, what are (edit) some nice characterizations of sets of functions that commute? What about in a more general space?   Bonus: Is this notion of commutativity important anywhere in analysis? It is well known that quantum mechanics and (general) relativity do not fit well. I am wondering whether it is possible to make a list of contradictions or problems between them?  E.g. relativity theory uses a space-time continuum, while quantum theory uses discrete states.  I am not merely looking for a solution or rebuttal of such opposites, more for a survey of the field out of interest. What causes close votes to be annotated with "(deleted)"? In the "Votes Cast" section of my profile, my vote to close  is annotated with "(deleted)":    However, the close vote does not appear to have been deleted: it successfully closed the question:    Why was this vote marked as "(deleted)"?    If the vote was deleted my some internal process after the question was closed and the closers were recorded, I call that a . Regardless of what happens internally, it's irrelevant to users if close votes are deleted after they have taken effect. How many cpu sockets does Windows 10 support? I would like to build a new computer (it's been 7 years since the last one). Does Windows 10 support more than one ? How to Upgrade Ubuntu 12.04.2, 12.04.3 to 12.04.4, the next Hardware Enablement Stack? I am currently using Ubuntu 12.04.2 32bit. I installed it using LiveCD.  Tomorrow, 23rd August 2013,Ubuntu 12.04.3 is released. I want to upgrade from Ubuntu 12.04.2 to Ubuntu 12.04.3 without using any LiveCD. Is it possible? If so please suggest me how can I do.  Actually while using Ubuntu 12.04.2 I have troubled with graphics. My graphics card is Intel i845G 64 MB. When Ubuntu starts it works fine and smooth without any lagging, but after sometime it hangs for few seconds (1 or 2 seconds) with a garbage screen and becomes sluggish. All windows and browsers start lagging and also it is not possible to play any video in any player (VLC, Movie Player, Xnoise, SMPlayer etc..).  I think Upgrading to Ubuntu 12.04.3 could fix my problem.  Any help will be greatly appreciated..    I've posted an answer to upgrade Ubuntu 12.04.x to 12.04.4. Apply a string replacement on the citation as returned by \cite I have biblatex with options  \usepackage[backend=bibtex, style=authoryear]{biblatex}   The citations made with \cite look like this: Smith, 2019 or Smith and Baker, 2019 and so on. I would like to define a command that automatically replaces the occurrence of my name with my initials. Namely I need  \cite{SmithsPaper}  % --&gt; Smith, 2019 \cite{MyPaper}      % --&gt; Manny, 2019 %%% \newcite{SmithsPaper}  % --&gt; Smith, 2019 \newcite{MyPaper}      % --&gt; MC, 2019   I have tried with the package xstring to do something like  \newcommand{\newcite}[1]{%   \begingroup   \edef\@temp{\cite{#1}}%   \StrSubstitute{\@temp}{Manny}{MC}   \endgroup }   The problem is that I can't figure out how to tell LaTeX to expand \cite{#1}. As a result the citation comes out without the replacement. If I change \cite{#1} by simply #1 and I call \newcite{bla Manny bla} it gives bla MC bla as expected.  It shouldn't be relevant but I'm using this within the beamer documentclass. How to have separated but vinculated multiple Ubuntu One accounts? Should we allow adding rep to bounties to extend their duration? There are a few variables here that I was thinking about:   Spend rep to extend a bounty for a certain amount of time Allow the rep spent to extend duration to add into the original bounty Create minimums on the amount necessary to extend dependent on how long it has been up   These are just ideas and can be tweaked as necessary, but the idea in whole is to encourage people to spend more on rep and avoid "wasted" rep because there wasn't a good answer to a question while minimizing the amount of possible abuse. This was part of the idea to spend a small amount of rep to extend duration without adding to the rep so that you wouldn't have to spend the whole amount over again for a couple more days.  The typical use case that I am thinking of is when you create a bounty and it still gets no attention. I think it would be cool if you could then add onto it to turn it into a higher bounty instead of having those points completely gone.  Possible abuses:   Keeping bounty questions alive for inappropriately long times. There is already an answer but the author does not want to award the bounty.   For 1, you can resolve this by increasing the amount necessary to keep a question alive exponentially similar to what is already in place. You could also halve the amount of extended duration per extension. For 2, this is a problem with the existing system as well, but the author does not have a positive incentive not to award the points since he himself still cannot get them back. After Factory Reset, In order to use Play store and Gmail I want to setup Google account on Samsung GT-S6802. When I tries to setup Google Account, In-spite of right user-name and password, following window appearers:    When I open gmail form browser, I've mail from google subject:Sign-in attempt prevented and says:     Someone just tried to sign in to your Google Account hidden@gmail.com from an app that doesn't meet modern security standards.     When I review, it shows unknown device but on browser it detects my device.  So, How do I face this issue and setup google account? Can't replace block with a Command Block I am making a Sell Shop, but I need to replace some things using /setblock.  For one of the replacements, I am using the command:  /setblock 579 62 1053 minecraft:command_block 0 replace {Command:"testfor @p {Inventory:[{id:"minecraft:log",Count:32b}]}",TrackOutput:0}  But it won't work! When I try it using a Command Block, I get this message:     [19:14:38]   Data tag parsing failed: Unexpected token 'm' at: minecraft:log",Count:32b}]}",TrackOutput:0   Is there any way I can fix this? Black and white beads on a circle There are $n$ beads placed on a circle, $n\ge 3$. They are numbered in random order as viewed clockwise. Beads for which the number of the previous bead is less than the number of a next bead are painted in white color,and others - in black.  Two colourations that can be made equal by rotation are considered identical. How many different colourations can occur?  I've write a programm and for $n=3...11$ I've got answers $2 , 1 , 6 , 7 ,  18 , 25 , 58 , 93 , 186$ Deploying a static site on AWS EC2/nginx: what am I doing wrong? Why are the longer edges being beveled more? I'll preface this by saying I'm very new to Blender - I'm trying to put a bevel on an edge, looks something like this:    As you can see, the vertical side is much longer than the horizontal side.  When I apply to bevel to the edge there, the bevel stretches proportionally - so there's 'more' bevel on the longer side.  I want to bevel without any 'ratio' like that - just a 45-degree bevel, if that makes any sense.  Do I have to put in a loop cut to make the side lengths equal?  I tried using a sub-surf modifier, but it applies on a bunch of nearby edges, when I just want to round this one corner. Gnome terminal will not start I just tried to install python 3.6 on my Ubuntu 16.04 system, and now I can't run the terminal from the launcher or from Ctrl + Alt + T. I tried to run gnome-terminal from XTerm and got the following message:  Traceback (most recent call last):   File "/usr/bin/gnome-terminal", line 9, in &lt;module&gt;     from gi.repository import GLib, Gio   File "/usr/lib/python3/dist-packages/gi/__init__.py", line 42, in &lt;module&gt;     from . import _gi ImportError: cannot import name '_gi' Error in sys.excepthook: Traceback (most recent call last):   File "/usr/lib/python3/dist-packages/apport_python_hook.py", line 63, in apport_excepthook     from apport.fileutils import likely_packaged, get_recent_crashes   File "/usr/lib/python3/dist-packages/apport/__init__.py", line 5, in &lt;module&gt;     from apport.report import Report   File "/usr/lib/python3/dist-packages/apport/report.py", line 30, in &lt;module&gt;     import apport.fileutils   File "/usr/lib/python3/dist-packages/apport/fileutils.py", line 23, in &lt;module&gt;     from apport.packaging_impl import impl as packaging   File "/usr/lib/python3/dist-packages/apport/packaging_impl.py", line 23, in &lt;module&gt;     import apt   File "/usr/lib/python3/dist-packages/apt/__init__.py", line 23, in &lt;module&gt;     import apt_pkg ModuleNotFoundError: No module named 'apt_pkg'  Original exception was: Traceback (most recent call last):   File "/usr/bin/gnome-terminal", line 9, in &lt;module&gt;     from gi.repository import GLib, Gio   File "/usr/lib/python3/dist-packages/gi/__init__.py", line 42, in &lt;module&gt;     from . import _gi ImportError: cannot import name '_gi'   How can I fix this error?  It should also be noted that:   My gnome-terminal file is now a python script. The gnome-terminal.real file will open the terminal as expected. python3.5 gnome-terminal will open the terminal as expected. Consider the space of continuously differentiable functions, $$C^1([a,b]) = \{f:[a,b]\rightarrow \mathbb{R}\mid f,f' \text{ are continuous}\}$$ with the $C^1$-norm $$\lVert f\rVert := \sup_{a\leq x\leq b}|f(x)|+\sup_{a\leq x\leq b}|f'(x)|.$$ Prove that $C^1([a,b])$ is a Banach Space.   This was the proof we were given: Assuming $C^1([a,b])$ is a normed linear space all we need to show is completeness. Let $(f_n)$ be a Cauchy Sequence in $C^1([a,b])$ with respect to the $C^1$-norm. Then each $f_n,f'_n\in (C([a,b]),\|\cdot\|_{\sup})$. We know that $C([a,b])$ is complete and thus there exists $f,g\in C([a,b])$ such that $f_n\rightarrow f$, and $f'_n\rightarrow g$ (uniformly) with respect to $\|\cdot\|_{\sup}$. If we let  $$ F_n(x) = \int_a^x f_n(t)dt, \hspace{2mm}  F(x) = \int_a^x f(t)dt $$ then $F_n\rightarrow F$ uniformly because  $$\lVert F_n-F\rVert_{\sup}\leq \sup_{a\leq x\leq b}\int_a^x|f_n(t)-f(t)|dt\leq \lVert f_n-f\rVert_{\sup}&lt;\epsilon.$$ From the fundamental theorem of calculus: $$f_n(x)-f_n(a) = \int_a^x f'_n(t)dt $$ Since $f'_n\rightarrow g$ uniformly then  $$ \int_a^xf'_n(t)dt\rightarrow \int_a^x g(t)dt $$ Since we know that $f_n\rightarrow f$ uniformly, $$f(x)-f(a) = \int_a^x g(t) dt $$ which by the fundamental theorem of calculues implies $f'=g$. So we know have $f_n\rightarrow f$ and $f'_n\rightarrow g=f'$ which mean $f_n\rightarrow f\in C^1([a,b])$ with respect to $C^1$-norm. So every cauchy sequence converges. Hence $C^1([a,b])$ is a Banach Space.   So I understand most of the proof. Where I get confused is that how did we actually show this satisfies the $C^1$-norm? Maybe I don't understand what this norm actually does.   Thank you for any help, comments and advice! What Scoping Class Will  Use? In reading through the release notes I was excited to discover the introduction of a new  tag. That should help lower the barriers to entry! However, the release notes do not specify what the name of the scoping class should be. And since , we're left guessing.  To be explicit about what I'm trying to understand, take  for example:  &lt;apex:page showHeader="false" standardStylesheets="false" sidebar="false" applyHtmlTag="false" applyBodyTag="false" docType="html-5.0"&gt;     &lt;html xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" lang="en"&gt;         &lt;head&gt;             ...             &lt;apex:stylesheet value="{!URLFOR($Resource.REPLACE_WITH_NAME_OF_SLDS_STATIC_RESOURCE, 'assets/styles/salesforce-lightning-design-system-vf.min.css')}" /&gt;         &lt;/head&gt;         &lt;body&gt;              &lt;!-- REQUIRED SLDS WRAPPER --&gt;             &lt;div class="REPLACE_WITH_NAME_OF_CUSTOM_SCOPING_CLASS"&gt;             ...         &lt;/body&gt;     &lt;/html&gt; &lt;/apex:page&gt;   If I replace the &lt;apex:stylesheet&gt; with &lt;apex:slds&gt;, what should I specify for REPLACE_WITH_NAME_OF_CUSTOM_SCOPING_CLASS? Proof: How many digits does a number have? $\lfloor \log_{10} n \rfloor +1$ I read recently that you can find the number of digits in a number through the formula $\lfloor \log_{10} n \rfloor +1$ What's the logic behind this rather what's the proof? Limit the post for differents custom post type in the same wp_query I have three custom post type:    books magazine videos   Now i want to limit the number of post for custom post type, for example:   books => 3 post magazine => 2 post videos => 1 post   I used a query post like this:  query_posts( array(     'post_type' =&gt; array(     'books',     'magazine',     'videos' ), 'paged' =&gt; $paged, 'posts_per_page' =&gt; 6,  )); $counter = 1; if (have_posts()) :     while (have_posts()) : the_post();   if (($counter == 2) || ($counter == 3) || ($counter == 4)) {         $div = 'alpha';     } elseif(($counter == 6)) {         $div = 'omega';     } else {         $div = '';     }   The problems is i cant limit the numbers by custom post type.  Any idea?  Thank you :)