I came across the following multiple-choice question:     She devoted herself to (      ) for poor people.   The choices are:   caring care be caring have cared   As the preposition "to" can be followed by either noun or gerund (...ing), the most suitable answer is #1, "caring." And I am OK with this.  However, some of my students chose #2 care, as the word can be noun. Is "She devoted herself to care for poor people" an acceptable sentence? I feel it a bit odd, and feel like adding something like "the" to make "the care," but I'm not pretty sure.   I'd appreciate it if anyone could give me some advice on this from native  speaker's point of view.
Some verbs are followed by ing, e.g. I enjoy swimming. We can't say I enjoy to swim. Likewise, some verbs are followed by to, e.g. I decided to make a plan.   Which particular verbs are followed by ing and to? Can you please provide a list for that?  Moreover, which verbs can be followed by both without having the meaning changed?
What is the name of this castle part? A cashier wants to work five days a week, but he wants to have at least one of the Saturday and Sunday off.  In how many ways can he choose the days he will work?  So, in this case, what should I count first?  How do I start?  I know how to solve this if the cashier doesn't want a weekend off, but what do I do if the cashier do?  Thanks! Semicolons at the end of list items In school, we were taught to end each list item with a semicolon. But I have never actually seen this. Can somebody please confirm this? Should we end each list item with anything at all?  I've seen people use periods after each list item, colons, and even commas. But I've never seen a semicolon at the end of each item — and even if I have, it would be that rare that I've forgotten.  Example:   item; item; item; item Reading/Writing a MS Word file in PHP Is it possible to read and write Word (2003 and 2007) files in PHP without using a COM object? I know that I can:  $file = fopen('c:\file.doc', 'w+'); fwrite($file, $text); fclose();   but Word will read it as an HTML file not a native .doc file. Ratio test and the Root test Recently I encountered a problem (the first exercise from chapter four of Atiyah &amp; McDonald's Introduction to Commutative Algebra) stating that if $\mathfrak{a}$ is a decomposable ideal of $A$ (a commutative ring with unity), then the prime spectrum of $A/ \mathfrak{a}$ has finitely many irreducible components. This follows easily from the recognition that the maximal irreducible subspaces of $\textrm{ Spec } (A / \mathfrak{a})$ are precisely the "zero loci" of the minimal prime ideals of $A /\mathfrak{a}$.   I'm curious about the converse - the proof isn't easily reversed since the notion of minimal ideals of $\mathfrak{a} $ doesn't make sense before we know what we are trying to prove. My intuition says that it is false based on the general premise that images are badly-behaved (and the fact that it isn't part of the exercise.) However, I've had some difficulty constructing a counterexample, so that the main purpose of this post is to ask for a reasonable procedure or heuristic for doing so (or, of course, proof that my intuition is false.)   If it helps, if $\textrm{Spec }(A / \mathfrak{a})$ is irreducible then the nilradical $\mathcal{R}_{A /\mathfrak{a}}$ is prime so that $r(\mathfrak{a}) = \rho^{-1} ( \mathcal{R}_{A / \mathfrak{a}} ) = \displaystyle\cap_{i=1}^n \rho^{-1} (p_i),$ where $p_i$ are the minimal prime ideals of $A /\mathfrak{a}$ and $\rho $ is the associated projection, is also prime. Thanks! Rsync, include only certain files types excluding some directories Find the ratio of $\frac{\int_{0}^{1} \left(1-x^{50}\right)^{100} dx}{\int_{0}^{1} \left(1-x^{50}\right)^{101} dx}$ $$I_1=\int_{0}^{1} \left(1-x^{50}\right)^{100} dx$$ and $$I_2=\int_{0}^{1} \left(1-x^{50}\right)^{101} dx$$ Then find $\frac{I_1}{I_2}$  I tried by subtracting $I_1$ and $I_2$   $$I_1-I_2=\int_{0}^{1}\left(1-x^{50}\right)^{100}\left(1-(1-x^{50}\right))dx$$ so  $$I_1-I_2=\int_{0}^{1} \left(1-x^{50}\right)^{100} x^{50} dx$$ Now using Integration by Parts we get  $$I_1-I_2= \left(1-x^{50}\right)^{100} \times \frac{x^{51}}{51}\bigg|_{0}^{1} -\int_{0}^{1} 100 \left(1-x^{50}\right)^{99} \times -50 x^{49} \times \frac{x^{51}}{51} dx$$  So $$I_1-I_2=\frac{5050}{51} \times \int_{0}^{1}\left(1-x^{50}\right)^{99} x^{100} dx$$  Now $x^{100}=\left(1-x^{50}\right)^2-(1-x^{50}-x^{50})$ so  $$\frac{51}{5050}(I_1-I_2)=\int_{0}^{1} \left(1-x^{50}\right)^{99} \times \left(\left(1-x^{50}\right)^2-(1-x^{50})+x^{50}\right)dx=I_2-I_1+\int_{0}^{1} \left(1-x^{50}\right)^{99} x^{50} dx$$  Need a hint to proceed further. I'd like to map an int value pbs_errno declared as a global in the library libtorque.so using ctypes.  Currently I can load the library like so:  from ctypes import * libtorque = CDLL("libtorque.so")   and have successfully mapped a bunch of the functions. However, for error checking purposes many of them set the pbs_errno variable so I need access to that as well. However if I try to access it I get:  &gt;&gt;&gt; pytorque.libtorque.pbs_errno &lt;_FuncPtr object at 0x9fc690&gt;   Of course, it's not a function pointer and attempting to call it results in a seg fault.  It's declared as int pbs_errno; in the main header and extern int pbs_errno; in the API header files.  Objdump shows the symbol as:  00000000001294f8 g    DO .bss   0000000000000004  Base        pbs_errno A big thank you, Tim Post As you may have seen, this was ’s last week at Stack Overflow. To say that he has been a staple of this company for a very long time is an understatement. Tim has served , evangelist, thought leader, anthropologist, psychologist, and mediator for this site for almost as long as it’s been around. For me personally, Tim has been my right hand in this role. He has educated me on the history of our community, been the person I’ve gone to to ask “why is this thing this way?“, bounced ideas off of, collaborated with, and relied on as a steady voice and a thoughtful teammate. We’re all proud to send him off and support him in any way we can in his next role. Tim has agreed to meet with me once a month to talk these things through moving forward and I’m excited to continue getting his feedback on our initiatives and goals. Thank you, Tim, for being such a stalwart here for so long. We’ll miss you, and look forward to sneaking you into our “Among Us” games for as long as we can. We're also excited to see you request to rejoin the ranks of Stack Overflow moderators and continue to be a pillar in the community. How to remove the Unity Amazon package in 16.04? I was able to go to the ubuntu software center before and remove it and now it doesn't show up since the switch to the gnome software store. Trying the terminal method of removing the shopping lens doesn't work in this release. Launch apps full screen I have connected speakers to the back panel of my computer at work and I would like to have them always enabled (I can switch them off on the speaker casing). However when I connect headphones on the front panel system automatically says that the rear output is unplugged.  I found a solution to disable auto detection with Alsamixer and it works almost ok except the fact that after system restart I need to reconfigure the settings again... How can I set this once and forget about it? FoxTrot Bill Amend Problems So I found this on the Wolfram website today:     So I was wondering about how one might be able to (if possible) solve those four problems by hand. Here are the problems, $\LaTeX$ed:    $ \lim_{x \to +\infty} \dfrac {\sqrt{x^3-x^2+3x}}{\sqrt{x^3}-\sqrt{x^2}+\sqrt{3x}} $ $ \displaystyle\sum_{k=1}^{\infty} \dfrac {(-1)^{k+1} k^2}{k^3+1} $  $ \dfrac {\mathrm{d}}{\mathrm{d}u} \left[ \dfrac {u^{n+1}}{(n+1)^2} \cdot \left[ (n+1) \ln u - 1 \right] \right] $  $ \displaystyle\int_0^{2\pi}\displaystyle\int_0^{\frac{\pi}{4}}\displaystyle\int_0^4 \left( \rho \cos \phi \right) \rho^2 \sin \phi \, \mathrm{d}\rho \mathrm{d}\phi \mathrm{d}\theta$     Ideas   The degree of the numerator is $\frac{3}{2}$. The degree of the denominator is $\frac{3}{2}$. The expression is of an indeterminate form, namely $\frac{\infty}{\infty}$, so we use l'Hoptial's Rule.  No ideas, really.  Derivatives are always pretty easy, although this one is a bit bashy. Basically bash Product and Chain Rules, etc.  Integration by Parts bash? The $\mathrm{d}\theta$ part is very trivial. I mean for the $\rho$ and $\phi$. 2 orderby in wp_query with 2 custom fields I'm triyng to display hotels (taxonomy which i have created) by two 'orderby' with wp_query but i'm not success.  Results looks likes:  Hotel 1 :       2 persons          5 stars Hotel 2 :       2 persons          4 stars Hotel 3 :       2 persons          3 stars Hotel 4 :       3 persons          5 stars Hotel 5 :       5 persons          5 stars Hotel 6:        10 persons         2 stars Hotel 7:        10 persons         1 star   The first 'order by' is on the number of persons(the biggest in first) and the second 'order by' is on the rating in stars (so, if several hotels have the same number of persons, the hotel with the biggest stars rating would be in first).  Below my code. I have tried to add an array inside an array with meta_query but it doesn't work.  $args=             array(                                     'post_type' =&gt; 'hotel',                                     'Services' =&gt; $Services,                                     'Town' =&gt; $Town,                                      'meta_key' =&gt; 'Number_persons',                                     'orderby' =&gt; 'meta_value_num',                                     'order' =&gt; 'ASC',                                        'meta_query' =&gt; array(                                                            array(                                                                'meta_key' =&gt; 'Rating',                                                                'orderby' =&gt; 'meta_value',                                                                'order' =&gt; 'DESC',                                                               )                                                        )                  );   $the_query = new WP_Query( $args );   Thanks a lot :) Repeat String - Javascript What is the best or most concise method for returning a string repeated an arbitrary amount of times?  The following is my best shot so far:  function repeat(s, n){     var a = [];     while(a.length &lt; n){         a.push(s);     }     return a.join(''); } How do I close a terminal without saving the history? More than once I've accidentally run a number of commands and polluted my bash history. How do I close my terminal without saving my bash history? I'm using Fedora. "Whether" Vs. "If" Solve $[2^{(2^{403})}] = [a]$ in $\mathbb Z_{23}$ where $0 \le a < 23$. Solve $[2^{(2^{403})}] = [a]$ in $\mathbb Z_{23}$ where $0 \le a &lt; 23$.  I've tried to combine corollaries of Fermat's little theorem and various other methods to solve this, but have always been stuck. Please explain the meaning of "otherwise than" in this sentence Please explain the meaning of the second part and explain "otherwise than" in part b     a person’s UK property business consists of:      (a) every business which the person carries on for generating income from land in the United Kingdom; and      (b) every transaction which the person enters into for that purpose otherwise than in the course of such a business.