Wondering the proper grammar for "is" or "are"
IS or ARE? "The only thing that I want you to hit right now IS/ARE the books"
I'm not sure how to prove these basic theorems in propositional calculus. Instead of using the standard axioms, we're supposed to use:   Deduction Theorem (if $\Phi, \alpha \vdash \beta$ then $\Phi \vdash \alpha \to \beta$),  Reductio (if $\Phi, \alpha \vdash \, $, then $\Phi \vdash \lnot \alpha$), Cut Rule (if $\Phi \vdash \alpha$ and $\Psi, \alpha \vdash \beta$ then $\Phi \cup \Psi \vdash \beta$),  Inconsistency Effect (if $\Phi \vdash \, $, then $\Phi \vdash \beta$ for every formula $\beta$), and  the Principle of Indirect Proof (if $\Phi, \lnot \alpha \vdash \, $, then $\Phi \vdash \alpha$),    as all the axioms can be deduced using these theorems.  I don't really know how to start the proofs without using the axioms:  i) prove that $\lnot(\alpha \to \beta) ⊢ \alpha$  ii) prove that $\lnot\alpha \vdash \alpha \to \beta$  Any suggestions on how to start these proofs or any insight at all would be greatly appreciated!  Thanks! Using simple quotes "" instead of \text{} Is there a way to use newcommand or some other nice technique to transform any occurence of  "bla"   in math mode into  \text{bla}   The reason I ask is because it is easy, and doesn't interrupt the flow of reading the (La)TeX code as much.  I would like to keep Xe(La)TeX's nice quote behavior (ie it can use the regular "" instead of backticks to quote some text outside math mode). Code after bullet list isn't rendered correctly Possible Duplicate:         If there is a list immediately followed by a code block the code block is not recognized as code (Even though there is a newline between the two).  int answer = 42;  Note: This happens both in the WMD preview and in the final (server rendered) post. Singular or plural verb form where subject includes a "parenthetical" element My question arises from , where OP asks whether he should use the singular or plural verb form after "the title, as well as the tone,"  As luck would have it, when I searched Google Books for , I found...        ...and...        At the risk of having this question closed as just peeving, I feel that the first one should have been plural "err", because without the commas it seems to me both "the title" and "the tone" have more or less equal status as "joint" subjects of the verb, making it plural.  On the other hand, I feel the commas in the second example effectively demote "the tone" to "parenthetical" status (the clause is almost incidental). Since this encourages us think of "the title" as the primary subject, it should have been singular "derives".  I'm no great fan of "grammatical rules", but it seems weird to me that the only two relevant examples for this specific wording should both (in opposite ways!) contradict my inclinations.  What's going on? Why is $a^n - b^n$ divisible by $a-b$? Raster generalization - buffers in rasters, expand pixels? Is it possible to create buffers for pixels of raster files? Actually I need to expand the pixels classified as 1 (in white in the figure) with a spatial range of 1 or 2 pixels, in order to perform some generalization.  I'm using QGIS, is this possible with gdal or something? show that $a^2+b^2+c^2+2abc+3\ge (1+a)(1+b)(1+c)$ let $a,b,c&gt;0$. Show that   $$a^2+b^2+c^2+2abc+3\ge (1+a)(1+b)(1+c)$$   By the $$(1+a)(1+b)(1+c)=1+a+b+c+ab+bc+ac+abc$$ it is suffient to show  $$a^2+b^2+c^2+abc+2\ge a+b+c+ab+bc+ac$$ How? I have an internet connection that I'd like to be enabled only during the day. With multiple household internet devices, this would need to be something disabled at the level of the router.  I don't believe the router offers this sort of functionality, but I'm reasonably familiar with setting up web servers and the like, and I'm wondering if I can set up some sort of proxy server on the internet that the router must go through and have that proxy only active at certain times of day.  It's a bit vague I know, but is something like this even possible?  If not, are there other solutions to the problem? I need to use binary variables (values 0 &amp; 1) in k-means. But k-means only works with continuous variables. I know some people still use these binary variables in k-means ignoring the fact that k-means is only designed for continuous variables. This is unacceptable to me.  Questions:     So what is the statistically / mathematically correct way of using binary variables in k-means / hierarchical clustering? How to implement the solution in SAS / R? "Series" – a noun of multitude similar to "lot", "majority", "percentage", "proportion"– verb agreement According to Garner's fourth edition  Though serving as a plural when the need arises, series is ordinarily a singular noun. But it is also a noun of multitude, so that phrases such as a series of things take a plural verb. However, the collocation there {has been - is} a series has predominated in print sources. Common nouns of multitude: lot, majority, mass, minority, multitude, percentage, proportion, variety.  However,  reads  When it has the singular sense of &quot;one set,&quot; it takes a singular verb, even when series is followed by of and a plural noun: A series of lectures is scheduled.  Are these dissimilar usages stylic advice? Secondly, the inversion after there also chooses singular elsewhere; why is it so?  When the verb precedes the noun percentage, a singular verb is required. That is, a higher percentage of them are, but there is a higher percentage of them. Proving that $(3n)!$ is divisible by $n! \times (n + 1)! \times (n + 2)!$ if $n$ is greater than 2 Prove that:  If $n$ is greater than 2, then $(3n)!$ is divisible by $n! \times  (n + 1)! \times  (n + 2)!$  From Barnard &amp; Child's "Higher Algebra".  I know that the highest power of a prime $p$ contained in $N$! is  $$ \left\lfloor{\frac{N}{p}}\right\rfloor + \left\lfloor{\frac{N}{p^2}}\right\rfloor + \left\lfloor{\frac{N}{p^3}}\right\rfloor ... $$  I'm unable to show that the formula above gives a higher value for $N = 3n$ than for the sum of its values when $N$ = $n$ , $n + 1$ and $n + 2$, considering the condition that $n &gt; 2$. Long sites break the layout on the front page The long name pushes the stats to a weird place. And what's with the "Stack Exchange" at the end anyway? Implement a Selective Comment Ban The number of divisors I am reading a math book. It states the following rule:      For an integer $n$ greater than 1, let the prime factorization of $n$ be $$n=p^a_1p^b_2p^c_3...p^m_k$$    Here $a, b, c,..., m$ are nonnegative integers, and $p_1,p_1,...,p_k$ are prime numbers. Then the number of divisors of $n$ is: $$d(n)=(a+1)(b+1)(c+1)...(m+1)$$   I can use the rule to solve problems correctly, but I don't understand the rule. How to prove it? How to deal with cross-thread access exceptions? I'm using Maverick with Compiz enabled.  I've searched AskUbuntu and Google. AskUbuntu doesn't have anything on this topic and everything Google turns up is a couple years old.  I'm doing browser tests and my tests are constantly spawning new Firefox windows. The problem is, when the window is spawned it takes focus. This is incredibly annoying as I'm usually in the middle of typing somewhere else. This doesn't only happen with my tests, but is the most common example I run into. Sometimes my IDE decides it wants focus when something special happens (like when something is done compiling) and then later I'll find fragments of IM messages I've typed in my code. This is driving me crazy. I've looked in both Gnome settings and Compiz settings and can't find a way to prevent that from happening.  Does anyone know of a way to prevent an app from stealing focus when it is opened? I'd rather have the taskbar flash at me or something to get my attention. How to remove shortcut key for Unity , which is "Meta" key on keyboard How to completely remove virtualbox I had installed VirtualBox but it started giving me problems. So I uninstalled it using:-  sudo apt-get remove virtualbox-\* sudo apt-get purge virtualbox-\*   But when I reinstalled VirtualBox it again resumed to previous settings and started giving same problems. How can i completely remove VirtualBox from my laptop and then reinstall it such that it wont give same problem again? Inequality ${n \choose k} \leq \left(\frac{en}{ k}\right)^k$ After viewing episode 5 of season 6 of Game of Thrones, we have come to know that      the Children of the Forest created the White Walkers.   But it seems that the White Walkers attack the Children of Forest. My question is why they would do so, given their origin.