adding booleans (as integer)
Elegantly determine if more than one boolean is "true"
Please help me to draw the following diagram:  \begin{displaymath} \xymatrix{ H\ar[r]&amp;H .1={}_HI_Q\supset 1.Q&amp;Q\ar[l]_\epsilon^{\cong}  \\  &amp;R\ar[u]\ar[r]&amp;R\ar[u] } \end{displaymath} Comma usage with compound sentences {actually compound predicates as per Rob's answer} Rule 101 of compound sentences is that a coordinate conjunction must be accompanied by a comma most of the time when joining independent clauses, yet I stumble across sentences all that time that seem to abuse this rule. Normally, it's a case of the subject not being present in the second clause, as in the following example:      "They usually start out as an abbreviation, but turn into acronyms   when they become well known."   (taken from the Oxford Style Manual)   To me, this comma cannot be correct because the clause after the comma doesn't contain a subject and therefore cannot be independent (right?). As far as I'm concerned, it's not the 'Comma to set off a contrast rule because I can find plenty of other where 'and' is used and the subject's missing in the second clause.  what's the deal here?   Thanks in Advance for any responses I may receive! What is the relation between linear purity and von Neumann entropy of a state? Does $\lim_{z\rightarrow0}\frac{\bar{z}^2}{z^2}$ exist? Systems of linear differential equations - eigenvectors Turnstile package Python BeautifulSoup findAll by "class" attribute Proving Cauchy condensation test I have to prove the  by tomorrow and I am really unconfident about what I did:  $$\sum_{n=1}^\infty a_n\text{ converges } \iff \sum_{n=1}^\infty 2^n a_{2^n}\text{ converges}$$  I did the following:  Let $(b_n)$ be a sequence as follow: $b_{2^k+m}:=a_{2^k}$ with $k\in\mathbb N_0$ and $0\leq m&lt;2^k$.  It's $a_{n+1}\leq a_n$ and so $0\leq a_{n+p}\leq a_n$ for all $n,p\in\mathbb N$.  So $\sum\limits_{n=1}^\infty b_n$ converges by the majorizing series $\sum\limits_{n=1}^\infty a_n$. And it's $\sum\limits_{n=0}^\infty b_n=\sum\limits_{n=0}^\infty\sum\limits_{m=0}^{2^n-1}a_{2^{n+1}}=\sum\limits_{n=1}^\infty 2^{n-1}a_{2^n}$ so $\Rightarrow$ is done.  For $\Leftarrow$ consider $c_{2^k+m}:=a_{2^k}$ with $k\in\mathbb N_0$ and $0\leq m&lt;2^k$.  It's $|a_n|\leq c_n$ and $\sum\limits_{n=0}^\infty c_n=\sum\limits_{n=0}^\infty\sum\limits_{m=0}^{2^n-1}a_{2^{n}}=\sum\limits_{n=1}^\infty 2^{n}a_{2^n}$ and so $\sum\limits_{n=1}^\infty a_n$ converges by the majorizing series $\sum\limits_{n=0}^\infty c_n$.  Is this in form and content correct? Rice with worm and possibly their eggs I bought a bag of brown rice from a store. After having opened and used for a while, I found there were moths flying in the house. At the same time, I found worms in the rice. I suspect that the moths are from the worms(rice-size, white body, dark head). I guess but am not sure if they are called rice moths. There were also many little sand-like things in the rice bag, are they the eggs of the rice moths?  Will eating this infested rice pose a health risk? How to prove $\cos\left(\pi\over7\right)-\cos\left({2\pi}\over7\right)+\cos\left({3\pi}\over7\right)=\cos\left({\pi}\over3 \right)$ Is there any well-ordered uncountable set of real numbers under the original ordering? I know that the usual ordering of $\mathbb R$ is not a well-ordering but is there an uncountable $S\subset \mathbb R$ such that S is well-ordered by $&lt;_\mathbb R$?   Intuitively I'd say there is no such set but intuitively I'd also say there is no well-ordered uncountable set at all, which is obviously wrong. I still struggle to grasp the idea of an uncountable, well-ordered set. When reading lens reviews on the Internet, I often find subjective statements about the image quality that a lens produces, such as "good contrast" or "sharp". The problem is that I don't think I am capable to actually see these qualities on an image. I don't even think I could tell the difference between a cheap kit lens and a top lens, if not by "this just looks better".  So my question is: without looking at sharpness tests and MTF curves, how do you learn to judge the quality of a lens based only on sample images? What are the characteristics you look for and what constitutes good or bad in each of them? Consider the sequence defined as  $x_1 = 1$  $x_{n+1} = \sin x_n$  I think I was able to show that the sequence $\sqrt{n} x_{n}$ converges to $\sqrt{3}$ by a tedious elementary method which I wasn't too happy about.  (I think I did this by showing that $\sqrt{\frac{3}{n+1}} &lt; x_{n} &lt; \sqrt{\frac{3}{n}}$, don't remember exactly)  This looks like it should be a standard problem.   Does anyone know a simple (and preferably elementary) proof for the fact that the sequence $\sqrt{n}x_{n}$ converges to $\sqrt{3}$? Equivalent of "both" when referring to three or more items? Does a monk's Unarmored Movement speed increase apply to the fly speed gained from a Fly spell? Can't boot XP after Ubuntu Installation, how to fix? I installed Ubuntu and after the installation, i can't boot to XP. When i choose XP from the Grub menu, I got black screen for like 30 sec, and then it returns to the Grub menu.  Thanks! ! LaTeX Error: Undefined color `BLACK' i have written all the text in black color, but i get this error several times in the same page:  ! LaTeX Error: Undefined color `BLACK'.   i tried to solve it by writting this: \definecolor{black}{gray}{0,0,0} but it didn´t work.   what should i do? String processing in windows batch files: How to pad value with leading zeros? What's the C++ way of parsing a string (given as char *) into an int? Robust and clear error handling is a plus (instead of ). Grandi's Series; tends to $1/2$, but why is this considered a valid sum?