How to typeset stacked, unrelated equations? I fail to find a way to typeset a stack of unrelated equations. As an example, I would like to have these two unrelated equations one under the other: ax+by+c=0 and E=mc^2. I could go for \begin{align}...\end{align} but there is no particular reason to align them against something. I tried to break them via \\ in a \begin{equation}...\end{equation} environment but this is not taken into account (the equations are concatenated in one line). I tried \begin{multiline}...\end{multiline} and \\ but it breaks the equations and justify them one to the left and one to the right. I finally broke them into two \begin{equation}...\end{equation} but they are too much spaced vertically. Is there a simple &quot;multiline left justified&quot; environment I could use? As a workaround, if there are no straightforward solutions I will probably go for align.
Left-align all equations in a block align environment without any explicit alignments points (given by &amp;) right justifies the equations in the block. They can be left justified by putting &amp; at the beginning of each equation. Is there any way to left justify them without starting &amp;-s? Maybe some special environment or option? It seems to be an extra work to tell the compiler again and again that I want left alignment on each line.
I've been told that when "the" is proceeded by a vowel sound, like "apple" or "hour", it's pronounced as "thee" and not as "thu".  But after listening to a couple of songs, I noticed that sometimes this "rule" is not followed. Take for example the two Katy Perry's songs, "Roar" and "The one that got away". In the first she sings "I got thee eye of thu tiger", but in the second she sings "Thu one that got away".  I don't know if it was sang this way to better suit the song melody (I understand nothing about those techniques), but I got confused. What's the correct pronunciation?  Thanks in advance. Can I buy PSN games and DLC without giving Sony my credit card info? On per-site metas, users are given a rank based on meta participation, and this ranking is seen on the default tab of the users page on each per-site meta. How is this participation numerically calculated to give a ranking? Is it by votes? Something else? Are community wiki posts included in this? I'm trying to have a surface with soft body hold obects that are falling on it with rigid body physics, but for some reason, no what matter what mass I give it, the objects just fall trough the softbody enabled surface.  Is there a toggle or a value I need to change to make them stay there? Will I still receive OTA updates after rooting my Nexus 5? How to analyze lightly varying senses of adjective *very* Use of very as an adjective is (in my experience) most frequently attested in phrases like     ...the very person I was looking for.   To use adjective very with the indefinite article sounds quite bizarre in this case:     ?...a very person I was looking for.   But consider this sentence, where indefinite a is used:     Visualizing a very transformation of the master-slave relation, Thomas presses further: the slave is brother to the master, even doubly a brother.   OED treats the two uses as separate senses of the word, with the following definitions:           (first use):&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;With limitation (usually expressed by the or a possessive) to particular instances      (second use): Really or truly entitled to the name or designation   Here are two respective examples quoted in OED:     What would you say to me now, and I were your verie, verie Rosalind? (1616)   Thence we went into Queen Mary's room, and saw that beautiful portrait—that very queen and very woman. (1857)   Clearly, the difference in meaning between the two senses is quite light, and it seems to me like a kind of difference which is recurrent enough to have its own term. What is the proper term? Are there other English words having similarly related pairs of senses? And lastly, is OED jumping the gun in treating these as two senses? Could the difference in meaning instead be due to the choice of determiner? Proving that $\lim\limits_{x\to\infty}f'(x) = 0$ when $\lim\limits_{x\to\infty}f(x)$ and $\lim\limits_{x\to\infty}f'(x)$ exist I've been trying to solve the following problem:  Suppose that $f$ and $f&#39;$ are continuous functions on $\mathbb{R}$, and that $\displaystyle\lim_{x\to\infty}f(x)$ and $\displaystyle\lim_{x\to\infty}f&#39;(x)$ exist. Show that $\displaystyle\lim_{x\to\infty}f&#39;(x) = 0$.  I'm not entirely sure what to do. Since there's not a lot of information given, I guess there isn't very much one can do. I tried using the definition of the derivative and showing that it went to $0$ as $x$ went to $\infty$ but that didn't really work out. Now I'm thinking I should assume $\displaystyle\lim_{x\to\infty}f&#39;(x) = L \neq 0$ and try to get a contradiction, but I'm not sure where the contradiction would come from.   Could somebody point me in the right direction (e.g. a certain theorem or property I have to use?) Thanks I couldn’t find any proof on the internet. I would appreciate an elementary proof , but any help would be appreciated!  Thank you. Copy & Pasting from Photoshop to Illustrator loses transparency I often run into this issue. I'm creating a file in Photoshop with masked layers etc. I want to make the final output available for some mock-ups in Illustrator, so I rasterize the layers and marquee select the entire area, copy and move to Illustrator.  Pasting the area in Illustrator flattens all transparencies, which is quite annoying. I'm left with my object and a flat white background.  Is there a reason for this? Why is it that Frisian is considered the closest related language to English? It is commonly asked "What is the closest language to English?" and the equally common answer is         Except that there is rarely a reason given for this connection; the most that is given are baldly stated 'facts' (e.g. "English and Dutch are in the same 'Low German' group")  Can anyone give any substantive reasons? For example, an comparative overlap of vocabulary, a distance metric of phonology, privately shared syntactic rules among all the rules in West German languages. Let $A=\begin{pmatrix}0&amp;5\\ 7&amp;4\end{pmatrix}$.      1) Write $A$ as a product of $4$ elementary matrices.      2) Write $A^{-1}$ as a product of $4$ elementary matrices.   My work. I have managed to find $A^{-1}$, which came out to be this:  \begin{pmatrix}-\frac{4}{35}&amp;\frac{1}{7}\\ \frac{1}{5}&amp;0\end{pmatrix}  However, I am struggling to figure out how I would split each of these matrices into $4$ elementary matrices. Any help? How strong is Superman on Krypton? When Superman goes back to visit his home planet (using his ability to travel through time, I guess), is he:    an exceptionally strong and athletic Kryptonian? just an average Kryptonian male? a weakling on account of spending a lifetime in the comparative microgravity of Earth?   A possibly related question: why is Superman so muscular? What kind of weights does he lift to stay in shape?  The answers to  are all about Superman's superpowers on Earth compared with other visitors from Krypton; I'm asking about Kal El without his superpowers.  Clarification: I'm asking about the "classic"  Superman, say late Golden to early Silver Age, roughly 1945-1960. (Yes, I know the concept evolved during those years.) I'm not sure what that would be in terms of "numbered Earths", those came along after my time. I'm pretty sure the Kryptonians of that era had no superpowers in their native milieu, nor would Kal El if he were deported in space-time to his native world. How to interpret busybox "top" output? I am using BusyBox on a small embedded ARM system.  I'm trying to read the "top" output, in particular for the Python process listed.  How much real memory is this process using?  Also what does VSZ stand for?  The system only has 64MB of RAM.   Mem: 41444K used, 20572K free, 0K shrd, 0K buff, 18728K cached CPU:   3% usr   3% sys   0% nic  92% idle   0% io   0% irq   0% sirq Load average: 0.00 0.04 0.05 1/112 31667   PID  PPID USER     STAT   VSZ %VSZ %CPU COMMAND   777   775 python   S     146m 241%   3% /usr/bin/python -u -- dpdsrv.py What are the chances of getting $K$ identical outcomes in a row in a series of $Y$ independent events? Each event has two possible outcomes: a and b.  Each event is independent.  Outcome a has $X\%$ chance of happening.  If we run $Y$ number of such events, what are the chances of getting $K$ outcomes a in a row, at least once?  To put it in practical terms imagine a series of coin tosses. Each coin toss has two possible outcomes: a = heads and b = tails. Outcome a = heads has a chance of $50\%$. If we run $Y = 100$ number of coin tosses, what are the chances of getting $K = 10$ outcomes a=heads in a row, at least once?   I'm using the practical example only so I can express the idea more clearly. I'm interested in finding out the general formulas and computations so that I can run the calculations for any $X$, $Y$, or $K$.  I would also be very interested in knowing how the probabilities would change if the events would not be independent. What if the more outcomes a we have in a row the bigger the chance of getting an outcome a in the next event? What if it's the other way around, and the more outcomes a in a row we have the lower the chance of getting another a? Head or tail sound fine to my ESL ears.  What's the reasoning behind the plural usage?  I looked it up on etymonline but didn't find anything interesting. Emacs: Symbol's value as variable is void Can I use film that's 20+ years old? How to get Microsoft Search to index common file types like .pdf and .pub I'm trying to get Windows Search (4.0) to index PDFs and .pub, .doc, etc. files.  The files are on an XP Pro PC acting as a file server. But I don't have MS Office, etc. installed (no need, trying to keep it "slim and trim") but WS 4.0 is doing the indexing of those files and not indexing .pdf and .pub.  I've found a few  (from Foxit PDF reader) rated 3/5 and only support WS 2.0 or 3.0.  Looking for other solutions and also a way to index .pub files. Question about preposition -of- Stack Overflow provides good tools in the question editor, like "Links" and "Styling".  Another thing that for me would be nice is a color selector. Although an HTML editor is available, a direct click on tool would be good, and users can select different colors, as for marking errors in their program with red, and more important data with blue.