Characters per line and font size
Nicely force 66 characters per line
'Just' and 'only' carry a similar meaning, and while my feel for language usually helps me decide which one to use, there are times when I'm at a loss.  From my understanding, 'just' is used as a softener, to add flexibility and politeness. 'Only', on the other hand, is a relatively sharp exclusion. 'Just' also has a wider range of meanings, for instance to denote time.  While this sounds simple enough, it can get messy in practical usage. The sentence that made me stumble was "Not only airports are part of the target customer group, but also other large infrastructures".  Would the meaning of this sentence change when using 'just' instead? The way I see it, there is no difference in this case, except 'just' would make it sound a tad more colloquial. I want to put a table and a figure side-by-side. The table should fill two third of the text width, and the figure the last third.  So I'd like to achieve one of the following effects (which are equivalent in my case):   One table with 3 columns. The first two columns contain text, the third column contains a lengthy image. The height of the image should be determined by the height of the whole table, if that's possible Or, a divided page like in newspapers. On the left side I have the table, on the right side the image.   What I have tried:  \begin{multicols}{2} \begin{tabular}{ l l } Text &amp; Text \\ Text &amp; Text \\ ... &amp; ... \\ \end{tabular} \vfill \begin{figure}[H]     \includegraphics[]{images/image} \end{figure} \end{multicols}   But this places the picture directly on top of the table.  I also tried using \usepackage[export]{adjustbox} and \includegraphics[right]{images/image} but the caption is still in the center of the page and therefor on top of the table. Is the set of all finite sequences of letters of Latin alphabet countable/uncountable? How to prove either? Today in Coding/Cryptography class, we were talking about basic definitions, and the professor mentioned that for a set $A=\left \{ \left. a, b, \dots, z \right \} \right.$ (the alphabet) we can define a set $A^{*}=\left \{ \left. a, ksdjf, blocks, coffee, maskdj, \dots, asdlkajsdksjfs \right \} \right.$ (words) as a set that consists of all finite sequences of the elements/letters from our $A$/alphabet. My question is, is this set $A^{*}$ countably or uncountably infinite? Does it matter how many letters there are in your alphabet? If it was, say, $A=\left \{ \left. a \right \} \right.$, then the words in $A^{*}$ would be of form $a, aa, aaa, \dots$ which, I think, would allow a bijection $\mathbb{N} \to A^{*}$ where an integer would signify the number of a's in a word. Can something analogous be done with an alphabet that consists of 26 letters (Latin alphabet), or can countability/uncountability be proved otherwise? And as mentioned before, I am wondering if the number of elements in the alphabet matters, or if all it does is change the formula for a bijection.   P.S. Now that I think of it, maybe we could biject from $\underset{n}{\underbrace{\mathbb{N}\times\mathbb{N}\times\mathbb{N}\times\dots\times\mathbb{N}}}$ to some set of words $A^{*}$ whose alphabet $A$ has $n$ elements? Thanks! How to fix slow wireless on machines with Intel wireless cards? I have looked through all the previous questions but turning power management off for the Wi-Fi card didn't work. This problem seems to be with the Lenovo Thinkpads. I switched to Ubuntu 11.10 from Windows 7 3 days ago so I'm new to the operating system. I am looking for the title of a novel that I only caught part of on audio. It takes place within our current time frame and deals with the Moon getting struck and fragmented into (initially) 7 pieces by a high-speed asteroid that they called "The Agent".  Within a few weeks of this episode, scientists figure out the the Moon will continue to break down in a cascade reaction over the next couple of years until the planet gets bombarded by so much debris that it sterilizes Earth. The governments of the world frantically start to build a series of ships using swarming concepts to evacuate the planet as much as possible... and that's all I have heard so far.  Thanks for any info. I have been trying to use Sidecar in the public betas of macOS Catalina and iPadOS 13.  I have a 2019 Macbook Pro, and a 3rd generation iPad Pro, so I know I have supported devices.  Both devices are on the same Wifi network, and both have Bluetooth enabled.  Both devices are logged into iCloud with the same AppleID.  Both devices have two-factor authentication enabled.  I have tried this both with and without a USB-C cable connection between the two devices.  The Sidecar preference pane in System Preferences does appear, and when I go into it I can see in the "Select Device" dropdown that my Mac can "see" my iPad Pro.  However, when I try to connect to it, I get the following after a pause:    I keep  for troubleshooting tips, but none have been useful for me thus far.  FWIW, I have been a "good citizen" and reported my problems to Apple via the Feedback Assistant apps on both devices, so in case this is a temporary bug, I've reported it.  I'm just asking here in case someone else has encountered this issue.  Edit: Eventually, Sidecar started working for me (sometimes) after some of the later public betas came out.  I'm not sure exactly which version(s) of Catalina and/or iPadOS made the difference for me.  So far it has worked without any timeouts in the final versions. I didn't need to downgrade and then re-upgrade as the submitted answer suggests, although I'm glad that has worked for some. How does one parse XML files? Is there a simple method of parsing XML files in C#? If so, what? Back transforming regression results when modeling log(y) I'm fitting a regression on the $\log(y)$.  Is it valid to back transform point estimates (and confidence/prediction intervals) by exponentiation?  I don't believe so, since $E[f(X)] \ne f(E[X])$ but wanted other's opinions.  My example below shows conflicts with back transforming (.239 vs .219).  set.seed(123)  a=-5 b=2  x=runif(100,0,1) y=exp(a*x+b+rnorm(100,0,.2)) # plot(x,y)  ### NLS Fit f &lt;- function(x,a,b) {exp(a*x+b)}  fit &lt;- nls(y ~ exp(a*x+b),  start = c(a=-10, b=15))  co=coef(fit) # curve(f(x=x, a=co[1], b=co[2]), add = TRUE,col=2,lwd=1.2)  predict(fit,newdata=data.frame(x=.7)) [1] 0.2393773  ### LM Fit # plot(x,log(y)) # abline(lm(log(y)~x),col=2) fit=lm(log(y)~x) temp=predict(fit,newdata=data.frame(x=.7),interval='prediction') exp(temp)         fit       lwr       upr 1 0.2199471 0.1492762 0.3240752 Need help with a question regarding the Big Oh In class we are currently covering upper/lower bounds, big Oh and omega and the like. I am pretty good on the "typical" functions one would do, but at a complete loss at "general" statements. This ons function, for example:  $$\forall f\in\mathcal{F}: \lfloor \sqrt{\lfloor f(n)\rfloor }\rfloor \in O(\sqrt{f(n)}).$$  the domain F by the same is all natural numbers that return a real positive number when inputted. My first instinct with something like this is to remove the floors, the general strategy I though to solve this is remove the outer floor, then get rid of the square root, and then the inner floor. But I have no idea how to go about this or if this is even the right way to do it.  Help please? Thanks in advance. Redirecting stdout to a file you don't have write permission on When you attempt to modify a file without having write permissions on it, you get an error:  &gt; touch /tmp/foo &amp;&amp; sudo chown root /tmp/foo &gt; echo test &gt; /tmp/foo zsh: permission denied: /tmp/foo   Sudoing doesn't help, because it runs the command as root, but the shell handles redirecting stdout and opens the file as you anyway:  &gt; sudo echo test &gt; /tmp/foo zsh: permission denied: /tmp/foo   Is there an easy way to redirect stdout to a file you don't have permission to write to, besides opening a shell as root and manipulating the file that way?  &gt; sudo su # echo test &gt; /tmp/foo Common lines between two files Are there substitutes for chain lubricant? With long journeys and particularly during winter I have noticed that the salt erodes the chain very quickly, even when I have lubricated the chain beforehand. When you are missing proper chain lubricants, what would you use as a substitute? Could you use cooking oil if you are missing the right stuff, or should I keep a small bottle of oil with me on my rides?  Related The situation is my  has been enchanted with .  The creature has      when it dies, return it to his owner’s hand   The enchantment says     When enchanted creature dies, return that card to the battlefield under your control with a +1/+1 counter on it.   Who gets the creature? Me or my rival?  Does the creature ability trigger before or after enchantment? How restrict page for users logged? Minecraft Inventory Saving I am making an RPG map, and was wondering how to "save" the game.  If you die, you would revert back to a save that happens automatically or manually, and I was wondering how to have it so that you will have all the items you had then, and none of the items you got after you saved (so /gamerule keepInventory won't work).  The only way I can think of doing this is having this long, long, annoying set of command blocks to test for all the items in the game, and then have another 64 command blocks for each of those items, testing for the amount of the item. I will soon be attending a Ph.D program in mathematics. I do not know how common this practice is, but the department has a requirement that graduate students must learn a foreign language and be able to read and write mathematics in that language. The three choices are French, German, or Russian. I personally have no preference on which to learn, but I was wondering if there were other reasons that would make one language more advantageous over the others in terms of a general mathematical career. Thanks in advance in any response. What books, journals, and electronic resources are most valuable for expanding knowledge of GIS? What books, journals, and/or electronic resources have you found most valuable for expanding your knowledge in the GIS field, and why? What is the physical significance of dot & cross product of vectors? Why is division not defined for vectors? I get the physical significance of vector addition &amp; subtraction. But I don't understand what do dot &amp; cross products mean?   More specifically,    Why is it that dot product of vectors $\vec{A}$ and $\vec{B}$ is defined as $AB\cos\theta$? Why is it that cross product of vectors $\vec{A}$ and $\vec{B}$ is defined as $AB\sin\theta$, times a unit vector determined from the right-hand rule?   To me, both these formulae seem to be arbitrarily defined (although, I know that it definitely wouldn't be the case).   If the cross product could be defined arbitrarily, why can't we define division of vectors? What's wrong with that? Why can't vectors be divided? I am currently working through the problems in , with the goal of hopefully understanding how magnets work. At the moment I am a little stuck on one of the early problems in the first chapter. And I would like a Hint about how to proceed. The problem is to solve the time derivative of the expectation value of momentum of a particle. ie: $$ \frac{d\left&lt;p\right&gt;}{dt}. $$ My working so far Just prior to that question the text gives an expression for momentum, $$\int\limits_{-\infty}^{+\infty}{\Psi^*\left[-i\hbar \frac{\partial}{\partial x}\right]\Psi}dx, $$ (Where $\Psi$ is a function satisfying Schrödinger's equation, $i$ is the square root of negative 1, and $\hbar$ is Planck's constant divided by $2\pi$.) So my initial approach was to try and differentiate this with respect to $t$. $$ \frac{d}{dt}\int\limits_{-\infty}^{+\infty}{\Psi^*\left[-i\hbar \frac{\partial}{\partial x}\right]\Psi}dx. $$ However I didn't know how to do that, so I asked around in the maths chatroom, and got a lot of help. Specifically  from @RobJohn: $$ \begin{align} \int vv'\,\mathrm{d}x &amp;=vv-\int vv'\,\mathrm{d}x\\ &amp;=\frac12vv+C \end{align} $$ So I suppose it would follow that, $$ \begin{align} \int\limits_{-\infty}^{+\infty}{         \left(             \Psi^*                 \left[                     \frac{\partial}{\partial x}                 \right]             \Psi         \right)         }\,\mathrm{d}x &amp;=  \left[\Psi^* \cdot \Psi\right]_{-\infty}^{+\infty} - \int\limits_{-\infty}^{+\infty} {\Psi\frac{\partial \Psi^*}{\partial x} }\,\mathrm{d}x\\ &amp;= \frac{1}{2}|\Psi|^2 \Big|_{-\infty}^{+\infty}, \end{align} $$ And then, $$ \begin{align} &amp;\frac{d}{dt}\int\limits_{-\infty}^{+\infty}{\Psi^*\left[-i\hbar \frac{\partial}{\partial x}\right]\Psi}dx \\&amp;=-i\hbar \frac{d}{dt}\left( \frac{1}{2}|\Psi|^2 \Big|_{-\infty}^{+\infty} \right). \end{align} $$ But this feels wrong. I'm not sure exactly why. (Maybe it's just because it is the limits of my maths)  For reference, regarding what I understand, my maths is pretty low-level, I took a course in undergrad calculus over 10 years ago and only just passed that at the time, and my physics knowledge is not much further than that of an enthusiastic lay person. Avoiding IF ELSE due to variable been NULL