Is there any way to define a \newcommand that behaves like a normal word?  I have a few names for Objects, that might change later.   To keep my flexibility i use \newcommand{\superprod}{superPRODUCT}. If later on the name of "superPRODUCT" has to be changed to "uberPr0duct", I just have to change the new command. But it really bothers me, that i have always have to type \superprod\or \superprod{} in my text.  Is there any way to make latex realise that a space has to be inserted after the word (except at the end of a sentence)?  Edit: No real solution, best way:  \newcommand{\superprod}{}% To make sure that \naive isn't already defined     \def\superprod/{superPRODUCT}  in text: Lorem \superprod/ ipsum \superprod/.
With a macro such as:  \def\naive{na\"{\i}ve}   I find that the space which I would hope to follow it, is absent. So, with  the \naive approach   I get     the naïveapproach   in the output. How do I bring back the space?
Understanding slice notation Do these leaves signify anything? I'm trying to identify a book I read in school, though I can't recall at what grade level; let's say it had to have been published before I graduated high school in 2000. Despite being required reading, it didn't feel much like a classic.  The story took place on Earth, after some catastrophe had caused the air to become poisonous. However, one teenage girl was able to survive because her house was in a valley which was somehow protected from the poisonous winds and was able to sustain its own ecosystem. One day, a man wearing a protective full-body suit and gas mask appears in the valley, and both are rather surprised to find someone else alive. She feeds and shelters the man and shows him how she had come to survive in the valley. Rather abruptly…      the man attempts to rape her, but she overpowers him somehow. She steals his protective suit and starts to leave the valley. He tells her that he had seen birds in a certain direction away from the valley, indicating there might be life there as well, and she leaves.   I believe there was an author's note either at the beginning or end of the book stating that the author had actually died while writing the manuscript, and that their friends or family had finished the book by going off the author's original notes, which I suppose may explain the abruptness of the ending.  In case it wasn't clear from the above, I didn't really like the book. But I'm curious about it regardless. What are the uses of "using" in C#? Can I have multiple background images using CSS? how to prove the chain rule? I have just learnt about the chain rule but my book doesn't mention a proof on it. I tried to write a proof myself but can't write it. So can someone please tell me about the proof for the chain rule in elementary terms because I have just started learning calculus. At the end of a letter, is it correct to omit "I am" in this sentence?     I am looking forward to hearing from you   Then it will become:     Looking forward to hearing from you "You've earned (badge)" panel layouts are broken When I visit  I see this:     The "Congratulations! You've earned (badge)" section has dropped down completely beneath the tabs under it. The "You've earned a new privilege!" section has a gap at the bottom:     Shog9 says in comments how to reproduce this:     Gotta have earned a badge, not dismissed the notification, and be looking at your own profile. GCD of two numbers divided by their greatest common divisor is 1 Can I leave the Schengen Area (and come back) while my non-eea spouse resident card application is being processed? My wife and I recently moved to Germany. She's a Swedish citizen, and I'm American. It'll be December before I can actually apply for my residence card, because my appointment to register our address is so far out - the local police station was all booked out and we didn't get an apartment right away.  I imagine that I won't be getting my residence card until well after Christmas, by which time my 90/180 days will be passed. What if I want to leave to, say, London for the holidays? Will I be allowed back in? I hit day 90 around the 21st of December. I could maybe leave on day 89 and come back on day 90 (with my wife and our marriage cert), or use this Polish solution: , since I can't be expelled from Germany for overstaying my visa while my application is processing.  Both of those seem a bit risky though. Am I reading too far into it, or is this a legitimate concern? Will I get some sort of documentation saying I have a residence card application processing? Proving that the general linear group is a differentiable manifold We know that the the general linear group is defined as the set $\{A\in M_n(R): \det A \neq 0\}$. I have a homework on how to prove that it is a smooth manifold. So far my only idea is that we can think of each matrix, say $A$, in that group as an $n^2-$dimensional vector. So i guess that every neighborhood of $A$ is homeomorphic to an open ball in $\mathbb{R}^{n^2}$ (However, i don't know how to prove this.)  Now, I'm asking for help if anyone could give me a hint on how to prove that the general linear group is a smooth manifold since I really don't have an idea on how to do this. (By the way, honestly, I don't really understand what a $C^{\infty}-$smooth structure means which is essential to the definition of a smooth manifold.) Your help will be greatly appreciated. :) Will higher temperatures damage a computer over time, even when not reaching the maximum temperature? For example, if the maximum is 105 degrees celcius, will the computer break faster when continually having it on 80 degrees celsius instead of, for example, 60 degrees celcius. How to prove by induction that $\frac{a^n+b^n}{2}\geq\left(\frac{a+b}{2}\right)^n$? I'm about to prove that for any $a,b&gt;0$ and $n\in\mathbb{N},$ the inequality: $\frac{a^n+b^n}{2}\geq\left(\frac{a+b}{2}\right)^n$ holds.   By induction I get: $$\left(\frac{a+b}{2}\right)\cdot\frac{a^n+b^n}{2}$$ $$=\frac{1}{2}\cdot\frac{a^{n+1}+b^{n+1}+ab^n+ba^n}{2}$$ $$=\frac{1}{2}\left(\frac{a^{n+1}+b^{n+1}}{2}+\frac{ab^n+ba^n}{2}\right).$$  Now I have to prove that $$\frac{1}{2}\left(\frac{a^{n+1}+b^{n+1}}{2}+\frac{ab^n+ba^n}{2}\right)$$ $$\leq\frac{a^{n+1}+b^{n+1}}{2}$$ $$\Leftrightarrow a^{n+1}+b^{n+1}\geq ab^n +ba^n.$$ But I don't know how to prove that one, is it possible to be proved by induction ? Thank you. It's common in C++ to name member variables with some kind of prefix to denote the fact that they're member variables, rather than local variables or parameters. If you've come from an MFC background, you'll probably use m_foo. I've also seen myFoo occasionally.  C# (or possibly just .NET) seems to recommend using just an underscore, as in _foo. Is this allowed by the C++ standard? Did Harry Potter lose Voldemort's powers when he lost his connection to Voldemort? Harry noted to Dumbledore that he had a number of things in common with Voldemort. And it was later revealed that some of Voldemort's power was transferred to Harry when Voldemort tried to kill him. So, what powers did Harry get from Voldemort (i.e. Parseltongue and others) and did they all leave him when he stopped being a horcrux?    Update In the Chamber of Secrets Dumbledore states that Harry has many qualities that Salazar Slytherin values in his hand picked students. Parseltongue - resourcefulness - determination - a certain disregard for rules.    So, does anyone know what specific powers Harry got from Voldemort and is there anyway to tell if he lost anything else besides Parseltongue? Prove that a limit doesn't exist In my assignment I have to prove that the following function doesn't have a limit:  $$f(x)=\frac{x}{x-\lfloor{\sin x}\rfloor}$$ when $${x \to 0}$$  In other words, I have to prove that for every $\delta$ such that $0&lt;|x-{x_0}|&lt;\delta,$ $|f(x)-L|&gt;\epsilon$.  In fact, I don't even know how to start. Do I choose my $\delta$? I know that the sin function has certain values that's supposed to help me. How do I use it?  I have to prove this by definition, so I can't use limit arithmetic for example  Thanks. How to automatically resize the vertical bar in a set comprehension? I have a simple command which I use to write set comprehensions so that the braces automatically resize with respect to size of the enclosed arguments, e.g.  \usepackage{amsmath} \newcommand{\set}[1]{\left\lbrace #1\right\rbrace}  \begin{equation*} \set{x \in X \mid x &gt; \frac{1}{2}}   \end{equation*} % Produces something like: { x : X | x &gt; 1/2 }   However, the \mid vertical bar wont resize like the braces { .. } do. How can I get the \mid to resize as well? Cleaning Contaminated Disc Rotors I've had an eternal struggle with my current bike over brake contamination. The levers and calipers are shimano ultegra r8000, so the latest and (almost) greatest.  I first noticed it when I took it to a repair shop (i no longer use) for a bleed, it came back and the front brake would squeal like crazy and at low speeds had little to no braking force. You can stop from speed but then struggle to come to a halt without using your foot.  At around 2000 miles I tried to replace the brake pads, when I took them out they were black with grime on both sets (front &amp; back), not to mention worn down to the metal. I replaced them with the L04C sintered pads, gave the callipers a good cleaning with a towel (no chemicals) and fitted the new set.  Annoyingly all of my braking issues are back, now I probably should have cleaned the rotors, I simply used some muc off disc brake cleaner on them. I would like to know the best way to clean the rotors, I've inspected the pads and they are looking fairly black now, with plenty of tread left. I'm going to abandon these pads and fit a new set. For the rotors I plan to completely remove them from the wheels (they are center lock fitted) and try and treat them off the bike, what is the best way to fully clean them? They have plenty of wear left in them but you can see these black grooves in them, and plenty of muck on the back that I struggle to get off.  Below are images of the rotors after soaking them in disc brake cleaners, waiting and then wiping them down with a clean, microfiber towel.   Front Wheel Outside Rotor   Front Wheel Inside Rotor - note the increased dirt on this side  Looking at ways people clean their disc rotors, I've seen plenty of suggestions that I would need to burn the contaminants off the discs. Would the best approach be to remove them and use a blowtorch, should I soak them in some nasty chemicals overnight before I try to heat them? Do I try baking them in the oven?  And finally, what is the best way to prevent the brakes from becoming contaminated in the future? it's really off putting when they squeal and don't perform how I'd expect because it means I'm more reserved whilst out riding on the bike, leading to reduced time riding around outside. I commute on this bike (50 miles a week) and then ride about 50 on the weekends also, so it see's it's fair share of road use. I tend to wash it once after my big ride on saturdays and will rinse it off if it's been raining, any day that occurs (since I live in north east england, the acid rain..). I've owned disc brake bikes before and never had half the issues I've had with this, I had a cheap trek with tektro brakes and the brakes were sharper and never had any issues with contamination whatsoever (i did around 500 miles on that bike before a motorist happened).  Thanks for any and all advice :) A recent quandary came up with some friends in a game of Ticket to Ride.  If, in the last turn, you have the cards to play a route longer than the number of trains that you have left, can you do so?  Or are you limited by your number of trains? What are the best strategies for assessing if a journal is a &quot;vanity&quot; or &quot;predatory&quot; journal that should be avoided (both for publishing in and reviewing for)? For example, how would one go about determining if a journal/publisher belongs on ?