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Suppose that f is continuous on $(a,b)$ and $\lim_{x\to a^+}  f(x) = \lim_{x\to b^-} f(x) = \infty$. Prove that $f$ has a minimum on all of $(a,b)$.  I was thinking of applying the extreme value theorem, but I realized that it applies only to closed intervals. So I was thinking of defining a closed interval that is in $(a,b)$, and using the definition of one sided limits to go about the problem, but I don't know how to proceed. Help please? List of Ubuntu Versions with Corresponding Linux Kernel Version Is there a list of Ubuntu versions with default corresponding Linux kernel versions somewhere?  I would specifically like to know the most recent version of Ubuntu that still used Linux Kernel 2.x. If $X$ takes on a Gamma Distribution, how can I find $X^2$, $X^3$, etc? Why are addition and multiplication commutative, but not exponentiation? We know that the addition and multiplication operators are both commutative, and the exponentiation operator is not.  My question is why.  As background there are plenty of mathematical schemes that can be used to define these operators. One of these is   where $H_0(a,b) = b+1$   (successor op) $H_1(a,b) = a+b$   (addition op) $H_2(a,b) = ab $   (multiplication op) $H_3(a,b) = a^b$   (exponentiation op) $H_4(a,b) = a\uparrow \uparrow b$   (tetration op: $a^{(a^{(...a)})}$ nested $b$ times ) etc.    Here it is not obvious to me why $H_1(a,b)=H_1(b,a)$ and $H_2(a,b)=H_2(b,a)$ but not $H_3(a,b)=H_3(b,a)$  Can anyone explain why this symmetry breaks, in a reasonably intuitive fashion?  Thanks. Need help identifying the fantasy book about a portal to a fantasy land in the basement of a house I can't remember any names of characters or locations where the story took place but I do remember the basic plot of this early 90's novel; a human man inherits his father's house. In the basement there is a doorway to a fantastic land where adventure ensues. He fights elves and wins their deadly elf swords which he buries under concrete at the end of the novel (because if you don't get rid of them they will come back and get you).  At the end of the novel he must remake the world in his own imagination, turning the tough Elf King into a cobbler and making Jesse Jackson President. I have been looking high and low and have drawn a blank.  Any help would be appreciated. Thanks! Why do Jedi use lightsabers instead of blasters? Blasters seem to be more practical. Is there a special bond or something between lightsabers and Jedi? Is it possible to have f.lux (software that adjusts display's color temperature) on Ubuntu 14.04? f.lux is software which adjusts temperature of your display according to time of the day. Is it possible to make f.lux work in Ubuntu 14.04? If so, maybe you can share your knowledge or point me to a guide. What's the best way to version CSS and JS URLs? Is a clean install better than upgrading? How to pass anonymous types as parameters? Can the weak force create a bound state? Can I remove inline event handlers using jQuery? How to use classes from .jar files? I read the Java tutorials on Sun for JAR files, but I still can't find a solution for my problem. I need to use a class from a jar file called jtwitter.jar, I downloaded the file, and tried executing it (I found out yesterday that .jar files can be executed by double clicking on them) and Vista gave me an error saying "Failed to load Main-Class Manifest attribute from [path]/jtwitter.jar".  The guy who coded the .jar file wants me to import it, but where do I store the .jar file to import it in my code? I tried putting both the .jar file and my .java file in the same directory, didn't work.  The file I'm trying to work for is here:   I'm using JCreator LE. I'm on a MacBook Pro (15-inch, 2018) with Mojave 10.14.1. When I connect MBP to a external displays (either via HDMI or via Thunderbolt 2 adapters), the temperature raises sensibly (i.e., CPU temperature lies constantly over 90°) and fans start running fast (i.e., more than 50%) frequently, even if I am doing very simple tasks (e.g., writing in Word with a couple of Chrome tabs open with stackoverflow).  I'm not sure that the problem started with Mojave or if it isn't actually related to the OS version.  I'm wondering if there is a way to limit this annoying overheating as well as fans activity, while using external monitors. Indirect return of all elements in an array The Bash man page describes use of ${!a} to return the contents of the variable whose name is the contents of a (a level of indirection).  I'd like to know how to return all elements in an array using this, i.e.,  a=(one two three) echo ${a[*]}   returns  one two three   I would like for:  b=a echo ${!b[*]}   to return the same.  Unfortunately, it doesn't, but returns 0 instead.  Update  Given the replies, I now realise that my example was too simple, since of course, something like:  b=("${a[@]}")   Will achieve exactly what I said I needed.  So, here's what I was trying to do:  LIST_lys=(lys1 lys2) LIST_diaspar=(diaspar1 diaspar2)  whichone=$1   # 'lys' or 'diaspar'  _LIST=LIST_$whichone LIST=${!_LIST[*]}   Of course, carefully reading the Bash man page shows that this won't work as expected because the last line simply returns the indices of the "array" $_LIST (not an array at all).  In any case, the following should do the job (as pointed out):  LIST=($(eval echo \${$_LIST[*]}))   or ... (the route that I went, eventually):  LIST_lys="lys1 lys2" ... LIST=(${!_LIST})   Assuming, of course, that elements don't contain whitespace. What happens if no one survives the Hunger Games? It is possible that the remaining last two tributes might get killed at the same time, for example, by a land mine explosion, and in that case the games will end with no victor standing.  Is there a reference in the original books as to what happens if nobody emerges victor in the Hunger Games? I have a question about using the phrase "some kind of _".  Is it incorrect to say "some kind of + plural noun"?     For example, is it wrong to say "are these rock-like things some kind of chocolates?"   I didn't use "kinds" and that kind of adds to my question. Is "kind" always plural, like "some kinds of chocolates"? Because although I'm using "some", it feels like "kind" shouldn't be a countable noun.  Anyway, I don't think I've heard of "some kind of + plural", but I think it makes more sense then using singular, since I think chocolates are countable. Please help! What is the default 'backup' user for? I am setting up multiple-machine backup plan and I was hoping to use a user called 'backup' on each machine as the backup destination.   My problem is, there is already a user called 'backup' on my machine.  What is it for, and can I hijack it for my own purposes?  root@frodo:~# useradd backup useradd: user 'backup' already exists How to change default viewport shading in 2.8? Is it possible to change the default mesh color/shading in 2.8 to be more like 2.79? I'm finding it hard to see finer detail in 2.8. On the left is 2.8 and the right is 2.79 For all $x,y\in\mathbb{R}$   define that $x\equiv y$   if $x^{2}=y^{2}$  . Then $\equiv$  is an equivalence relation on $\mathbb{R}$  , there are infinitely many equivalence classes, one of them consists of one element and the rest consist of two elements.  Solution  True. To show that \equiv  is reflexive we need to show that \forall x\in\mathbb{R}  :x=x.  Let x\in\mathbb{R}  , x\equiv\mbox{\ensuremath{x}}  if x^{2}=x^{2},   which is obvious.  [x]  ={y\in\mathbb{R}  |x\equiv y}  =[0]={y\in\mathbb{R}|0\equiv y}={0}  . Hence y^{2}  =0^{2}   =0   which implies that y=0  .