sorting with Map from highest to lowest
Sort a Map by values
Iterate a list with indexes in Python CSS - Make divs align horizontally I have a container div with a fixed width and height, with overflow: hidden.  I want a horizontal row of float: left divs within this container. Divs which are floated left will naturally push onto the 'line' below after they read the right bound of their parent. This will happen even if the height of the parent should not allow this. This is how this looks:  ![Wrong][1] - removed image shack image that had been replaced by an advert  How I would like it to look:  ![Right][2] - removed image shack image that had been replaced by an advert  Note: the effect I want can be achieved by using inline elements &amp; white-space: no-wrap (that is how I did it in the image shown). This, however, is no good to me (for reasons too lengthy to explain here), as the child divs need to be floated block level elements. Which configuration of armor enchantments gives maximum protection? Given $a,b,c,d \in \mathbb{Z}$, there is $x,y$ such that  $$(a^2 + b^2)(c^2 + d^2) = x^2 + y^2$$  One can show this by considering the complex number $a + bi$ and $c+ di$, using complex properties to deduce that $x = ac - bd, y = ad + bc$ is a solution.   However, given that either $a^2, b^2$ are distinct or $c^2,d^2$ are distinct, then how can one can find nonzero solutions $x,y$?  Sorry, I am assuming $a,b,c,d$ are nonzero. What would be the nicest proof of the following theorem:  If $\lim\limits_{n \rightarrow \infty} a_{n} = \infty$, then $\lim\limits_{n \rightarrow \infty} \left(1 + \frac{1}{a_{n}} \right) ^ {a_{n} } = e$. If $\lim\limits_{n \rightarrow \infty}b_{n} = 0$, then $\lim\limits_{n \rightarrow \infty} \left(1 + b_{n} \right) ^ {\frac {1} {b_{n}} } = e$.  I somehow failed to find a proof here on the website and in the literature. Making a string out of a string and an integer in Python Consecutive/Rolling sums in a vector in R Past tense: learned/learnt, dreamed/dreamt? In my very first question, Carlo made an edit stating that learnt is a rare past tense of learn. I am accustomed to using learnt for past tense and learned as an adjective (as in He is a learned scholar.) I checked into a couple of dictionaries and they say both are valid past tenses. Do I stand a risk of not being understood if I use learnt?  In a similar vein, should dreamed be used as a past tense for dream instead of dreamt? I can't think of other such conflicts, but I guess there must be more. No non-trivial clopen sets in $\mathbb{R}$? How to give a direct proof? How to give a direct proof of the following result?     Let $A$ be a subset of $\mathbb{R}$ such that $A$ is both open and closed. Then $A$ is either empty or all of $\mathbb{R}$?   My work:   If $A$ is not empty, let $u \in A$. Then there is some open interval $(a,b)$ such that $$u \in (a,b) \subset A.$$  Now if $\mathbb{R} - A$ is not empty either, then let $v \in \mathbb{R} - A$. Then there is some open interval $(c,d)$ such that  $$v \in (c,d) \subset \mathbb{R} - A.$$  Suppose that $u &lt; v$.   Since $$\emptyset \subset (a,b) \cap (c,d) \subset A \cap (\mathbb{R} - A) = \emptyset,$$ we must have $$(a,b) \cap (c,d) = \emptyset.$$ So we can conlclude that $$b \leq c.$$ But $b \in A$ and $c \in \mathbb{R} - A$. So we must have $$b &lt; c.$$  What next? Can anybody here please help complete the proof from here on?  An edit based on a comment by Marc Paul:   Let us assume that the set $A$ is a non-trivial clopen set in $\mathbb{R}$. Let us define a function $f \colon \mathbb{R} \to \mathbb{R}$ as follows:  $$f(x) \colon= \begin{cases} 1 \ \mbox{ for } \ x \in A; \\ 0 \ \mbox{ for } \ x \in \mathbb{R} - A. \end{cases}$$   Let $V$ be an open set in the range space $\mathbb{R}$. We show that the inverse image set $f^{-1}(V)$ is open in the domain space $\mathbb{R}$.   The following cases arise:   If $0, 1 \in V$, then $f^{-1}(V) = \mathbb{R}$.   If $0 \in V$ but $1 \not\in V$, then $f^{-1}(V) = \mathbb{R} - A$.   If $1 \in V$ but $0 \not\in V$, then $f^{-1}(V) = A$.   And, if $0 \not\in V$ and $1 \not\in V$, then $f^{-1}(V) = \emptyset$.   Thus, $f^{-1}(V)$ is open in the domain space $\mathbb{R}$.   Hence the function $f$ is continuous.   What next? How does this lead to our desired conclusion?   [Yet another edit, again based on valuable comments from Marc Paul: ]  So if both $A$ and $\mathbb{R} - A$ were non-empty, then let's suppose $a \in A$ and $b \in \mathbb{R} - A$, and we can assume without any loss of generality that $a &lt; b$.   Then $f(a) = 1$ and $f(b) = 0$. So by the intermediate value theorem there is a real number $c \in (a,b)$ such that $f(c) = 1/2$, which is a contradiction because the image set of $f$ does not contain $1/2$. I have written an essay last year, as a personal exercise. I now have a course at uni on the topic and could basically just hand in this essay now, the topic fits perfectly. I have also never submitted this essay to any other course or so.  Could I just hand in this essay, or would I violate some rules with that? Is this maybe already self-plagiarism? I am studying the function and characteristic of an op-amp to build a line-following robot with the schematics below. However, in many tutorials, the way to differentiate an inverting and non-inverting op-amp is by looking at the connection to ground via the inverting or non-inverting terminal.  However, in the schematics, the op-amp is considered to have connections to ground, thus in this case, how do I differentiate it then?  I may have understood the whole concept wrongly. Pls help!    EDIT: Please ignore the switch as it may have been drawn wrongly by the supplier. Copy game data from one PS4 to another? I want to completely replace Ubuntu with Lubuntu I accidentally issued some commands I thought were safe in the terminal, and I ended up with no System Settings and lots of other missing functionality, but the OS still boots normally. I've decided I want to install Lubuntu instead of fixing Ubuntu for a fresh start and since my laptop is running on a 1GHz dual core AMD CPU.  I created a bootable USB as I usually do and placed Lubuntu 17.10 amd64 using Rufus 2.14.1086. I have GRUB that was installed with Ubuntu upon first install I still have Win8.1 which I still want to keep.  PS: I also tried creating a startup disk from Ubuntu  The question is: How can I boot from USB with GRUB2 so I can overwrite Ubuntu? If I multiclass into 2 or more spellcasting classes, how do I determine my known/prepared spells? If I multiclass into 2 or more classes/subclasses that can cast spells, how do I determine what spells I know or can prepare?  For instance, if I am playing a multiclassed character with 1 level in warlock, 2 levels in bard, and 3 levels in paladin, how do I determine which spells I know/have prepared?    Related: Which option is grammatical?        There will be readings from Nikki Giovanni’s and Alice Walker’s writings.   There will be readings from Nikki Giovanni and Alice Walker's writings.      Saying it out loud the latter sounds right, but looking at it the former looks better. "A flea hops randomly on the vertices of a triangle with vertices labeled 1,2 and 3, hopping to each of the other vertices with equal probability. If the flea starts at vertex 1, find the probability that after n hops the flea is back to vertex 1."  Could someone provide a hint to help me start this? Why is the Ideal Norm Multiplicative? If $a,b$ are the roots of the equation $2 x^2 -3 x +1 = 0$, find an equation whose roots are $a/(2b +3)$, $b/(2a +3)$ Integral $\int\csc^3{x} \ dx$ Independence of Gaussian variables