ruby difference between class ClassName and class ::ClassName
What is Ruby's double-colon `::`?
How to set custom keyboard shortcuts from terminal? Prove if $|a_{n+1}|/|a_n| \leq |b_{n+1}|/|{b_n}|$ and $\sum |b_n|$ is convergent, then $\sum |a_n|$ is convergent In C++, what is the purpose of the scope resolution operator when used without a scope? For instance:  ::foo(); How can I play sound in Java? A single word for someone who spends their wealth very foolishly $L^p$ and $L^q$ space inclusion Let $(X, \mathcal B, m)$ be a measure space.  For $1 \leq p &lt; q \leq \infty$, under what condition is it true that $L^q(X, \mathcal B, m) \subset L^p(X, \mathcal B, m)$ and what is a counterexample in the case the condition is not satisfied? We add negative numbers and zero to natural sequence to make it closed under subtraction, the same thing happens with division (rational numbers) and root of -1 (complex numbers).  Why this trick isn't performed with division by zero? Would approaching a distant star at near the speed of light unfold its entire history in "fast-forward"? Finding the volume of the tetrahedron. Find the volume of the tetrahedron with the vertices $P(1,1,1)$, $Q(1, 2, 3)$, $R(3, 1, 2)$, and $S(2, 3, 1)$. These wonderful icon overlays that give you useful information in the Windows Explorer are not showing up.   It's the most annoying with Dropbox (I already read ). I just tried reinstalling Dropbox - no help. I have this problem also with the  so I don't think that it is a dropbox problem specifically; and something is wrong in my OS. The OS is actually a pretty fresh clean-install...  OS: Win8 Pro 64-bit. Why can't energy be created or destroyed? My physics instructor told the class, when lecturing about energy, that it can't be created or destroyed.  Why is that?  Is there a theory or scientific evidence that proves his statement true or false?  I apologize for the elementary question, but I sometimes tend to over-think things, and this is one of those times. :) How does wizard & cleric spell preparation and casting work? In 3.X wizards had spellbooks, while clerics had their entire spell list, but they both memorized/prepared spells every day from those lists, and had a certain number of slots for preparing spells in.  Now in 5e preparing spells and spell slots aren't the same thing. What's going on here? How does their spellcasting work now? "I will appreciate your help" I encounter the phrase "I will appreciate your help" from time to time and it doesn't sound too honest to me. To be more specific, I don't have a problem with this phrase coming from a friend, because he will appreciate my help by "owing me one". But a stranger from the Internet, that's different, methinks.  "How will you appreciate it?" pops in my mind every time I see it, because to me, appreciation equals reward and, well, you can't reward people over the internet much. It is quite possible that I am just wrong and this is a perfectly fine figure of speech. Which one of these two statements is correct?     Our staff do ...      Our staff does ...   And is staffs ever correct? How to use PSTricks in pdfLaTeX? I thought that PSTricks package was not possible to use in pdfLaTeX but .   How can I force pdfLaTeX to use PSTricks then? Simple extension fields If I am correct simple extension fields are extensions generated by one element. I have learned that this means that elements of a simple extension can be written as powers of that element as long as the power is greater than the degree of that element. Also this means that all elements of the simple ext. Can be written in terms of decending powers of the generating element where the highest power is the degree of the generator minus 1. This concept seems to work for generating elements whose irreductable in a certain field is a descending degree polynomial. Looking at the construction of the complex numbers by starting with $\Bbb R$ (and doing $\Bbb R [x]/\langle x^2+1\rangle$), it is said that all elements are of the form $a+b\cdot \text{generator}$. But when the generator is evaluated for the irreductable, $x^2+1$, we see... $(\text{generator})^2=-1$. Thus there is no first power of gen. Can someone explain where all elements of the extension just explained are of the form $a+b\cdot \text{generator}$ comes from or explain this situation for anytime where the irreduc ( gen, F)  is not a descending degree polynomial. I hope my question is clear.  Thank you My processor is 64-bit - does that mean I need the amd64 image? In Ubuntu 13.04 I used to use the ppa:upubuntu-com/tor64  PPA to install the 64-bit Tor Browser Bundle. However, in Ubuntu 13.10 it doesn't work anymore. How do I install the Tor Browser Bundle in Ubuntu? The integral $\int_0^8 \sqrt{x^4+4x^2}\,dx$ Original sentence:     Prince Andrew, looking again at that genealogical tree, shook his head, laughing as a man laughs who looks at a portrait so characteristic of the original as to be amusing.    (War and Peace, Tolstoy, English translation)     In the sentence above, shouldn't the comma before laughing be omitted if this is about the participle clause denoting "an action that happens at the same time in the past"?  I mean it should be      Prince Andrew…shook his head laughing as a man…   Plus, shouldn't the verb laugh after a man be in the past tense in order to be in accordance (agreement) with shook his head?   You know, the whole sentence should be consistent….