Which of the following to use, especially in the context of programming:   hashtag well number pound sign
I used to say "sharp sign" to refer to the # sign.   Today a friend told me that the correct term is number sign or hash sign or even just hash.  What is the difference between these options and what's the correct usage of the names for this sign?
I need something explained or corrected:  In my number theory class we proved that there are an infinite number of primes using Euler's Phi Totient. It went something like this:  Let $M = p_1 p_2 \dots p_n$ be the product of all primes. Consider $1 &lt; A \le M$:  Some prime must divide $A$, call it $q$. Since $q$ must be one of the primes, $q$ must divide $M.$  So the $gcd(A,M) &gt; 1.$ Thus $\phi(M) = 1$ ...?   Which is not even and contradicts the theorem that $\phi(N)$ is even for $N&gt;2.$ Therefore there exists an infinite number of primes.  I get confused by the statement "Thus $\phi(M) = 1$"....  Did i possibly copy this proof down wrong? or am I missing something? Thank you in advance.   Edit: by consider a such that...i meant consider an integer '$a$' I replaced it with $A$ to hopefully make it more clear.   Edit2: I'm sorry I am not familiar with using the equation editor. This is not a homework assignment, just studying for my exam. I just want to be able to understand this or clearify it. I have added an mp3 file as a static resource, can someone please help me to call that resource in the lightning component so when I hit the button it will play that static resource  as per the Salesforce documentation I have tried below but instead of playing the sound it is displaying the message. Determine if the convergence of $f_n(x) = \sqrt{x^2 + \frac{1}{n^2}}$ is uniform. $f_n(x) = \sqrt{x^2 + \frac{1}{n^2}}$ converges pointwise in a set $E = [0, \infty)$ to $f(x) = x$.   This problem reminds me a lot of how $\frac{x}{n}$ fails to converge uniformly to $f=0$ on $[0,\infty]$, but does converge uniformly on $[0,a]$. However, when we proved that we used the definition of uniform convergence. I do not wish to do that here.  I wish to use the Weierstrass test here. And that is where I'm stuck. I cannot find $M_n = \sup\limits_{x \in E} |f_n(x)-f(x)|$. Can someone help me out here? Is there a size limit on external USB hard drives? The internal SATA hard drives have a limit on a lot of motherboards of 2TB and if I want to get a 3TB HDD then I need to connect it using a PCI card (or get a new motherboard).  But I wanted to ask: If I connect a 3TB harddrive to a external USB enclosure, will it work? The  I want to buy says it supports up to 3TB HDD but I want to make sure. Integral $\int\csc^3{x} \ dx$ I found these step which explain how to integrate $\csc^3{x} \ dx$. I understand everything, except the step I highlighted below.  How did we go from: $$\int\frac{\csc^2 x - \csc x \cot x}{\csc x - \cot x}\,dx%$$ to  $$\int \frac{d(-\cot x + \csc x)}{-\cot x + \csc x} \quad?$$  Thank you for your time! $$ \int \csc^3 x\,dx = \int\csc^2x \csc x\,dx$$ To integrate by parts, let $dv = \csc^2x$ and $u=\csc x$. Then $v=-\cot x$ and $du = -\cot x \csc x \,dx$. Integrating by parts, we have: $$\begin{align*} \int\csc^2 x \csc x \,dx &amp;= -\cot x \csc x - \int(-\cot x)(-\cot x\csc x\,dx)\\ &amp;= -\cot x \csc x - \int \cot^2 x \csc x\,dx\\ &amp;= -\cot x\csc x - \int(\csc^2x - 1)\csc x\,dx &amp;\text{(since }\cot^2 x = \csc^2-1\text{)}\\ &amp;= -\cot x \csc x - \int(\csc^3 x - \csc x)\,dx\\ &amp;= -\cot x\csc x - \int\csc^3 x\,dx + \int \csc x\,dx \end{align*}$$ From $$\int \csc^3 x\,dx = -\cot x\csc x - \int\csc^3 x\,dx + \int \csc x\,dx$$ we obtain $$\begin{align*} \int\csc^3x\,dx + \int\csc^3 x\,dx &amp;= -\cot x \csc x + \int\csc x\,dx\\ 2\int\csc^3 x\,dx &amp;= -\cot x\csc x + \int\csc x\,dx\\ \int\csc^3x\,dx &amp;= -\frac{1}{2}\cot x\csc x + \frac{1}{2}\int\csc x\,dx\\ &amp;=-\frac{1}{2}\cot x\csc x + \frac{1}{2}\int\frac{\csc x(\csc x - \cot x)}{\csc x - \cot x}\,dx\\ &amp;= -\frac{1}{2}\cot x \csc x + \frac{1}{2}\int\frac{\csc^2 x - \csc x\cot x}{\csc x - \cot x}\,dx\\ &amp;= -\frac{1}{2}\cot x \csc x + \frac{1}{2}\int\frac{d(-\cot x+\csc x)}{-\cot x +\csc x}\\ &amp;= -\frac{1}{2}\cot x\csc x + \frac{1}{2}\ln|\csc x - \cot x|+ C \end{align*}$$ Greatest and Least Resistance and Current Characteristics of Parallel vs Series circuits Which type of circuit would have the greater resistance?  Which type would have the greater current? and Why?  My book says that parallel has the greater resistance than current as parallel wiring if thought as water pump tubes has greater resistance during water flow.  Contrary to my book, if I make up numbers to solve for which has the greater resistance, i find that  series has greater resistance.  Equivalent resistance of 2 Ohm resistor in series is greater than that of 2 resistors with 2 ohms in parallel. I Entity Framework and SQL Server View JavaScript: Bitwise shift of long long number I need to bitwise shift a value 64 times in JavaScript. But JavaScript starts rounding after 32.  For example:  for(var j = 0; j &lt; 64; j++) {     mask = mask &lt;&lt; 1;     console.log(mask); }   This prints value from 0 to 1073741824 but then rounds of and starts printing 0. What's with the Japanese SO's stats? I took this screenshot just now, and  about the new . I refreshed the page, went back, and nothing changed.    And, here's what I find odd:  It clearly isn't almost 2014 years old. That's more likely when it was started.  How can there be 8.7 questions a day, while there are 0 visits a day? That's kind of impossible.   I'm hoping here that it's not just me. I know very limited Japanese, not even enough to hold a conversation with a toddler. I'm merely observing. Monotonicity of the sequences $\left(1+\frac1n\right)^n$, $\left(1-\frac1n\right)^n$ and $\left(1+\frac1n\right)^{n+1}$ Trying to wrap my head around the ways to properly handle collision in a game designed around components.  I see many examples have some sort of PhysicsComponent that gets added to the entity's list of components but the actual implementation is confusing me.  For this to work, the PhysicsComponent would need access to the world around it. This doesn't make intuitive sense to me. Shouldn't a component be unaware of not only its container (the entity), but its container's container (the world)?  To me, it sounds like the level or scene should maintain a list of these entities and every game update, loop through the entities to determine which collide.  My question is firstly, whether or not this is good design, and secondly, how to determine which entities can collide. I suppose solid entities could implement an empty IRigidBody interface so the level could determine which entities in the list support collision. But is this breaking the component design?  Instead, should they contain an empty RigidBody component? This may actually be better because it may not always be empty and this approach is more future-proof. The only problem with this is the complexity. The scene would have to loop through not only every entity, but also every entity's components to determine if it had this RigidBody component.  Thirdly, when they do collide both entities should be informed somehow and I am unsure on how to accomplish this either.  Let's say that both entities contained a HealthComponent and when they collided both their healths would be decreased by some arbitrary value, 5. I suppose it would be the scene's responsibility to handle this when it detects a collision between two entities?  But then is the scene responsible for too much? I could see this possibly getting out of hand and becoming unwieldy when the scene is responsible for many things entities should not (?) have access to.  Edit: Question updated with more details. My office is a converted garage about 30 feet from my house.   I have a coaxial cable already running from my house to the office.   I want to attach a Ethernet cable from my DSL modem, in my office, to a computer in my house.   Since I already have the coaxial cable installed, I bought two coax to Ethernet converters (NVA-P-860-BP78 Video Balun), but when I hooked them up I am getting no signal. It was my understanding that an Ethernet signal could travel over a coaxial cable.   Is that wrong? Any ideas why this isn't working? Detecting superfluous #includes in C/C++? Coefficient growth in the power series $\sum u_n z^n = e^{1/(1-z)}$? How to show $x_1,x_2, \dots ,x_n \geq 0 $ and $ x_1 + x_2 + \dots + x_n \leq \frac{1}{2} \implies (1-x_1)(1-x_2) \cdots (1-x_n) \geq \frac{1}{2}$ How to show  $x_1,x_2, \dots ,x_n \geq 0 $ and $ x_1 + x_2 + \dots + x_n \leq \frac{1}{2} \implies (1-x_1)(1-x_2) \cdots (1-x_n) \geq \frac{1}{2}$ Class moderncv moving footer I am using documentclass moderncv to style my resume, and I'd like to put the information that normally goes at the bottom of the document, such as phone number and email, to the space next to the name aligned on the left of the document. I'm a beginnner user, so I'd love to get some enlightenment on this.  \documentclass[11pt,letterpaper,sans]{moderncv}  % moderncv themes \moderncvstyle{casual} \moderncvcolor{blue} \usepackage[scale=0.75]{geometry}  % personal data \firstname{John} \familyname{Doe} \mobile{+1~(234)~567~890}  % content  \begin{document} \makecvtitle \pagestyle{empty}  \section{Education} \cventry{1998-2007}{Degree}{Institution}{City}{\textit{Grade}}{Description}   \section{Computer skills}  \thispagestyle{plain} \end{document}    Simply put, I want to move \mobile from the bottom to the top left. Prove that $T^2$ is the zero transformation if and only if $\mathrm{range}(T) \subseteq \ker(T)$. $\newcommand{\range}{\mathrm{range}}$The full question: $T^2$ means the composition, i.e. $T(T(x))$ Let $V$ be a vector space and let $T: V \rightarrow V$ be linear.  Prove that $T^2$ is the zero transformation if and only if $\range(T) \subseteq \ker(T)$. So far I know that for ($\implies$).  Assume $T^2$ is the zero transformation.  Then $\ker(T^2)=\{0 \in V: T^2(v)=0\}$.  Note that this is $\forall v \in V$. We also know that the $\range(T)=\{0\in V: \exists v \in V: T^2(v)=0\}$. Not sure where to go from here.  Also for the other way, I don't know where to go. Are there infinitely many primes of the form $6^{2n}+1$ or only finitely many? Does anyone know whether there are only finitely many of primes of the form $6^{2n}+1$, where $n$ zero or any natural number? Books for Hyperbolic Geometry. I want to read hyperbolic geometry. Can any one suggest some good books on the topic. Homeomorphism is bijective Here is my question:  Is a homeomorphism, that is, a continuos function whose inverse function is also continuous, always bijective?