Ra's al Ghul story line
Who killed Ra's Al Ghul first, Batman or Arrow?
Use of "Or", inclusive or exclusive? My wife and I are playing a game where you roll dice and move so many spaces in a grid "vertically or horizontally".   In the use of English it is very common to say, this or the other when it comes to making a choice  (exclusive or). Now I know that "or" can also be inclusive, for example "she couldn't read or write", or can be clearly used as an xor "you either come or not" making the statement true for only one of the options but not both.   My issue is where it is not clear whether it is an inclusive/exclusive or, the best example being our game.   I argue that you can move in either direction (inclusive) and the normal use of this conjunction in English should be inclusive unless specified otherwise.   Is this right? How to show $\lim_{n \to \infty} \sqrt[n]{a^n+b^n}=\max \{a,b\}$? how many terms will there be once you collect terms with equal monomials? What is the sum of all the coefficients? If you expand $(x_1+x_2+\cdots+x_k)^n$, how many terms will there be once you collect terms with equal monomials? What is the sum of all the coefficients?  I'm kind of lost here. This came up with other questions on the topic of binomial coefficients, and i have figured those out. I have spent almost an hour trying to figure where to start and haven't made any progress. How can I set default value in ActiveRecord?  I see a post from Pratik that describes an ugly, complicated chunk of code:   class Item &lt; ActiveRecord::Base     def initialize_with_defaults(attrs = nil, &amp;block)     initialize_without_defaults(attrs) do       setter = lambda { |key, value| self.send("#{key.to_s}=", value) unless         !attrs.nil? &amp;&amp; attrs.keys.map(&amp;:to_s).include?(key.to_s) }       setter.call('scheduler_type', 'hotseat')       yield self if block_given?     end   end   alias_method_chain :initialize, :defaults end   I have seen the following examples googling around:    def initialize      super     self.status = ACTIVE unless self.status   end   and    def after_initialize      return unless new_record?     self.status = ACTIVE   end   I've also seen people put it in their migration, but I'd rather see it defined in the model code.  Is there a canonical way to set default value for fields in ActiveRecord model? Why do DNGs only show in low resolution on Google Photos? Through my NAS at home I store and backup all my photos on Google Drive. These photos also show up on Google Photos. I use Lightroom and convert all photos to DNG when copying to my NAS.  When I look at the photos in Google Photos the image is rather small. Clicking the (i) info button tells me the image has a resolution of 1024x680, file size 9.8 MB and a MP of 0.7. This is probably just a preview or thumbnail of some sort, but how do I view the image in larger resolutions in Google Photos? In the Futurama episode "" they save the world by rotating the Earth backwards saying it shouldn't matter (which direction Earth rotates). If Earth rotated clockwise and remained in it's current counter-clockwise orbit around the Sun, would it affect anything beyond the direction the constellations move across the sky? How to add modifiers using python script and set parameters? I've found some code that could add a modifier but none can set parameters like Octree. Got 2,919 PB/s in Ubuntu Terminal I have problem (seems to be trivia) about Ubuntu Terminal. Once my network connection slow down then it (sometimes but very rare to happened) showed some information like this.     I shocked because I have been got 2,919 PB/s. Sorry my mouse block some part of letter 'P' (I actually rush to print screen) but I believe you can recognize it.    EDIT    based on answer given to me, and I got similar info then, I'd like to add more clearly new image after.    Can someone explain it to me?  Best Regards! Series $\frac{x^{3n}}{(3n)!} $ find sum using differentiation Find sum of the series $$\sum_{n=1}^{\infty}\frac{x^{3n}}{\left(3n\right)!}$$ using differentiation. So far I found that $$S(x)+1=S'''(x)$$ but it does not help. Then I tried different interesting ideas  like $$S(x)+S'(x)+S''(x)=e^x-1\,.$$Maybe if I get the third equation it will allow me to construct a kind of differential equation. Then, by solving it, obtain $S(x)$. Question about the Euclidean ring definition I recently came across the following definition for a euclidean ring:  There exists a function $g:R\to\Bbb N_0$ with the following properties:  1.) $\forall x,y \in R$ with $ y \neq 0$ there exist $q,r \in R$ with $x = qy + r$ where $r=0$ or $g(r) &lt; g(y)$.  2.) $\forall x,y\in R\setminus\{0\}$ we have $g(xy)\ge g(x)$  What I don't understand, is the point of the second requirement. I have seen definitions where this is not a requirement. What does 2.) achieve?   Thanks very much Upgrading straight handlebars to drop handlebars Specify a bijection from [0,1] to (0,1]. $n$ Lines in the Plane How am I to "[u]se induction to show that $n$ straight lines in the plane divide the plane into $\frac{n^2+n+2}{2}$ regions"? It is assumed here that no two lines are parallel and that no three lines have a common point. Further, this is not a non-Euclidean problem, but I wouldn't mind a discussion on the non-Euclidean nature of the problem.  I was thinking it might be easier to show using the unit sphere.    A GOOD REFERENCE I FOUND THAT WILL BE USEFUL TO ANYONE COMING ACROSS THIS PROBLEM IS Concrete Mathematics, Graham, Knuth, Patashnik pp. 4–8. What is the correct pronunciation of the word “processes”? How do you set a default value for a MySQL Datetime column?  In SQL Server it's getdate(). What is the equivalant for MySQL? I'm using MySQL 5.x if that is a factor. If $\operatorname{rank}\left( \begin{bmatrix} A &B \\ C &D \end{bmatrix}\right)=n$ prove that $\det(AD)=\det(BC)$ Let $A,\ B,\ C,\ D \in \mathcal{M}_n(\mathbb{C})$. If $\operatorname{rank}\left( \begin{bmatrix} A &amp;B \\ C &amp;D \end{bmatrix}\right)=n$, prove that $\det(AD)=\det(BC)$. Explain briefly What is meant by interpolation.How is it related to the concept of regression?  interpolation is art of reading between the lines of a table and in elementary mathematics the term usually denotes the process of computing the intermediate values of a function from a set of given or tabular values of that function.  I can't give the answer of second question. Privilege banner buggy? Or am I just confused? On the main Stack Overflow site, I arrived and had a banner: "Congrats, you've gained the privilege – create wiki posts and 3 other privileges" This confuses me, because I only see two privileges listed at 100%. Is the banner just buggy?  Or is there a better place to see my privileges that the page linked to by that banner? A Polygon is inscribed in a circle $\Gamma$ A regular polygon P is inscribed in a circle $\Gamma$. Let A, B, and C, be three consecutive vertices on the polygon P, and let M be a point on the arc AC of $\Gamma$ that does not contain B. Prove that  $MA\cdot MC=MB^2-AB^2$  I inscribed the polygon P in the unit circle and let B=1. Past this, I'm not really sure how to proceed. It might be helpful to have M at 1 as well but given that the polygon would have the n-th roots of unity in it B seemed like a good choice. What would be a good way to proceed from here? Show that $e^3 > 20$