How do we define interior and exterior of a geometric figure?
What makes the inside of a shape the inside?
Where, how and when I can acquire HM's? hierarchical retreival of records in postgresql Why do most 2D platformers start off in the left and progress in the right direction? In almost all 2D platformers I've played, your avatar always starts off on the left side of the world, and continues on to the right. Is there something designers gain by doing this? See these sentences:     See there, it seems that someone is inside the house. OVER   See there, it seems that someone is in the house.   Another example:     The doctors found two bullets in his body. OVER   The doctors found two bullets inside his body.   Certainly, both are interchangeable, aren't they? But in the bullet's example, the second one looks natural. I'm not sure why. Is it something that bullets were first out and then they went inside? But if that's the case, someone is in the house is also okay. That person too was out first! Resize (enlarge) an image without resampling (in favor of quality loss)? How to resize an image or selection without resampling the pixels? I have some pixel art that I want to enlarge without losing the hard, non-anti-aliased, pixel edges. In other words, 1px should become 4px of the same color— fake big pixels. Is there any way to achieve this procedurally?  Example (of what I don't want):  before resize:    after resize:    Open to other tools/methods beyond photoshop, thanks in advance. How to prove this binomial identity $\sum_{r=0}^n {r {n \choose r}} = n2^{n-1}$? How to fix byte array java.lang.NullPointerException iPad 1 update from 5.1.1 to 7.1 How can I update iPad 1 from iOS 5.1.1 to iOS 7.1?  I tried checking for updates but I get a message "your software is up to date". I'm trying to prove commutativity of addition for vector spaces, using the axioms for vector spaces. Apparently commutativity can be proven! Im having trouble getting a good feel for what is allowed and what is not. Here's my work so far:  $u+v+u+v = 2(u+v) = 2u + 2v = u+u+v+v = u+(u+v)+v$  Here I just wanna claim that $u+(v+u)+v = u+(u+v)+v$   $\Rightarrow -u+u+(v+u)+v+(-v) = -u+u+(u+v)+v+(-v)$ : here im just adding -u to the right, and -v to the left. Question: is this "adding to both sides" really legit in this context? Why?   Quick help proof: $-v+v = (-1)v+(1)v = (-1+1)v = 0v = 0 = v-v$  And another: $ 0+v = v+(-v) + v = (1)v + (-1)v + v = (1-1)v + v = v = v+0$  We have $0 + (u+v) + 0 = 0+(v+u)+0 \Rightarrow u+v = v+u$  This feels ugly and not at all elegant, especially the great leap "add -u to both sides" feels completely out of place. Do I need more lemmas? Is there a more elegant way?   //not homework or anything, just for my own pleasure, feel free to provide theory, as it is more insightful than solutions. :) Thanks!   EDIT: corrected notation a little. Spatial reference for dummies? Can anyone recommend a good reference or tutorial that explains the principles of spatial references, projections, and coordinate systems?   We are a small team of programmers working with GIS technology, and we often get snagged when working with data in different SRS/CS because we don't understand the concepts. Is it possible to delete the "useless" apps pre-installed on my Mac? When would you use the Builder Pattern? What are some common, real world examples of using the Builder Pattern?  What does it buy you?  Why not just use a Factory Pattern? Which repository source do I need to add to my sources.list to access the package firmware-linux-nonfree?  I am using Deb 6 testing 32 bit. centos: using epel repository on a server machine Are there any downsides in enabling epel repository on a server machine or is it something every sysadmin does? I would have read this around 1985-1998 because I remember being in school at the time. It may have been in a short story collection with "The Ugly Little Boy" and a story about a family dealing with people in the future coming back to enhance the intelligence of their baby with enfante terrible results. A boy, grade school age or so and very intelligent, discovers (or possibly just decides) that there are drugs in the food that prevent one from thinking critically. The details are kind of fuzzy in my head, but I remember that he at one point distills the chemical from his cereal, which he'd detected as having a high concentration, and overdoses. He's convinced that the government is trying to silence him — a scene that sticks out in my mind was him falling on a moving sidewalk and tearing his clothing as he tries to escape two "men in black" type figures that are pursuing him. The short story ended with him deciding that he was better off just consuming the food and being happy in his ignorance.  Years later, as an adult learning about mental illness, it struck me that the story was slightly ambiguous as to whether there actually were chemicals, and that the use of drugs that dulled his creativity and intelligence, and the decision to take them anyhow, was reminiscent of the feelings that manic people have toward their medications.  Anyone know what this one was? $_POST vs. $_SERVER['REQUEST_METHOD'] == 'POST' Some guy called one of my Snipplr submissions "crap" because I used if ($_SERVER['REQUEST_METHOD'] == 'POST') instead of if ($_POST)  Checking the request method seems more correct to me because that's what I really want to do. Is there some operational difference between the two or is this just a code clarity issue? Why doesn't the Go statement execute in parallel? The particle number on my settings appear in gray, I don't think i'm able to change the number even thought i need it, how can i make it white again? Formatting OGR VRT file to convert CSV to KML? Shrink Tempdb log file when reaching a specific size how I can shrink tempdb log file when reaching a specific size?? I'm scheduling job to shrink tempdb but still I face a problem of disk space due to tempdb is full!