Velleman exercise 1.5.7a
Finding minimal form -- Velleman exercise 1.5.7a
Rules for the usage of "me" VS. "myself"? What are general guidelines for the use of "me" and "myself"?     Did I describe me or did I describe Maria?   OR     Did I describe myself or did I describe Maria? For example, here are top five accounts in each site (this picture was taken when I was in Biology SE).    As you can see, all the badges are DNA, while Academia's badges should be hats, so on.  What do you think? What is this heart in the crimson biome? I found this heart while exploring the crimson biome - what is it? How is double negation interpreted in English? Install 18.04 server without network connection Understanding GeoTIFF tags? Where can I find 32-bit version of Ubuntu? I need to find the 32-bit version, and all I keep finding is the 64-bit. Can anyone provide me with a link? ResultSet: Retrieving column values by index versus retrieving by label When using JDBC, I often come across constructs like    ResultSet rs = ps.executeQuery(); while (rs.next()) {     int id = rs.getInt(1);     // Some other actions }   I asked myself (and authors of code too) why not to use labels for retrieving column values:    int id = rs.getInt("CUSTOMER_ID");   The best explanation I've heard is something concerning performance. But actually, does it make processing extremely fast? I don't believe so, though I have never performed measurements. Even if retrieving by label would be a bit slower, nevertheless, it provide better readability and flexibility, in my opinion. So could someone give me good explanation of avoiding to retrieve column values by column index instead of column label? What are pros and cons of both approaches (maybe, concerning certain DBMS)? If I run along the aisle of a bus traveling at (almost) the speed of light, can I travel faster than the speed of light? Let's say I fire a bus through space at (almost) the speed of light in vacuum. If I'm inside the bus (sitting on the back seat) and I run up the aisle of the bus toward the front, does that mean I'm traveling faster than the speed of light? (Relative to Earth that I just took off from.) When to throw an exception? How do I drop an object to the sand? Gravity as a gauge theory Currently, (classical) gravity (General Relativity) is NOT a gauge theory (at least in the sense of a Yang-Mills theory).   Why should "classical" gravity be some (non-trivial or "special" or extended) gauge theory? Should quantum gravity be a gauge theory?  Remark: There are some contradictory claims in the literature to this issue. To what extent gravity is "a gauge" theory?Obviously, GR is not a YM theory. So, why do some people say that gravity "IS" a gauge theory? I found this question relevant, e.g., then we handle GR in the Einstein-Cartan theory or any other theory beyond GR, like teleparallel theories or higher-derivative gravitational theories. So I think it could be useful to discuss the "gauge flavor" of gravity here. When should com­pound words be writ­ten as one word, with hy­phens, or with spaces? Some compound words are written without hyphens (nonaggression, nonbeliever), some with hyphens (well-intentioned), and others with spaces (post office).  Is there a rule or good guide as to which option should be used? iPhone Apps in Waiting mode for the last 4 days I tried to download the "Dictionary Free" app from the App Store four days ago, but it's been stuck in "Waiting" ever since. I've tried everything: rebooting the phone, restoring from an iTunes backup, side-loading the app from iTunes, but nothing has worked.  When I turn Airplane Mode on and then off again, I get an alert popup that says "Unable to download application. It will be available for download when you log in to the iTunes Store on your computer".  I've tried what it recommends, but nothing seems to work. Express $\sqrt{3}\sin\theta - \cos\theta$ as: $a\cos (\theta + \alpha) $ Prove the Probability of Two Events I'm taking my first course in Probability and one of my homework problems is to prove that for any two sets:  $$P(A \cup B) = P(A) + P(B) - P(A \cap B) $$  Note that the function $P$ is the probability of an event happening.  From the third axiom, we are given that for any two disjoint sets, that is $ A \cap B = \emptyset$:  $$P(A \cup B) = P(A) + P(B)$$    My thought process follows from this third axiom, but I run into a problem near the end:  Since $A$ and $B$ are disjoint sets, $P(A)=P(A-B)$ and $P(B)=P(B-A)$, so  $$P(A \cup B) = P(A) + P(B)=P(A-B)+P(B-A)$$  From this, it appears that we are essentially taking the symmetric difference of A and B.  This, to me, seems to be equivalent to:  $$P(A-B)+P(B-A)=P(A)+P(B)-P(A \cap B)$$  Hence, by my logic:  $$P(A \cup B) = P(A)+P(B)-P(A \cap B)$$  Which, in essence, doesn't care whether two sets are disjoint or not as we are subtracting the intersection of them.  If the sets are disjoint, then the intersection is merely null.  If they intersect, then we are removing the "extra pieces".  I feel like this is inadequate proof despite my ability to convince myself that it is true..  Where, if anywhere, did I go wrong?  Thanks! JavaScript get clipboard data on paste event (Cross browser) Can you use a Pensieve-memory to explore a place? I have installed the developer preview for Yosemite.  Huge mistake. Everything in my workspace is broken.  I don't have any sort of backup image. I was wondering if I could re-download Mavericks and run the installer - would that effectively downgrade me back to Mavericks? What are these tags related to on the Newest Questions page? On the right, there is a widget that lists "Related Tags" (left − SO April 2013, right − MSE May 2014):         What are they related to? There isn't even a question selected. Are they related to the whole displayed list?  This can be seen on every SE site.