Is it "time off of work" or "time off work" without 'of'?  Ex: I need to take some time off (of) work next month.
What is the difference when you say "get off of something" and "get off something"?
Proving $(A\le B)\vee (B\le A)$ for sets $A$ and $B$ Why does my front derailleur not work when it is cold? When it is warm outside my front derailleur works just fine. But when it gets colder (40F) the lever on the handle bar does not catch and I can move it without any resistance the whole way without the derailleur shifting.  Update: The wire is not moving and the shifter is a Shimano Deore.  Any idea what can cause that and how to fix it? What is the difference between a predicate and function? I need to to understand the difference between predicates and functions in the context of Clasual Form Logic in order to define the Herbrand universe.  If I have p(x) :- q(f(x)) would I be right in saying that p and q are predicates while f is a function because it is "nested"?  By this thinking then if I have p(x) :- q(x) both p and q are predicates and I have no functions?  If this is incorrect then how can I tell the difference between a predicate and function? Can fresh pasta sheets be used to assemble a lasagne, then left in the fridge overnight before baking? Or will this make them mushy or otherwise degrade them?  I have recently gotten into making fresh pasta, and I want to prep a lasagne the night before. I have done this before with store-bough dried noodles, but I'm not sure if doing this will have a negative effect on fresh, more delicate pasta. Don't revert reputation from suggested edits when reviewer's account is deleted I noticed something strange in the reputation of one of my accounts today:        Never saw "reverted" event before, so went to  and realized what happened: the user who approved my suggested edit has been removed/deleted their account.  The edit is still there. The post is still there. The effort spent in editing is still there, untouched. I really can't see any reason to take the reputation away in such a case.  Can this please be changed so that the reputation won't be lost? Personally I don't care that much, and got lots of reputation from other sources, but many people have low reputation and each point matters to them.  P.S.  This might be a bug introduced when implementing this recent change about "", so tagging as a bug too. Why did Voldemort stop employing Occlumency against Harry in Deathly Hallows? Why are American-style options worth more than European-style options? Why are American-style options worth more than European-style options?   I realize I can exercise American-style options anytime before the  expire, but I can only exercise European-style options during their  "exercise period" (usually right when they expire, but no earlier).   So it makes sense that an American option is worth at least as much as  a European option.   But why is it worth more? If I exercise my American option early, I  may make more money than waiting until expiration, but I also may make  less. Mathematically, there's no advantage, since I'm equally likely  to make as much money by waiting for expiration.   Mathematically speaking, is there ever a good reason to exercise an  American option early?   I realize people don't always behave logically, but even the formulas  that valuate options show that American options are worth more.   EDIT (answering comments):    Many of the comments people made would apply to lookback options  (), but not to American  options.  American options can do everything European options can and more. I  understand that, and that means American options can't be worth any  LESS than European options, but I'm still not clear on how you would  mathematically calculate this extra value.  @Aaronaught: "The difference between an American and European  option is the difference between getting N chances to get it right (N  being the number of days 'til expiration) and getting just one  chance. It should be easy to see why you're more likely to profit  with the former, even if you can't accurately predict price  movement."    REPLY: I don't think you really get N chances. Once you exercise the  option, that's it, no more chances. And, if you decide not to exercise  the option today, and the underlying's price falls, you can't go back  in time and exercise it yesterday.    @jdsweet: Think of it this way, if you traveled back through time  one month - with perfect knowledge of AAPL's stock price over that  period - which happens to peak viciously then return to its old price  at the end of the period - wouldn't you pay more for an American  option?    REPLY: Well, no. I'd simply buy a cheaper European option that expires  right at the spike. Or, I'd buy a European option that expires later,  and sell it when the spike occurs. American options don't give you  precognition, so you're still guessing as to when to sell/exercise.    @jdsweet: "one of the more common reasons people exercise (as  opposed to sell) an American option before expiration is if an  unexpected dividend (larger than remaining time value of the option)  was just announced that's going to be paid before the option contract  expires"    REPLY: This makes sense. I'm actually trading FOREX options, so there  is no dividend. In that scenario, are European and American options  worth the same? Why is the t-test designed for small samples? 14.04 LTS No Dash / Launcher after update through Software Updater Can't download any app from AppStore! I'm using iPhone 6s 16 GB. My storage isn't full but still I can't download anything. Every time I wanted to start a download it keeps telling:  app name* could not be download at this time Why aren't particles constantly "measured" by the whole universe? Let's say we are doing the double slit experiment with electrons. We get an interference pattern, and if we put detectors at slits, then we get two piles pattern because we measure electrons' positions when going through slits. But an electron interacts with other particles in a lot of different ways, e.g. electric field, gravity. Seems like the whole universe is receiving information about the electron's position. Why is it not the case and the electron goes through slits "unmeasured"?  Bonus question: in real experiments do we face the problem of not "shielding" particles from "measurement" good enough and thus getting a mix of both patterns on the screen? Export Track Markers to csv I am trying to export markers from the Blender motion tracker and found the following script that will do exactly that:  for clip in D.movieclips:     for track in clip.tracking.tracks:         fn = 'data/tr_{0}_{1}.csv'.format(clip.name.split('.')[0], track.name)         with open(fn, 'w') as f:             frameno = 0             while True:                 markerAtFrame = track.markers.find_frame(frameno)                 if not markerAtFrame:                     break                 frameno += 1                 coords = markerAtFrame.co.xy                 f.write('{0} {1}\n'.format(coords[0], coords[1]))   It works but I have two questions:   How can I save the data on my Desktop rather than in folder in MacOS blender content where it saved right now. The following won't work:   fn = '/User/me/Desktop/data/tr_{0}_{1}.csv'.format(clip.name.split('.')[0], track.name) The resulting values I get do not represent the more user friendly marker values in den Blender GUI. Instead of x/y coordinates in screen coordinates, I get a value between 0/1. How can I convert them to those screen coordinates ?    Thanks for your help Which comes first: cat or dog? Which comes first in a sentence?  I know some word pairs such as bacon and eggs, where bacon always comes first. E.g:     Make me bacon and eggs for dinner, honey.   Cats and dogs are the two most common pets I know of. What is the preferred order?   Dogs are superior.     Don't put dogs and cats together, they might fight!  Cats are superior.     Don't put cats and dogs together, they might fight! What kind of behaviour causes an interrupted exception? I'm relatively new to Threading in Java and I've noticed that everytime I use Thread.sleep() I have to catch InterrupetdException.  What kind of behaviour causes this, and in simple applications where I have a monitor thread can I just Ignore the exception? How to clear current “read-only” state on a USB flash drive I setup with Rufus? Three weeks ago I used  2.2 to install Windows 10 on my machine, and it has write-protected my flash drive. I’ve tried diskpart:  diskpart att disk clear readonly  clean create partition primary format fs=fat32 quick   And it kinda worked, it removed the image off the USB, but now it’s showing:  Current Read-only State : Yes Read-only  : No Boot Disk  : No Pagefile Disk  : No Hibernation File Disk  : No Crashdump Disk  : No Clustered Disk  : No   And I can’t format it or write on it.    The drive is a a Kingston DataTraveler G4 32GB model, without physical switches. How would I restore it back to normal (rw) state? Apache SSL VirtualHosts on a single IP using UCC/SAN certificate I need to host several Apache virtual hosts with SSL from a single IP.  Now - I understand that because SSL wraps around the HTTP request, there's no way to know which host is being requested until a public key has been sent to the client first. This essentially breaks the possibility of SSL virtual hosts using a standard SSL certificate.  I have obtained a Unified Communications Certificate (UCC), otherwise known as a Subject Alternative Name (SAN) certificate. This allows me to serve the same certificate for multiple domains.  I would like this to be the certificate served by Apache for any SSL request - and then have Apache resolve the virtual host as usual, once the encryption has been established.  How should I configure Apache for this? I have tried to research how this can be done, but all I can find are quotes which say that it is possible, but no specifics:    wiki.apache.org/httpd/NameBasedSSLVHostsWithSNI     While Apache can renegotiate the SSL   connection later after seeing the   hostname in the request (and does),   that's too late to pick the right   server certificate to use to match the   request hostname during the initial   handshake, resulting in browser   warnings/errors about certificates   having the wrong hostname in them.   serverfault.com/questions/48334/apache-virtual-hosts-with-ssl     Incidentally, it is possible to have   multiple SSL-secured named virtual   hosts on a single IP address - I do it   on my website - but it produces all   sorts of warnings in the Apache logs,   and certificate warnings in the   browser. I certainly wouldn't   recommend it for a production site   that needs to look clean.   -David Jul 31 at 4:58   www.digicert.com/subject-alternative-name.htm     Virtual Host Multiple SSL sites on a single   IP address. Hosting multiple   SSL-enabled sites on a single server   typically requires a unique IP address   per site, but a certificate with   Subject Alternative Names can solve   this problem. Microsoft IIS 6 and   Apache are both able to Virtual Host   HTTPS sites using Unified   Communications SSL, also known as SAN   certificates.     Please help. How can I prove the IFF condition for this group of matrices? I'm tasked with showing that matrix $A$ commutes with every $2\times2$ matrix if and only if $A = \begin{bmatrix}a &amp; 0\\0 &amp; a\end{bmatrix}$ for some a.  I was able to prove in the first direction, assuming that $A = \begin{bmatrix}a &amp; 0\\0 &amp; a\end{bmatrix}$, by just multiplying the matrix by $\begin{bmatrix}a &amp; b\\c &amp; d\end{bmatrix}$ in AB = BA format, and showing how AB does equal BA.  $$ (=&gt;)$$  $$\begin{bmatrix}a &amp; 0\\0 &amp; a\end{bmatrix}\begin{bmatrix}a &amp; b\\c &amp; d\end{bmatrix} = \begin{bmatrix}a &amp; b\\c &amp; d\end{bmatrix}\begin{bmatrix}a &amp; 0\\0 &amp; a\end{bmatrix}$$  $$\begin{bmatrix}a^2 &amp; ab\\ac &amp; ad\end{bmatrix} = \begin{bmatrix}a^2 &amp; ab\\ac &amp; ad\end{bmatrix}$$  But now I have to prove in the other direction, assuming that A already does commute with every $2\times 2$ matrix, and I'm not particularly sure how I can do that. Somehow, I have to show that if A commutes with $\begin{bmatrix}a &amp; b\\c &amp; d\end{bmatrix}$, then A will be $\begin{bmatrix}a &amp; 0\\0 &amp; a\end{bmatrix}$, and I don't know how I can carry that out.   Where can I start? Ideas are appreciated. I've been reading about a lot of different types of philosophies, religions, ways of thinking etc. I was wondering what are the most recently created philosophical ways of looking at the universe? Where can one find out about new cutting edge ideas?  Example: Before we had Marxism, Communism, Zen, Christianity etc. Now X,Y, and Z have been created building on and evolving the ideas of A,B,C.   Everything I read about are ideas that were created a long time ago. What is new and updated? Recovering the data from a failed WD My Book NAS drive My Western Digital 500GB NAS drive (which is my main backup device) has recently broken. Windows can no longer use it as a network drive (using Map Network Drive), and the web-based control panel is INCREDIBLY sluggish, taking as much as 5 minutes to load a single page.  However, when it does load, it reports the Drive Status as OK, and has the correct disk usage values, which leads me to think the actual drive is OK, and it's the networking components that have failed.  I have checked the wires and router, and so it their isn't another point in the network causing the problem.  Is there any way to get the data back? It's a backup, so I still have about 80% of the data spread out across 3 computers (the only major loss being my music library, and I have the discs for a fair proportion of that).  However, it'd be much more convenient if I can get the data from the drive itself, as it is organised properly on the drive. Finding roots/zeros for collision detection? For the most simple of 2D games, I have implemented a posteriori collision detection (overlapping rectangles) on the x/y Cartesian plane, but am now interested in understanding the basics of a priori collision detection...  In the link , I noticed the reference to Newton’s Method.  So, I want to better understand the link b/w finding zeros of an equation and detecting a posteriori collision.    Let's start with the most obvious case of finding roots of an equation:  If you have a projectile's trajectory modeled as a quadratic function, you can find the roots to predict at what time the height will equal zero (or any other constant height, actually, by just solving f(x)=C to be f(x)-C=0 and then finding roots of that expression).    So, as I understand, finding the root can tell me the time at which the object will be at any chosen height.  More broadly, we basically know the (x,y) location of the object for any given time.  But how does root finding, in particular, translate to detecting collisions with another object?  (The other object may be stationary, or be moving.  If the latter, do you also determine roots/location of this moving object as well? Calculate the (x,y) trajectory of both objects and determine where they will intersect?)  Again, the basic question is where does root finding come into play?  Any links to a basic primer on this topic, with a simple example would also be greatly appreciated.