I booked a return journey with British Airways.   If I miss the first flight can I still use the return flight?
I was browsing flight price at Singapore Airlines website, and a one-way flight from SIN to SFO cost this much:    That's quite expensive. I tried browsing around and found that a return flight from SFO to SIN and back to SFO cost much cheaper:    It's really weird because the second ticket includes the exact same flight that cost 1900+, but it's almost half the price. The reason for this counter-intuitive situation is explained in the answers this question   If I am located in Singapore and my intention is to fly one-way to SFO, is it safe to book the flight in the second picture and only board SFO-SIN leg? Will they deny me because I miss the SIN-SFO flight?
For f continuous on $[0,1]$, show that there exist points $\alpha_k$ such that $\sum \limits_{k=1}^n \frac{1}{f'(\alpha_k)} = n $ $[S]$ means linear span of S. Then $[S] = [[S]]$ My definition of span:   Suppose a vector space $(V,+,\cdot)$, and       $$S = \{u_1,\cdots,u_n\}$$      (and $S$ is a subset of $V$, not a subspace)      $$[S]=:\bigcap_{W\subset V, W\supseteq S} W$$      In other words, $[S]$ is, by definition, the intersection of all $W$,   such that $W$ is a subspace of $V$ and $W$ contains $S$.   Well, then I need to prove that   $$[S] = [[S]]$$  My strategy:  $[[S]]$ means the intersection of all subspaces that contain $[S]$. If all the subspaces contains $[S]$, so does their intersection. Therefore, $[S]\subset[[S]]$  However, I'm having trouble proving the converse:  $$[[S]]\subset[S]$$  Any hints? I don't really know how to anticipate the changes in an option's price.  If I have an call set to expire the following Friday at $10 above the current share price, I know in the absence of other changes it loses value with each day that passes getting closer to its expiration. (Talking about American options.) But it gains value as the share price gets closer to the strike price.  So, if two days pass but the stock goes up $3, would the option have gained value or lost value? Is there any way to calculate this? I used to deploy metadata using ant migration tool successfully but from last night I am getting the below error:  John@John:~/mm_workspace/TEST_Project/deploy$ ant deployUnpackaged  Buildfile: /home/john/mm_workspace/TEST_Project/deploy/build.xml  deployUnpackaged:  BUILD FAILED /home/john/mm_workspace/TEST_Project/deploy/build.xml:72: Failed to submit request to https://cs19.salesforce.com/services/Soap/m/35.0/00D293456000Qaf for user john@test.com.dev. Error: {http://schemas.xmlsoap.org/soap/envelope/}Client - Maximum size of request reached. Maximum size of request is 52428800 bytes.  Total time: 2 minutes 10 seconds   I think this is because of too much metadata that I am trying to deploy. For now, I am deploying classes and then VF pages and so on but I am looking for an option to deploy everything in one go without running into the above error.  I am sure that people are working on more complex projects than mine with lots of metadata and I am wondering how are they deploying with out hitting this error?  Thanks Let $X$ be an infinite cofinite space and let $A \subset X$ be infinite. Then $\overline A = X$  I am having a tough time in trying to understand this. Why is every infinite set in an infinite cofinite space dense ? 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? In superluminal phase velocities, what is it that is traveling faster than light? I understand that information cannot be transmitted at a velocity greater than speed of light. I think of this in terms of the radio broadcast: the station sends out carrier frequencies $\omega_c$ but the actual content is carried in the modulated wave, the sidebands $\omega_c\pm\omega_m$. The modulation envelop has its group velocity and this is the speed at which information is being transmitted. We also know, for example, that x-rays in glass have a phase velocity which is greater than the speed of light in vacuum.   My question is, what exactly is it that is travelling faster than the speed of light?    EDIT: I know it couldn't be anything physical as its superluminal. My problem is, what is it that has absolutely no information content yet we associate a velocity with it. Novel about alien conquerers who conduct games to select servants I read this maybe 10-15 years ago.   Aliens have conquered earth. Possibly quite some time before the time then novel is set in. They have built their own cities. They conduct periodic athletic competitions for humans similar to the current olympics. The winners are take into the city to act as servants to the masters. The protagonist is part of a human resistance movement who is competing in the games. The plan is to infiltrate the city, gather intel and escape. He wins, get in, finally has to kill his master and escape down a waste disposal system which ends up outside the city.   Anybody knows which one I am talking about? Screen (not Lock Screen) Timeout Stuck at 1 Minute I recently got a new laptop (Lenovo T440p with Windows 8.1 Pro) and was having the following issue: the screen would lock (screen would go black and require a password to get back in) after 1 minute. I would prefer something more like 10 or 15 minutes. So, I tried the obvious changes (check the screensaver settings, power management settings for sleep, turning off the screen, etc.), with no success. I did, however, notice a rather odd behavior: if I changed the screensaver timeout from 1 minute to anything else (say, 15 mins), clicked OK, and re-opened the screensaver settings window, it would be back to 1 minute. Odd.  At that point, I turned to Google. I found posts ( in particular was helpful) suggesting all sorts of causes and resolutions:   If you have Cisco AnyConnect VPN client (which I did), try uninstalling it. I uninstalled, rebooted, no change. Open the User Accounts control panel and, on the left side of the screen, click Reset Security Policies. My User Accounts control panel, however, has no such link. Reboot into a repair console and run "sfc /scannow". It did indeed find and repair some issues, but didn't fix the screen timeout problem. Edit the Group Policy to force a particular timeout time; the setting showed up correctly (15 mins) in screensaver settings, power management settings, etc., but the screen would still go black and lock after 1 minute. In the registry, manually change the screensaver timeout and the "turn off the screen" timeout. No luck. What part of speech is there in the sentence “There is a book on the table?”  Also, while typing it out, another question pops up vis-à-vis punctuation. In my complete first sentence above, I ended it with a question mark since my main sentence is a question. The quote is not a question, but it looks like it because of the question mark. Is this the right way to punctuate? When writing letter to an academic professor (not necessarily from student to professor), what is the appropriate way to address his/her title?  I have seen in letters using  Dear Prof. X even when the addressee is not a full professor  Dear Dr. X though, knowing that the addressee is a full professor  Dear Mr/Mrs X though, knowing that s/he has an academic title I can do an eval("something()"); to execute the code dynamically in JavaScript. Is there a way for me to do the same thing in C#?  An example of what I am trying to do is: I have an integer variable (say i) and I have multiple properties by the names: "Property1", "Property2", "Property3", etc. Now, I want to perform some operations on the " Propertyi " property depending on the value of i.   This is really simple with Javascript. Is there any way to do this with C#? Does $\int_{0}^{\infty}\frac{dx}{1+(x\sin5x)^2}$ converge? I would like your help with deciding whether the following integral converges or not:  $$\int_{0}^{\infty}\frac{dx}{1+(x\sin5x)^2}.$$  I tried to compare it to other functions and to change the variables, but it didn't work for me.  Thanks a lot! Problem with the header/ footer width I have recently started using the geometry package to format the margins of my documents. Although, I've noticed that the width of the header/ footer remains the same. How can I correct this?    Here's a MWE:  \documentclass{article}  \usepackage{geometry} \usepackage{fancyhdr}     \pagestyle{fancy} \usepackage{blindtext}  \lhead{} \chead{Header} \rhead{} \lfoot{} \cfoot{Footer} \rfoot{\thepage} \renewcommand{\headrulewidth}{1pt} \renewcommand{\footrulewidth}{1pt}  \begin{document}  \newgeometry{margin=0.5in, bottom=1in, top=1in} \Blinddocument  \end{document} Should a gas water heater be shut down if the water main has to be turned off? I have a brand new AO Smith 50gal gas water heater. Today there was a burst pipe from the cold spell we're having currently, so I had to turn off the water main to the house until the plumbers get here tomorrow.  With that, nobody had used any hot water all day so it should be full, but do I need to turn the water heater off until the water can be turned back on tomorrow to avoid any damage etc? How do I fix 'Invalid JSON' errors? I've been at this for almost two hours and no one seems to have the same problem as I and I doubt this will be solved but I'll try anyway.  this is the code  /tellraw @p ["Would you like to teleport?",{"text":"Yes","color":"green","bold":"true","clickEvent":{"action":"run_command","value":"/tp @p ~ ~4 ~ "},"hoverEvent":{"action":"show_text","value":{"text":"Confirm"}},{"text":"No","color":"red","bold":"true","clickEvent":{"action":"run_command","value":"/tellraw @p{"text":"Come back when you want to teleport"}"}}}]   this part is fine  /tellraw @p ["Would you like to teleport?",{"text":"Yes","color":"green","bold":"true","clickEvent":{"action":"run_command","value":"/tp @p ~ ~4 ~ "},"hoverEvent":{"action":"show_text","value":{"text":"Confirm"}}   it's just when I add this  ,{"text":"No","color":"red","bold":"true","clickEvent":{"action":"run_command","value":"/tellraw @p{"text":"Come back when you want to teleport"}"}}}]   Minecraft gives me the error:     Invalid JSON at line 1 column 203   I've tried to space it out and figure out what column 203 is but I can't, I don't know what I did. Anyone got any ideas? How can I render bokeh circles?  Nothing I do seems to work.   I tried using an empty as the focus point for a cube, with some point lamps in the background with about 2000 strength, but it doesn't work. It just makes everything blurry.  I also raised the blades to 4/5/6/12, and it doesn't make a difference.  I'm using Blender 2.74. A few weeks back I was using std::ifstream to read in some files and it was failing immediately on open because the file was larger than 4GB. At the time I couldnt find a decent answer as to why it was limited to 32 bit files sizes, so I wrote my own using native OS API.  So, my question then: Is there a way to handle files greater than 4GB in size using std::ifstream/std::ostream (IE: standard c++)  EDIT: Using the STL implementation from the VC 9 compiler (Visual Studio 2008).  EDIT2: Surely there has to be standard way to support file sizes larger than 4GB. How to initialize all members of an array to the same value? I have a large array in C (not C++ if that makes a difference). I want to initialize all members of the same value.  I could swear I once knew a simple way to do this. I could use memset() in my case, but isn't there a way to do this that is built right into the C syntax? Formula for expected value of continuous random variable without using density