Which subsets are vector spaces of V? Let V be the vector space F(ℝ,ℝ). Which ones of the following subsets are vector subspaces of V ? Justify your answer! (a) {f ∈ V | f(1) = 0}  (b) {f ∈ V | f(0) = 1} (c) {f ∈ V | f only has a finite number of zeros} (d) {f ∈ V | f has infinitely many zeros}  I do not know how to proceed. Could you please give me a hint? Thank you in advance.
Determine Which of the following Sets is a Vector Space Determine which of the following sets is a vector space.  $V$ is the line $y=x$, in the $xy$-plane: $V =\{[x,y]: \; y=x\}$  $W$ is the union of the first and second quadrants in the $xy$-plane: $W=\{[x,y]: \; y\geq0\}$  $U$ is the line $y = x+1$ in the $xy$-plane: $U=\{[x,y]: \; y=x+1\}$    I know that the answer is that "$V$" is the only vector space. However how do I come up with a quick proof to show that $V $is a vector space and that the other $2$ aren't?
About big parenthesis larger than Bigg Navigation bar overlapped by status bar I am using XeTeX and have the following short document:  \documentclass[a4paper,12pt]{article} \usepackage{amsmath,amsthm} \usepackage[MnSymbol]{mathspec} \usepackage[no-sscript]{xltxtra} \defaultfontfeatures{Mapping=tex-text} \setallmainfonts{Minion Pro}  \begin{document}  $\phi, \varphi, \delta \ldots A \vee B$  \end{document}    Now no matter what font I am using the punctuation marks in math mode (commas, dots, \ldots etc.) come out in Computer Modern. Is there a way to change this? How many objects are being created? this is a follow up to the problem described .  I have the same problem and the proposed solution does not completely solve the problem. I mean, it does solve the problem but also creates another one. The new problem is that the theorems, lemmas and the rest are placed in such as way that they are not cut (of course), but this leaves then big empty spaces in many pages. So the problem is that, the problem described  does not seem to be fully resolved using the nocut option.   Do you any of you have a good idea on how to solve this?  Thanks! Please have a look at this sentence:     We haven't gotten a lot of Finnish groups that we liked here at Bananas but I'm pretty happy with this four tracker from Helsinki, apparently recorded in the same place where the Ramones played in the 70's.     The first verb is in present perfect (up to now) and the second is in simple past tense. I don't understand the simple past for the second verb.  Why "like" is not in its present perfect form as the first verb is? Reducing Lion OS Footprint by removing unnecessary files/folders I am trying to downsize my iMac 640Gb disk to make it fit onto a 120Gb (113Gb usable) SSD.  The total size of use files is currently approximately 340Gb, of which my home folder accounts for 265Gb (which I intend to not put on the SSD, or at least not all of it).  Very rough calculations suggest that my OS and application files are taking up roughly 75Gb, which puts me approximately 2/3rds full - not bad.  But, I would like to reduce this a little further if possible, to ensure that as and when I continue to use the computer (and I have a number of large apps that do not currently have installed including music production apps with a lot of data) I am not worried about running out of space on the boot drive.  To this end I already own XSlimmer which I will use periodically to remove PowerPC and language variants from my apps, but I was wondering if there are any areas of the Base OS that I can safely remove to save further space?  I am thinking about things like OS localisation, the location of the included screensavers and wallpapers, the voice files that are used for text-to-speech etc.  Is there a significant amount of such data that can be easily removed to save a few extra Gb on the boot disk? convert ceil to floor Free, open-source substitutes for Mendeley? I can't open/ping any antivirus sites I have a problem with a virus in windows 7, I don't know what kind of virus is infected my OS, I installed kasersky antivirus, and clear all detected viruses. After that I can't open any antivirus sites, can't ping any antivirus sites. example:  C:\Windows\system32&gt;ping kaspersky.com Pinging kaspersky.com [38.117.98.231] with 32 bytes of data: General failure. General failure. General failure. General failure.  Ping statistics for 38.117.98.231:     Packets: Sent = 4, Received = 0, Lost = 4 (100% loss),   When I ping to other sites, I get reply normally: example woth pinging to google.com  C:\Windows\system32&gt;ping google.com  Pinging google.com [31.7.160.224] with 32 bytes of data: Reply from 31.7.160.224: bytes=32 time=2ms TTL=61 Reply from 31.7.160.224: bytes=32 time=2ms TTL=61 Reply from 31.7.160.224: bytes=32 time=1ms TTL=61 Reply from 31.7.160.224: bytes=32 time=1ms TTL=61  Ping statistics for 31.7.160.224:     Packets: Sent = 4, Received = 4, Lost = 0 (0% loss), Approximate round trip times in milli-seconds:     Minimum = 1ms, Maximum = 2ms, Average = 1ms   I tryed any antispyware/antimalware softwares, but null results.  Anyone else encountered this problem? Two logos in beamer after certain frame I'm an elected diamond moderator on one site, and a user of several others. I think it would be extremely helpful for our flagging process if users had the option to enter freeform text explaining their flag on types of flags other than the "in need of moderator attention" flag.  An example of when this is relevant: Sometimes posts have had rude/abusive flags, but the rude/abusive part might be difficult to notice, or it might be a single word or sentence buried somewhere in the middle of the post. Users have to choose between "flag it as rude with no explanation" or "flag it as misc and explain what's going on". Often they'll pick the first because of course it seems like what they should do (e.g. they know the system has special handling attached to rude/abusive flags) but it means they can't explain what's going on to us, so we have to reach out directly in private to find out.  Sometimes it also helps to be able to explain why a comment is no longer needed, because past experience tells me the "no longer needed" flag on its own might be declined on a particular site -- so I pick the custom reason instead of "no longer needed" just so I can provide explanation.  I'd prefer users be able to understand they can pick the appropriate reason and be able to attach any explanation they deem necessary to further direct moderators to the issue. If not for all kinds of flags, then at least for spam or rude/abusive flags. Why an I getting Err 01 with my Canon camera and lens? So I just got a Canon Rebel T4i and I'm having trouble with my lens (18-135mm STM lens). It's when I have my camera on movie mode, when I'm setting my aperture the blades won't change. I can only set to f/3.5 and f/20, and when I keep trying to change it my camera will give me error 01. So I clean the lens contacts and when I try again, my lens makes a noise and error 01. please help. I don't know what to do... Series Summation,Convergence I am stuck on the 4 th one.I have done the rest.I have found out the value of a_n.But not getting how to proceed for the 4 th one. Mongo find documents where array contains x values of given array How can I get two Xbox 360's to be in "open nat" mode behind the same router? I have two Xbox 360's, one WiFi and the other wired through the same Linksys E3000 router with DD-WRT (v24-sp2 (04/13/11) std-usb-nas firmware).   Mine (the wired one, though hers has been wired in the past and it didn't appear to help) always seems to be open (green), and hers is either moderate or closed (oj/red)  Even with the original router firmware I've never been able to get both consoles into "open nat" mode, and it makes playing certain games together almost impossible for me and my wife  because we can't seem to get into the same game.   I have uPnP enabled and the DMZ disabled, and some minor port forwarding to allow for a Minecraft server (Ports 25565 and 25566 for a testing copy of the server), but other than that the settings are mainly at their default, on the xbox's and the router.   Are there any settings I can configure to allow this to work properly? In my work, we are comparing predicted rankings versus true rankings for some sets of data. Up until recently, we've been using Kendall-Tau alone. A group working on a similar project suggested we try to use the  instead, and that they preferred it. I was wondering what the differences between the different rank correlation algorithms were.  The best I've found was , which claims Spearman is used in place of usual linear correlations, and that Kendall-Tau is less direct and more closely resembles Goodman-Kruskal Gamma. The data I'm working with doesn't seem to have any obvious linear correlations, and the data is heavily skewed and non-normal.  Also, Spearman generally reports higher correlation than Kendall-Tau for our data, and I was wondering what that says about the data specifically. I'm not a statistician, so some of the papers I'm reading on these things just seem like jargon to me, sorry. How to get the Duke O' Death? I was watching some videos on YouTube showing how to get the Duke O' Death in GTA 5, however what I have seen is sort of unclear.  Some people say you must be a returning player on GTA 5 to get it (what does this mean too BTW?), some people don't say that. Some people say you have to be Trevor, some people don't. Some say the time of day matters, some don't. And apparently you can buy it from Warstock website (I can't).   Can someone please tell me how to get it?! GTA 5 came with my PS4 (I didn't play it on PS3) if that helps. Title does not specify "On Hold" Testing the app, I noticed the title does not specify if a question is "On Hold" ... I haven't checked specifically, but would assume it doesn't specify as "Duplicate" either ... Or am I missing it somewhere? Is it not in the title but located/displayed some other way? If it is, this could be very confusing to users. If it isn't there, it's definitely confusing to users :-)  Using: Version 1.0.1.125 on iPad3 with iOS8 Why does Ubuntu 14.04 LTS use a non-LTS kernel version?