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Why is $\mathbb{R}^2$ not a subspace of $\mathbb{R}^3$? I cannot understand why $\mathbb{R}^2$ is not a subspace of $\mathbb{R}^3$.   My reasoning is as follows: Choose any elements $v_1$ and $v_2$ from $\mathbb{R}^2$, add them together you get an element of $\mathbb{R}^2$ and same for scalar multiplication and $0$ vector is an element of $\mathbb{R}^2$. So where did I go wrong? Windows 10 Start Menu can't have multiple shortcuts with the same target Problem  If you create two shortcuts with the same target then only one of them is displayed in the Start Menu. This is true for:   search results within the Start menu manually browsing program folders within the Start menu pinned shortcuts within the Start menu   This is important because:   the shortcuts might have different settings defined in the Properties dialog, such as different compatibility settings, or be set to start in different directories. some programs install a shortcut to a command prompt which is set to open in the program's installation folder. This enables easy access to the program from the command line without having to modify %PATH%, but it means that users who are unaware of this "lose access" to CMD. Programs that do this:           Things I've tried   Renaming shortcuts   Only the shortcut that comes first alphabetically is displayed  Using folders doesn't help   Only the shortcut in the folder that comes first alphabetically is displayed  Pinning shortcuts doesn't help   the pinned shortcut updates to point to the displayed shortcut      Steps to reproduce  Fully up-to-date Windows 10 Home.   Start → search for "Command Prompt" (or "cmd"). (Optional) Right-click on Command Prompt → Pin to Start.   This makes Command Prompt available when you open the Start menu without searching for anything.  Right-click on Command Prompt → Open file location   This opens a File Explorer window in %APPDATA%\Microsoft\Windows\Start Menu\Programs\System Tools  Copy the Command Prompt shortcut and rename the copy "AAA Command Prompt"   This ensures it appears before Command Prompt when files are listed alphabetically.  (Optional) Right-click on the new AAA Command Prompt shortcut → Properties   Change something. (E.g. set the "Start in" directory to a different location, such as C:\)    Notice that it is now not possible to access Command Prompt from the Start menu - it has been replaced with AAA Command Prompt everywhere. If you rename AAA Command Prompt to ZZZ Command Prompt then you get back the ordinary version and lose the customised version. Moving the shortcuts to different folders within %APPDATA%\Microsoft\Windows\Start Menu\Programs\ doesn't help.    Any ideas? Can I travel within the Schengen area without a passport if I have my residency permit card? How about a "Vote not to close" option to counter the "Vote to close"? My request is simple: Many times, there will be a question where some people feel like it should be closed. At the same time, I'll feel like it's a perfectly legit question, and it should therefore NOT be closed. Right now, I have to wait till it gets enough close votes (which it always does for some reason, as soon as 1 or 2 people vote to close, e/o else decides to vote as well) and then vote to re-open. How about, as soon as there's one vote to close, there should be an option to counter the close vote, something like "vote not to close" or whatever. This would then bring the "Vote to close" number down by one. Only when the vote to close outnumbers the vote not to close by 5, that's when a question is indeed closed. Any thoughts? Is there any noun in English which changes the first letter in the plural? Plenty of nouns change the second letter to become plural (man->men, goose->geese) but does anything change its first letter.  I've hunted high and low over the internet, and spent ages browsing the questions at  but I can't find anything. broadcast receiver for missed call in android The program ed, a minimal text editor, cannot be exited by sending it an interrupt through using Ctrl-C, instead printing the error message "?" to the console.  Why doesn't ed just exit when it receives the interrupt?  Surely there's no reason why a cryptic error message is more useful here than just exiting.  This behavior leads many new users into the following sort of interaction:   $ ed hello ? help ? exit ? quit ? ^C ? ^C ? ? ? ^D $ su # rm -f /bin/ed    Such a tragic waste—easily avoidable if ed simply agreed to be interrupted.  Another stubborn program exhibiting similar behavior is less which also doesn't appear to have much reason to ignore C-c.  Why don't these programs just take a hint? Buffering in meters/km using WGS84 layers using QGIS I am using QGIS 1.7.4-Wroclaw and working with an SHP layer in WGS84. I want to buffer out to a certain number of kilometers from this layer using the ftools buffer tool.  I understand that the buffer tool always uses the layer units, which for WGS84 are decimal degrees. We all know that degrees don't convert consistently to meters, so how should I go about making my buffers?   Is it necessary for me to convert the shapefiles to a different CRS that natively uses meters?   If so, how do I choose one? Why are all snaps being mounted and listed as block devices or partitions for Ubuntu 18.04? As of Ubuntu 18.04 running lsblk shows 16 snap loops (2-3 times for each snap). The question is, why are they being listed as results for lsblk, fdisf-l, and blkid?    It creates a lot of clutter from the actual disks drive partitions I need to see, namely /dev/ partitions. I know a purported duplicate of this question exists, but it only asks why three loops are being listed per snap. I want to know why these snaps are being listed in the first place, and the purported duplicate does not answer this (perhaps those marking this as duplicate could help me by explaining why it is a duplicate). Technically, they qualify as file systems (which I neither created nor asked for), but they are getting in the way of the information output for the /dev/ partitions I am interested in. This becomes a problem when fdisk -l outputs a three page+ list filled mainly with snaps.  The output of a recent (1 week old) Ubuntu install and I have not installed any snaps:    $ lsblk   NAME   MAJ:MIN RM   SIZE RO TYPE MOUNTPOINT   loop0    7:0    0  14.5M  1 loop /snap/gnome-logs/37   loop1    7:1    0   2.3M  1 loop /snap/gnome-calculator/170   loop2    7:2    0  86.6M  1 loop /snap/core/4486   loop3    7:3    0  86.6M  1 loop /snap/core/4650   loop4    7:4    0   1.6M  1 loop /snap/gnome-calculator/154   loop5    7:5    0  14.5M  1 loop /snap/gnome-logs/34   loop6    7:6    0   3.3M  1 loop /snap/gnome-system-monitor/36   loop7    7:7    0   2.3M  1 loop /snap/gnome-calculator/178   loop8    7:8    0    13M  1 loop /snap/gnome-characters/101   loop9    7:9    0   3.7M  1 loop /snap/gnome-system-monitor/45   loop10   7:10   0 139.5M  1 loop /snap/gnome-3-26-1604/64   loop11   7:11   0   140M  1 loop /snap/gnome-3-26-1604/59    loop12   7:12   0   3.7M  1 loop /snap/gnome-system-monitor/41   loop13   7:13   0    21M  1 loop /snap/gnome-logs/25   loop14   7:14   0  12.2M  1 loop /snap/gnome-characters/69   loop15   7:15   0    13M  1 loop /snap/gnome-characters/96   sda      8:0    0 298.1G  0 disk   ├─sda1   8:1    0   512M  0 part /boot/efi   └─sda2   8:2    0 297.6G  0 part /   sr0     11:0    1  1024M  0 rom     (supplemental screen capture of above text):     My snap list shows 6 results:       core   gnome-3-26-1604   gnome-calculator   gnome-characters   gnome-logs   gnome-system-monitor     Meanwhile, gnome-disk-utility shows nothing at all for snaps, only showing my HDD and optical drive.    It won't be very efficient if every installed snap gets listed as a block device (2-3 times each to add). Should I expect future updates to deal with this?  Edit: fdisk-l also dumps out a very long list with 16 instances of these "disk loops" (Disk /dev/loop0, Disk /dev/loop1, etc., each with details which I won't show here because it's too long). This can't be intended behaviour, can it? blkid also lists 16 loops, as TYPE="squashfs". At least parted -l works as expected, only outing my actual disk partitions.    I just tested this, and installing more snaps does add more to the lsblk output. Therefore, fdisk, lsblk, blkid could have potentially huge output lists, according to the number of snaps available, and installed. Example of $f,g: [0,1]\to[0,1]$ and Riemann-integrable, but $g\circ f$ is not? Interpreting exp(B) in multinomial logistic regression This is somewhat of a beginner's question, but how does one interpret an exp(B) result of 6.012 in a multinomial logistic regression model?  1) is it 6.012-1.0 = 5.012 = 5012% increase in risk?  or  2) 6.012/(1+6.012) = 0.857 = 85.7% increase in risk?  In case both alternatives are incorrect, can someone please mention the correct way?  Ive searched many resources on the internet and I get to these two alternatives, and I am not entirely sure which one is correct. Non-Exchange address in Exchange GAL We just made the switch to Google Apps for part of our domain. We disabled the accounts that are now on Google Apps and mail routes correctly. Our problem is that now we have no way of seeing those users in the Global Address List.  So we have these users in our Active Directory, they have no mailbox on Exchange, and we want to be able to see/search for their addresses in the GAL. Is there any way to do this?  This is Exchange 2007, if that matters. Why doesn't the Sun appear green to our eyes? This is an idea I have seen around, but I have not seen a feature request for it, so here it is.  Downvotes that have no comments are frustrating and difficult to manage.  This is a way to help improve that:   Have a downvote initially cost more to cast for the downvoter (5 points for example) When a comment (from the downvoter) on the downvoted question/answer gets an upvote, you get your points back.   All points (ie all 5) could be refunded or just up till the traditional -1 that is in place now (ie 4 points refunded).    This would encourage good comments and downvotes for real reasons.  (Because comments for questions/answers that are bias related will not get the upvotes as readily.)  This could/should be limited to non-subjective tags.  (ie tags where a downvote just because you "don't like it" is not appropriate.) Hide c# windows application source code I wrote a windows application using C# .Net 2.0 and i want to do something which hide the source code, so when any one use refactor tool can't see the source code. I used dotfuscator but it just changed the function names but not all the source code.  UPDATE: I want to hide the source code, not because of hiding the key, but to hide how the code is working.  Thanks, How can I integrate $\ln \left( x+\sqrt{1+x^2} \right) $? From      Every linear function on a finite-dimensional space is continuous.   I was wondering what the domain and codomain of such linear function are?   Are they any two topological vector spaces (not necessarily the same), as along as the domain is finite-dimensional? Can the codomain be a different normed space (and may not be finite-dimensional)?  I asked this because I saw elsewhere the same statement except the domain is a finite-dimensional normed space, and am also not sure if the codomain can be a different normed space (and may not be finite-dimensional).  Thanks and regards! Converting case of all values in all fields of table using ArcPy & Python? Pages: How to put a word between horizontal rules How can I make something that looks like this?  --------   Text   ---------  where the horizontal rules extend to the margin on either side? In a table of contents that has been generated with LaTeX's \tableofcontents command, I would like to add a vertical space before a Chapter item in the table of contents. One way that I have in my notes is to use  \addtocontents{toc}{\protect\vspace{10pt}}   at a desired location in the document so that this gets processed by \tableofcontents to include an appropriate vertical space in the table of contents. I have two questions:   Is the above the correct way to get a vertical space in a table of contents? Why is it necessary to use the \protect command here?   Thank you...