Coordinate systems
How to enable projection transformation in QGIS
I need to show that for any countable ordinal $\alpha$ there is a set A $\subseteq \mathbb{Q}$ such that (A, &lt;) is isomorphic to ($\alpha, \in$).  To do it I am supposed to show the following stronger statement by induction on ordinals $\alpha$ &lt; $\omega_{1}$:  Let P($\alpha$) be the statement "For every interval (a, b) with rational endpoints, there is an A $\subseteq$ (a,b) such that (A, &lt;) is isomorphic to ($\alpha, \in$)."  I think that the purpose of breaking $\mathbb{Q}$ into intervals (a,b) is to make $\mathbb{Q}$ a countable set, but I don't see the significance of doing this or how it would make the proof easier.  I feel like I need to define a well-ordered set in (a,b) but I don't know how to do this since if a and b are both negative then there is no least element, so no well-ordering.  I believe that I am supposed to be using transfinite induction? But I don't know how P($\alpha$) implies P(S($\alpha$)) for S($\alpha$) successor of $\alpha$.  Any help would be greatly appreciated... thanks in advance. Recursive cast from SimpleXMLObject to Array GP 1.2.10(b) The tangent space $T_{(x,x)}(\triangle)$ is the diagonal of $T_x(X) \times T_x(X).$ If $\triangle$ is the diagonal of $X \times X$, show that its tangent space $T_{(x,x)}(\triangle)$ is the diagonal of $T_x(X) \times T_x(X).$   I don't have the slightest idea on how to do this.  By definition, the tangent space of $X$ at $x$ is the image of the map $d\phi_0: \mathbb{R}^k \rightarrow \mathbb{R}^N$, where $x + d\phi_0(v)$ is the best linear approximation to $\phi: V \rightarrow X$ at 0. $\phi: V \rightarrow X$ is a local parametrization around $x$, $X$ sits in $\mathbb{R}^N$ and $V$ is an open set in $\mathbb{R}^k$, and $\phi(0) = x$.  Thanks. Purpose of hole in stove leading to oven I'm staying in a hotel and have access to a "electric coil stove" for one of the first times.  I accidentally turned on the oven light and saw that the light was shining up through only one of the stoves:    There's only a port from the oven into the top right stove, and note that the stove is not on.  Here's a view from within the oven:    Is there a hole here as a vent for the oven for some reason, or is this for the stove? I typically use a glass "flat-top stove" that doesn't have an oven underneath it. I've never seen a direct hole from a stove to the oven before, and have to wonder what the purpose is. Left alignment in TikZ I would like to run  something &gt; file   on a remote system through ssh, but if I run  ssh host something &gt; file   the redirection is executed locally as ssh etc &gt; file  I've tried it with ' or '' or dd or with a pipe | instead, but I can't get it to work. How can this be done? Can't mount ISO file as loop device: Error: “failed to setup loop device” sudo mkdir -p /media/cdrom cd ~ sudo mount -o loop ubuntu-* / mount: ubuntu-*: failed to setup loop device: No such file or directory Add a duplicate:0|1 search operator I often search for closed questions and sift through the ones that are not duplicates to see if any of them need to be killed. Technically, closure is the first step towards deletion and the only closed posts that are actually useful are duplicates (unless it's a crappy one).  For the rest, if the community hasn't bothered to reopen it after a while or if the OP has made no effort to edit their question, I delete it if it has no redeeming content. For example, the only closed posts seen on  are exact dupes.  But this does become tedious when there are several results for various close reasons with duplicates interspersed between them. I'd like to be able to search as:  closed:1 duplicate:0   so that it gives a list of questions closed as OT/NaRQ/NC/TL. This will be similar in behaviour to migrated:0|1.   This will also be useful for 10k+ users on all sites (2k+ in beta) in the network, especially SO, so that they can search for questions to spend their delete votes on— especially closed, non-dupe questions in the tag they specialize in. More often than not, I hesitate to vote on questions that are outside my area of interest (unless it is crappy). the least possible value for :$ \lfloor \frac{a+b}{c}\rfloor +\lfloor \frac{b+c}{a} \rfloor+\lfloor \frac{c+a}{b} \rfloor $ How can I recover my external hard drive's free space? I had these partitions on an external hard drive:  /dev/disk2 (external, physical):    #:                       TYPE NAME                    SIZE       IDENTIFIER    0:      GUID_partition_scheme                        *2.0 TB     disk2    1:                        EFI EFI                     209.7 MB   disk2s1    2:                  Apple_HFS Android                 63.9 GB    disk2s2    3:                  Apple_HFS RiptideHUP              968.0 GB   disk2s3    4:       Microsoft Basic Data RiptideF                967.8 GB   disk2s4   My aim was to delete disk2s2 and then resize disk2s3 to occupy the leftover space by deleting disk2s2.  I deleted disk2s2 using this command:  diskutil  erasevolume  "Free Space"  ""  /dev/disk2s2   Now, to resize the volume, I used:  diskutil  resizevolume  /dev/disk2s3  R   However, I got this error:  Started partitioning on disk2s3 RiptideHUP Error: -69743: The new size must be different than the existing size   I did a bit of research and realised the free space was created before disk2s3 RiptideHUP so it cannot resize itself. Is there still a way I can reclaim the Free Space?  NOTE: Using diskutil list now shows:  /dev/disk2 (external, physical):    #:                       TYPE NAME                    SIZE       IDENTIFIER    0:      GUID_partition_scheme                        *2.0 TB     disk2    1:                        EFI EFI                     209.7 MB   disk2s1    2:                  Apple_HFS RiptideHUP              968.0 GB   disk2s3    3:       Microsoft Basic Data RiptideF                967.8 GB   disk2s4 How do I check if an element is hidden in jQuery? bisectors of an angle in a triangle intersect at a single point - proof verification Let´s consider a general triangle ABC. Let´s draw two angle bisectors from vertices A and B.  It is obvious that these two angle bisectors intersect at a single point X. Since X lies on the angle bisector from A its distance from side b is the same as its distance from side c. As X also lies on the angle bisector from B, its distance from side c is the same as its distance from side a.  By transitivity the distance from the point X to the side b has to be the same as the distance from X to the side a. Therefore the angle bisector from C (which is the set of points equidistant from b and a) has to go through X.  It seems as a very simple argument. Is it correct? Along the lines of , what reasons are there (if any) to favor \( ... \) over $ ... $? When will "Present Perfect vs. Past Tense" cases be affected by culture? Regarding actions taken in the past, besides the differences those two tenses have semantically, my teacher shared that it could be a British vs American English case.   When talking about past action, British prefers present perfect because they take into account that the effect from their past action still happens until now. As for American, they prefer to state the action only. It happened in the past, so past tense it is.     I have had dinner. [British]   vs.      I had dinner. [American]   I hope to hear it from the native speakers, both British and American. What do you think about this? Is it true?  If it is, I don't think it can apply to all cases of past actions. There have to be cases when both style agree to use the same tenses. Could you please help me define the situation when this kind of difference applies and when doesn't? I can describe "IMHO" as an acronym for "in my humble opinion."  How can I describe the reverse processes of translating the acronym into the actual phrase?  That is to say, if "IMHO" is the acronym, what do we call "in my humble opinion"? How to start git-gui? Unable to Change Apple ID and password I have tried repeatedly to change my Apple ID and password without success. I have followed all of the directions trying both my emails and asked for new passwords----no luck whatsoever. I need a graduate level, mathematically rigorous textbook on multivariate analysis and inference to enhance myself. I've been reading the  and doing the problems within, but I need a book with other focuses. Topics like famous distributions (Wishart, Wilks lambda, etc.), hypothesis testing, some theory on estimation (point, interval), and other more modern materials are welcome. I've checked , but the OP there was looking for something useful for his psychological analysis, which is not exactly what I want here. Currently I have the , so I would also like to hear the comments about this book and its exercises. Thank you. Deleting files from Remote FTP-Server older than x days i've got a remote FTP server where i store some backups via cronjob.  The Problem is that i only got a little amount of space so im doing incremental backups. I want to keep the backups about 14 days.  I don't have any other access to the server except FTP and i don't now how to delete files older than x days. Every file got a name with a date in it  yxzNamezxy-date-y-m-d.tar.bz2 (datev-20100111.tar.bz2(   Hope to get some help here.  Cheers and thanks for the hopefully coming answeres,  Dennis  /Edit  I'm trying to use the curl thing which is mantioned in an answere with this part of code  curl ftp://$FTP_SERVER --user $FTP_USER:$FTP_PASS --list-only &gt; files.tmp declare -a aFiles let iCount=0 exec &lt; files.tmp while read sLine do         aFiles[$iCount]=$sLine         ((iCount++)) done  echo -e "\n Files: \n\n\n" echo ${aFiles[@]}  echo -e "\nfor ...\n\n\n" for sFile in $aFiles do         echo -e "\nFile:" $sFile done   but the secound loop doesn't give me more than 1 filename  Cheers,  Dennis Is there a way to search for a question (or an answer) that mentions a tag?