Prove that for any two sets $|X|$ and $|Y|$, either $|X|\leq|Y|$ or $|Y|\leq|X|$.
Proving $(A\le B)\vee (B\le A)$ for sets $A$ and $B$
Story where people inject "books" in the back of their necks? I read this story in middle school or high school and I cannot for the life of me remember the name of it. I think it started off in a small clan of people, there was a young boy who had just come of age and he had some kind of gift that related to the books? Also I think the injecting was illegal, because I vaguely remember the boy encountering an old man who had a bunch of books that he had to keep hidden. There was also a city and he met a girl there that was Special some how. I may just be merging memories but I think at some point the boy and girl went to an underground city?  Does anyone know what I'm talking about? How to treat English questions which have code in a foreign language? Why is empty set an open set? I thought about it for a long time, but I can't come up some good ideas. I think that empty set has no elements,how to use the definition of an open set to prove the proposition. The definition of an open set: a set S in n-dimensional space is called open if all its points are interior points. Solving 4 Quadratic Simultaneous Equations Consider the equations:   $$\begin{cases} ab+c+d=3\\ bc+d+a=5\\ cd+a+b=2\\ da+c+b=6 \end{cases}$$   Where $a,b,c,d \in \mathbb{R}$. How can we find $a,b,c,d$?   The furthest I've got is by adding the first two equations and the last two equations together to get: $ab+bc+c+d+d+a=(b+1)(a+c)+2d=8$ and $(d+1)(a+c)+2b=8$ We can rearrange these (assuming $b,d \neq -1$) to get $$\frac{8-2d}{b+1}=\frac{8-2b}{d+1} \implies -d^{2}+3d+4=-b^{2}+3b+4$$ Which leads us further to $$b^{2}-d^{2}-3(b-d)=0 \implies (b-d)(b+d-3)=0$$ Now since $b=d$ gives us an absurdity (equations 1 and 4 reduce to 3=6), we must have $b+d=3$. This is as far as I can get unfortunately, since trying the same approach with the other pairs doesn't work in the same way.  Help would be much appreciated; the problem is from the BMO1 2004 paper. Why is the "Arnold Schwarzenegger" terminator referred to by two different product numbers (T-101, T-800)? Why does chown report "Operation not permitted" on OS X? I am trying to do the following on my Mac (10.6.7):  sudo chown myusername:wheel ./entries   but Unix/Mac is returning "Operation not permitted". When I ls -lash the culprit file, it looks as follows:  8 -rwxrwxrwx   1 myusername  staff   394B Apr 26 23:26 entries   I've tried sudo and sudo su; nothing works. Any ideas what's up?  I'm trying to chmod files I've copied from my old Ubuntu box. Most of the files have successfully chmod'ed recursively; just this one is stuck and I don't understand why. Why are these estimates to the German tank problem different? Quoting in ssh $host $FOO and ssh $host "sudo su user -c $FOO" type constructs I often end up issuing complex commands over ssh; these commands involve piping to awk or perl one-lines, and as a result contain single quotes and $'s.  I have neither been able to figure out a hard and fast rule to do the quoting properly, nor found a good reference for it.  For instance, consider the following:  # what I'd run locally: CMD='pgrep -fl java | grep -i datanode | awk '{print $1}' # this works with ssh $host "$CMD": CMD='pgrep -fl java | grep -i datanode | awk '"'"'{print $1}'"'"   (Note the extra quotes in the awk statement.)  But how do I get this to work with, e.g. ssh $host "sudo su user -c '$CMD'"?  Is there a general recipe for managing quotes in such scenarios?.. Norm and unit sphere Can I pass a System.Net.MailMessage to a WCF service? I'd like to setup a WCF service to send emails. The System.Net.MailMessage doesn't seem to be serializable, and cannot be passed in a [DataContract]  The error I receive is      Type 'System.Net.Mail.MailAddress'   cannot be serialized. Consider marking   it with the DataContractAttribute   Any suggestions? How to remove duplicate values from a multi-dimensional array in PHP How can I remove duplicate values from a multi-dimensional array in PHP?  Example array:  Array (     [0] =&gt; Array     (         [0] =&gt; abc         [1] =&gt; def     )      [1] =&gt; Array     (         [0] =&gt; ghi         [1] =&gt; jkl     )      [2] =&gt; Array     (         [0] =&gt; mno         [1] =&gt; pql     )      [3] =&gt; Array     (         [0] =&gt; abc         [1] =&gt; def     )      [4] =&gt; Array     (         [0] =&gt; ghi         [1] =&gt; jkl     )      [5] =&gt; Array     (         [0] =&gt; mno         [1] =&gt; pql     )  ) Android OS without Google Services? Why square the difference instead of taking the absolute value in standard deviation? What should be done with questions that have been resolved as a comment instead of an answer? I have a file containing lists on Solaris:  List A hi hello hw r u  List B Hi Yes  List C Hello   I need to transpose the lists as shown below:  List A    List B    List C hi        Hi        Hello hello     Yes hw r u   How can I do this on Solaris? Display lost/negative reputation in topbar achievements When you get reputation, you get a +X green spot on your reputation feed telling you that you gained reputation and if you drop down the menu, you get more detail.  How about we make it that when you lose more than you got since the last time you checked, you see it red with a little -X.  For example, let's say you've just looked at the reputation bar so any old rep notification is gone and you ask a new question. 3 users downvote your question and 1 upvotes it. You will see it green because you gained 5 rep but you should see it red because you are at -1 rep.   This would help people improve their questions / answer by seeing, as soon as they get on the site, that they got negative feedback and that something needs to be checked / changed.    It shows here so it could very well be applied to the notification count: I have a chromebook series 5. I want to install Ubuntu onto a USB stick. When I downloaded Ubuntu onto my USB stick, it won't start up.  Do I first have to download Ubuntu onto my chromebook hard drive, open Ubuntu and then make USB stick bootable? And then return back to chrome?  Or is there a way to download directly onto USB and make the stick bootable?  I appreciate any help. Consider the question :    The large number of down-votes displays as 199 rather than a score of -199.  This is clearly unintentional (and unfortunate for questions that possess such voting!), but can this be&nbsp;corrected? Changing pemalink structure to /%post_id%/%postname%/ I'm currently using permalink structure: /%year%/%monthnum%/%day%/%postname%/  I want to change that to: /%post_id%/%postname%/  I expect it to be:   faster (database is sorted by post_id?) shorter URLs (and clearly visible short verstions, just leaving the %postname%/ out) more SEO friendly - since my content is "evergreen" so publishing date is irrelevant (and written at each post, along with last update date) - so this would give shorter URLs, with no downsides compared to using year/month/day structure.   THE QUESTION: Does WordPress handle all the 301 redirects automatically? I can fix internal links to the new structure (though I'd expect that to be automatic as well), but worry about outsite links, pointing to my posts/articles.  If not, what's the best way to implement this change? Any links or full answers here are welcome.  I have about 120+ posts already, will this change affect the speed since it's not been done from the start? Okay setting the scene. I have three tables, (Table1, Table2 and DataTable) and I want to insert into Table1 and Table2 using DataTable as source. So for every row in DataTable I want a row in Table1 and Table2, and Table2 needs to have the inserted id (PK) from Table1...  If I were to do this...  INSERT INTO Table1 SELECT A, B, C FROM MyTable INSERT INTO Table2 SELECT IDENTITY_INSERT(), D, E, F FROM MyTable   I'd get the ID of the last inserted record into Table1.  Is a CURSOR or WHILE loop the only ways to do this?