In the theorem of , it is assumed that, given two sets $A$ and $B$, and  there is an injective map from $A$ to $B$ and an injective map from $B$ to $A$. It then concludes that there is bijection between $A$ to $B$.  My question here is based on hypothesis of the theorem, although it may not be closely related to the theorem, but it came to me when I first re-read the statement.  Question: Given non-empty sets $A$ and $B$, is it true that there is always an injective map from $A$ to $B$ or $B$ to $A$.
Let $A,B$ be any two sets. I really think that the statement $|A|\leq|B|$ or $|B|\leq|A|$ is true. Formally:     $$\forall A\forall B[\,|A|\leq|B| \lor\ |B|\leq|A|\,]$$   If this statement is true, what is the proof ?
How to add features to a PostGIS layer using Quantum GIS? I am using Quantum GIS and the PostGIS dbms. I am able to call the PostGIS layer into QGIS but i am unable to add feature to it. I am using the method of adding features to a Shapefile but still it is not getting reflected in the layer, and I don't know how to save it to the PostGIS database if I am able to add the feature to the PostGIS layer.  I may not have used some technical term for this problem because i don't know what to call it, I am expressing the problem in my own terms. Why didn't Harry die the first time Voldemort used the Killing Curse in the Forbidden Forest? Conjugate class in the dihedral group List all the conjugate classes in the dihedral group of order $2n$ and verify the class equation.  The dihedral group is generated by two elements $r$ and $s$.   The order of $r$ is two since $r^2=e$ and $s$ is $n$ since $s^n = e$. And I know all elements can be produced as either $s^k$ or $rs^k$. How can I list all the conjugacy class? CSV API for Java Can anyone recommend a simple API that will allow me to use read a CSV input file, do some simple transformations, and then write it.  A quick google has found  which looks promising.  I just wanted to check what others are using before I couple myself to this API. Interchanging the order of differentiation and summation What is moiré? How can we avoid it? What is the image defect called "moiré"? What causes it, and how can we avoid or reduce it? Is it related to "false color"? How to extrude and scale with an even offset? Can I use the Google font 'Lato' for a logo design? I am creating a logo and would like to use the Google Font 'Lato', can I use this font in my logo design or are there copyright/limitations I need to worry about? I can't find anything online other than that it is an open source font that can be used in anyway you want (maybe that's my answer but I just want to make sure). Also, is it a bad idea to use a web-based font for a logo? Please stop bounties from turning off community moderation Possible Duplicate:                tl;dr: Please get rid of "This question has an open bounty and cannot be closed"  Questions with bounties on them can't be closed:    This is by design, and the recommended course of action is to flag for moderator attention, at which point they'll decide whether to refund the bounty and close the question or not.   But why should a bounty disable regular community moderation?  We should be able to cast close votes on bountied questions as usual, and if a question gets enough, the bounty's refunded and the question closed.  An obvious benefit would be reduced burden on moderators, but I doubt that this is really a significant part of their workload.  More important is allowing the entire community's wisdom to be brought to bear.  Consider this question:      Having a simple MFC application with web browser controller that navigates to some site and then to another one on and on.      Using a powerfull machine (16 cores and lots of memory) OS is Server 2008 R2. I can see when launching my app over 30 instances I'm getting the OS UI (each window including my app, mspaint, taskmgr etc..) become very sluggish and slow.      I have monitored the machine resources (CPU, memory and GDI objects) but it seems that all of them are not even close to be in some level of stress.      What is the problematic resource that influence the machine in such way?      10x, Guy   It doesn't look like a good question: somewhat poorly written, vague, not a ton of information, etc.  I would vote to close this question.  However, I don't do much work with MFC and maybe there's something I'm missing.  (I can readily imagine a similarly bad looking question with the extremely concrete answer: .)  I'm comfortable casting a vote to close, not closing unilaterally.  Flagging for a moderator just passes the buck to them, when the correct action is letting the community weigh in. We have a SQL Server 2012 instance that contains a database with data for many product lines.   We are looking for a way to take subsets of this data into another database on the same instance.  This doesn't have to be continuous as we are looking for ways to make it easy to export backups of the subsets that we can send out to vendors (we have a company that loads this data into their own sql server to produce a product we sell, naturally its huge and we want to trim it down to just the product lines they work with on a regular enough basis) or use to load SQLite DB's for use with offline applications.  ProductDB - the superset of all product line data.  ProductLine1DB - A subset identical in structure to ProductDB, but with data only relevant to product line 1.  ProductLine2DB - A subset identical in structure to ProductDB, but with data only relevant to product line 2.  This can be done nightly, weekly, as often as we need to but not a continuous replication.  We don't want to add in distributor servers or even extra subscriber servers. We would like the replication to happen on the same server with the subscriber databases being on the same server.  Is this a good candidate for transactional replication?  Why or why not?  We obviously have other options to load this data, but it seems like this might be a good case to use something like transactional replication. I've heard its powerful but prone to issues when not setup optimally.  Note: I am not a DBA, simply a developer, but we are currently looking for a new DBA and some of us are taking over duties like this temporarily. Downgrading from OS X 10.9.2 to 10.9 Let's stop displaying a user's accept rate We roll a six-sided die ten times. What is the probability that the total of all ten rolls is divisible by 6? So the question is really hard I think. I tried using a simple way by calculating the probability of each combination that makes a sum divisible by six, but it would take forever. Does anyone have any ideas?  Suppose that we roll a six-sided die ten times. What is the probability that the total of all ten rolls is divisible by six? How to recover data from a failing hard drive? An external 3½" HDD seems to be in danger of failing — it's making .  I've acquired a replacement drive, and want to know the best strategy to get the data off of the dubious drive with the best chance of saving as much as possible.  There are some directories that are more important than others.  However, I'm guessing that picking and choosing directories is going to reduce my chances of saving the whole thing.  I would also have to mount it, dump a file listing, and then unmount it in order to be able to effectively prioritize directories.  Adding in the fact that it's time-consuming to do this, I'm leaning away from this approach.  I've considered just using dd, but I'm not sure how it would handle read errors or other problems that might prevent only certain parts of the data from being rescued, or which could be overcome with some retries, but not so many that they endanger other parts of the drive from being saved.  I guess ideally it would do a single pass to get as much as possible and then go back to retry anything that was missed due to errors.  Is it possible that copying more slowly — e.g. pausing every x MB/GB — would be better than just running the operation full tilt, for example to avoid any overheating issues?  For the "where is your backup" crowd: this actually is my backup drive, but it also contains some non-critical and bulky stuff, like music, that aren't backups, i.e. aren't backed up.  The drive has not exhibited any clear signs of failure other than this somewhat ominous sound.  I did have to fsck a few errors recently — orphaned inodes, incorrect free blocks/inodes counts, inode bitmap differences, zero dtime on deleted inodes; about 20 errors in all.  The filesystem of the partition is ext3. Let $\sim$ be the equivalence relation on $S_1 \times I$ given by $(x,t)\sim(y,s)$ if and only if $xt=ys$ where $I=[0,1]$  How do I prove that $(S_1 \times I)/\sim$ is homeomorphic to the unit disk $D^2$ with the induced topology? I'm looking to clarify the differences/overlaps between the three and, if the terminology isn't accurate establish the correct terminology If I play a spell with {X} in the mana cost, and I have a card out that reduces the casting cost by 2 generic mana, what happens to the X? Does it start at -2?  For example: I have  in play. If I play  for just 1 blue mana, do we draw 2 cards? Create instance of generic type in Java? Is it possible to create an instance of a generic type in Java? I'm thinking based on what I've seen that the answer is no (due to type erasure), but I'd be interested if anyone can see something I'm missing:  class SomeContainer&lt;E&gt; {     E createContents()     {         return what???     } }   EDIT: It turns out that  could be used to resolve my issue, but it requires a lot of reflection-based code, as some of the answers below have indicated.  I'll leave this open for a little while to see if anyone comes up with anything dramatically different than Ian Robertson's . Pretty much every application I use in full-screen (including Firefox, MacVim and the Terminal) have tabs on the top of the screen.  The problem is, when I move my mouse to reach the tabs I'll often accidentally touch the top of the screen, bringing in the OS menu OVER the tabs:    Is there any way to change this behavior? I'd prefer it if the menu bar would stay hidden when I'm using a full-screen app, even if my mouse does touch the top of the screen. How is the equation of motion on an ellipse derived?