I think this set is uncountable, but I don't really know how to prove this. Maybe somehow find an injection from $\mathcal{P}( \mathbb{N} \times  \mathbb{N}) \rightarrow A$?
Is the set of partial order relations over $ \mathbb{N}$ countable? I think it's uncountable but don't know how to prove this. I would be very helpful if someone could also give some kind of a strategy for proving uncountability, in particular how to find injective or surjective functions that help proving this.
Does $\int_{0}^{\infty}\frac{dx}{1+(x\sin5x)^2}$ converge? grub issues message at boot - "error - can't find command hwmatch" This question  is exactly what I'm asking but was closed as non reproducible. Mine is very reproducible.  Ubuntu 18.04 freshly installed on a 64-bit UEFI machine. Default grub boot options work fine, but I wanted to add a brief countdown (my normal config).  After editing /etc/default/grub as normal and running sudo update-grub, the countdown works, but I get the error shown in the question title.  I tried the solution (copying files) in the closed question but it didn't seem to fit my configuration. Frankly I found the answer confusing.  I also tried editing /etc/grub.d/10_linux to comment out the IF-THEN structure that uses hwmatch. After that I did a sudo update-grub but I still got the error.  How can I get my countdown and not see this error?  Edit per comments -  Stock grub as installed (all non-commented-out lines shown)  GRUB_DEFAULT=0 GRUB_TIMEOUT_STYLE=hidden GRUB_TIMEOUT=0 GRUB_DISTRIBUTOR=`lsb_release -i -s 2&gt; /dev/null || echo Debian` GRUB_CMDLINE_LINUX_DEFAULT="quiet splash" GRUB_CMDLINE_LINUX=""   Edited grub to give countdown (all non-commented-out lines shown)  GRUB_DEFAULT=0 GRUB_TIMEOUT_STYLE=countdown GRUB_TIMEOUT=5 GRUB_DISTRIBUTOR=`lsb_release -i -s 2&gt; /dev/null || echo Debian` GRUB_CMDLINE_LINUX_DEFAULT="quiet splash" GRUB_CMDLINE_LINUX="" Will be flying with easy jet and was wondering for retuning flights the old luggage tag we have on are suitcase. should we take them off before arriving at the airport to return home or leave it as the person will do it for us anyways? Im guessing even at self check in they will have someone who will make sure that old tags are taken off and that the new one is correctly done etc? RegEx match open tags except XHTML self-contained tags \pdfendlink ended up in different nesting level than \pdfstartlink Splitting of primes in the compositum of fields If $L_i/K$ are Galois extensions of number fields, $i=1,\ldots,n$, and $L=L_1\cdots L_n$ is the compositum. Then it's true that a prime $\mathfrak{p}$ of $K$ splits in $L$ if and only if it splits in all of $L_i$. Does this also hold if the $L_i$ are not Galois extensions of $K$?  The proof that I know regarding the compositum uses the fact that the $L_i/K$ are Galois, so is this true in the more general setting and how would one prove it? Google Chrome can't play some flash videos Some flash videos won't play in Chrome, while they play perfectly in other browsers. The player will load, but instead of showing a preview of the video and a play button on the middle of the video, the screen is black:    Here's an example of a  and here is a . The video that works is a Youtube video embedded on the site with , while the nonworking one is probably hosted by the website itself. In both cases it is using Flash. The site is popular and others don't seem to be experiencing this problem.  I am running Win7 64bit and I have no ad blockers installed.  I have found two common solutions to this problem, neither of which work:  Solution #1: .  Solution #2: .  Any suggestions? How to blur a texture node in cycles material? For a Cycles material I need to blur a texture. If the texture where a Texture Image node, I can blur the image before adding it but in my case I need to blur a Voronoi Texture and so I can't do it.  I have searched but I didn't find a blur node. Can this be achieved? Array initialization syntax when not in a declaration How does one type Chinese in LaTeX? Live notification shown for own edits When editing an answer, the &quot;new revision&quot; message is shown for a short moment. This makes no sense because the revision you just created is automatically displayed anyway. Polynomials with integer coefficients such that $p(a)=b,p(b)=c,p(c)=a$ I have a product key for windows 8.1 (Single language edition or not that i can't remember). I have currently windows 10 pro installed.  I am planning to install windows 10 Home so i activate with windows 8.1 key.  So my question is will i be able to activate it if the Product Key is Windows 8.1 Single Language and i install Windows 10 Home(Multiple language edition) or vice versa. How to get rid of navigation symbols in beamer? How can I return the current action in an ASP.NET MVC view? I wanted to set a CSS class in my master page, which depends on the current controller and action. I can get to the current controller via ViewContext.Controller.GetType().Name, but how do I get the current action (e.g. Index, Show etc.)? Inner product of two continuous maps is continuous Let f,g be continuous maps of S in $\mathbb{R}^n$, to $\mathbb{R}^m$. Show the inner product h(x) = $\langle f(x), g(x)\rangle$ is continuous.  My attempt: Since f,g are continuous, their product is a continuous mapping, so for $\epsilon \gt 0\: t.e\:  \delta \gt 0$ such that $\parallel x - a\parallel \lt \delta $ implies $\parallel \langle f(x),g(x)\rangle - \langle f(a)g(a)\rangle \parallel \le\parallel f(x)g(x) - f(a)g(a)\parallel \lt \epsilon$ by schwartz inequality. How do you explain the value of native files to an uneducated client? If you design a piece for print. It gets reproduced several times over the course of a few years. Then the client doesn't return for any work for a few more years. And suddenly you are contacted asking for native files (Indesign, Illustrator, Photoshop). As the client puts it, "We just want to be able to make minor changes, we aren't designers."  Now, there is absolutely value in the native files. They are my "secret recipe" as a designer and anyone asking for that recipe should provide compensation for the ease of reusing, repurposing, and altering the recipe.  How do you explain to this client that there is value in the native files?  How do you counter the "But we already paid for the design." argument?  Note: I know I own the files. I know my contract states I own the files. Heck even without a contract, US Copyright law states I own the files.  What I'm seeking is an elegant, less argumentative, method of explaining the file ownership to the uneducated client. Reciting legal statutes and contract clauses doesn't often make for friendly client relations. My goal is to find a method of explaining so it is fully understood by the client without the appearance of a contract clause which forces them to do something against their will. I want the client to respect and not resent these types of contract clauses. Possible A* Optimizations What is the plural form of "Software"? Is it correct to use softwares, as in the following sentence?  There are various video conversion softwares in the market. English proverb for when a solution comes too late In Flemish we have a saying "Vijgen na pasen". Translated: "figs after Easter". It means a solution comes too late to be of any use.  What is the English equivalent for this?  Some googling gives me "Closing the barn door when the cow has bolted", but the explanation seems to point more towards the wrong solution for a problem.