Proving density of $\mathbb{Q}^n$ in $\mathbb{R}^n$
Density of $\mathbb{Q}^n$ in $\mathbb{R}^n$
Probability Number A greater Number B Given $a \in \{1,2,...,250\}$ and $b\in \{0,1,...,1000\}$  What is the probability that $a &gt; b$?  I know there already is  question with a very similar question, however it's over an interval of $\mathbb{R}$ so I hope there is another way opposed to the Integral used in the formal solution.  How does one go about calculating said probability? What is recordSetVar and where is it used? I was looking at some code and in the 'apex:page' tag, an attribute called recordSetVar was mentioned. I'm new to VisualForce so could someone please tell me when and why is it used? Switching from MTB to road handlebars How do I backup a LVM partition to an image for recovery purposes?  I am trying to run dd on /dev/sda2, but it crashes after ca 8 hours, at around 380G   sudo lvmdiskscan   /dev/centos/swap [       3.89 GiB]    /dev/sda1        [     500.00 MiB]    /dev/centos/root [      50.00 GiB]    /dev/sda2        [     465.27 GiB] LVM physical volume   /dev/centos/home [     411.38 GiB]    /dev/sdb1        [     931.51 GiB]    3 disks   2 partitions   0 LVM physical volume whole disks   1 LVM physical volume   Anyway, could running from a stick make any difference? Why is variance squared? The mean absolute deviation is:   $$\dfrac{\sum_{i=1}^{n}|x_i-\bar x|}{n}$$   The variance is: $$\dfrac{\sum_{i=1}^{n}(x_i-\bar x)^2}{n-1}$$   So the mean deviation and the variance are measuring the same thing, yet variance requires squaring the difference. Why? Squaring always gives a non-negative value, but the absolute value is also a non-negative value. Why isn't it $|x_i-\bar x|^2$, then? Squaring just enlarges, why do we need to do this?  A similar question is , but mine is a little different. Thanks. Showing that the sample mean and variance are independent by showing two distribution are the same Direct product of abelian groups Let $G_1,\dots,G_n$ be groups. Prove that the direct product $G_1\times\cdots\times G_n$ is abelian if, and only if, each of $G_1,\dots,G_n$ is abelian. To prove that the direct product is abelian is straightforward but what I don't understand is the converse. Why are integers subset of reals? In most programming languages, integer and real (or float, rational, whatever) types are usually disjoint; 2 is not the same as 2.0 (although most languages do an automatic conversion when necessary). In addition to technical reasons, this separation makes sense -- you use them for quite different purposes.  Why did they choose to say $\mathbb{Z} \subset \mathbb{R}$ in math? In other words, why are 2 and 2.0 considered the same?  When you are working in $\mathbb{R}$, does it make any difference whether some elements, eg. 2.0, also belong to $\mathbb{Z}$ or not? Copy Physics To Multiple Objects Using the cell fracture addon, I created many objects from my mesh. I want to have a rigid body physics on all of them. How would I copy one of the fractured pieces physics to all the pieces? I tired ctrl L and the copy attributes addon, but none of them have the option. Any help is great. Disable drag and drop option for multiple file uploader These are the screenshots of multiple file uploader from the same SharePoint 2010 site. Some users are seeing the first and some are seeing the second one. Is it possible to disable the second view(drag and drop) by editing upload.aspx in the layouts folder?      Thank you Trying to identify a very old short story about aliens colonizing human bodies Don't remember the exact start to the story, but it went something like "walking along a path" or something, and when he hears what sounds like a shotgun blast behind him, he then feels something strike him in the butt. He passes out, and when he awakens, he discovers that the "shotgun blast" was actually a miniature spaceship that exploded and shot miniature aliens into his body. The aliens prove to be very beneficial because they clean up all the toxins and other poisons in his body. They can be transmitted through kissing or sexual activity.  Any help with the name of the story would be greatly appreciated.  Dan I have a text box that will have a currency string in it that I then need to convert that string to a double to perform some operations on it.   "$1,100.00" → 1100.00  This needs to occur all client side. I have no choice but to leave the currency string as a currency string as input but need to cast/convert it to a double to allow some mathematical operations. While browsing I have received notification on Google "Unusual traffic from your computer network"   We're sorry..."your computer or network may be sending automated queries. To protect our users, we can't process your request right now." See Google Help for more information.  Right now I am using the "Ubuntu 12.04" 32 bit version.  Any suggestion, why this is happens &amp; How it resolve?  Thank you for your worthy suggestion. How to set textbox value in jQuery? Is there a list of error codes for Minecraft? Disabled mac os SIP but still can't delete default apps I'm using mac os 11.2.1 Big Sur. My question concerns using the Terminal utility to delete Apple default apps protected by SIP. I have disabled System Integrity Protection and confirmed that it is off by typing: csrutil  Terminal duly returns &quot;disabled&quot; to confirm that SIP is definitely off. I then attempted to delete various Apple default apps, as follows: sudo rm -rf FaceTime.app/  sudo rm -rf TV.app/  sudo rm -rf Mail.app/  But nothing seems to happen. The apps are still in my Applications folder and launch normally. If I try to delete them manually, I get a beep and the deletion is rejected just as if SIP were still enabled. Can someone suggest a better way to remove Mail? (c) Let $\mathcal{L}^*\subseteq\mathcal{L}^{\text{FOPC}}$ be a first order language of predicate calculus consisting of three unary function symbols $f,g,h$.  (i) Write down an $\mathcal{L}^*$-sentence $\phi$ such if $\mathcal{A}$ is an $\mathcal{L}^*$-structure with $\mathcal{A}\vDash\phi$ then the restriction of $h_\mathcal{A}$ to the range of $f_\mathcal{A}$ gives a one-to-one function onto the range of $g_\mathcal{A}$.  (ii) Write down an $\mathcal{L}^*$-sentence $\psi$ such that if $\mathcal{A}$ is an $\mathcal{L}^*$-structure with $\mathcal{A}\vDash\psi$ and the domain $A$ of $\mathcal{A}$ is finite then the cardinality $|A|$ is a square.    Part (i) is easy enough, but I'm having trouble with part (ii). I assume that you can use part (i). My initial idea was to use $h$ to ensure $|Range(f_A)| =|Range(g_A)|$ but I'm not sure where to go from there. Thanks. Laptop using 14.04 won't get past login GUI Which profile details does an account merge preserve? When one has to merge two accounts, they're prompted by something like this with input fields for each account link:     Account 1:  Account 1 link.       Account 2:  Account 2 link.    When the merge completes, which account details are preserved, like the display name, or the profile description? Account 1, or account 2? Downgrade SQL Server Enterprise Edition to SQL Server Standard Edition