If $m_1 , m_2, \cdots m_n$ are natural numbers where at least one of them is not a perfect square, then how do I prove that the sum $$\sqrt{m_1}+\sqrt{m_2}+ \cdots + \sqrt{m_n}$$ is irrational? I'm hoping to prove this using methods from pre-calculus level algebra.
Can a sum of a finite number of square roots of integers be an integer? If yes can a sum of two square roots of integers be an integer?  The square roots need to be irrational.
When conducting multiple regression, when should you center your predictor variables & when should you standardize them? I remember reading a series when I was around 7th or 8th grade about aliens who had taken over Earth by putting metal caps on people when they were "entering adulthood" to control them (not direct control, but it would keep them from rebelling). There was a faction of people who able to escape and had fake caps and would save teens who were about to be capped.  The main protagonist was a teen boy who was a boxer (or training to be a boxer or something). The aliens would hold tournaments for the humans and whoever won would be "worthy" to serve as personal slaves to the aliens.     The protagonist won and was able to get inside to try and learn more about the aliens from the inside. Show that $a_{n+1}= 1 + \frac{1}{a_n}$ converges. Let $\{a_n\}$ be defined by $a_1 =1  $ and $a_{n+1} = 1 + {\dfrac{1}{a_n}}$ with $n \in N$. Show that $a_{n+1}= 1 + {\dfrac{1}{a_n}}$ converges.  I know the limit but how can I show that is a Cauchy sequence or that this sequence converges. Drag and drop not working inside Nautilus on Ubuntu 17.10 I'm having a strange problem on Ubuntu 17.10: when I try to drag and drop something inside Nautilus it simply doesn't work, it doesn't even select the item, it seems like it's ignoring the action... Also, I cannot select things inside nautilus by drawing rectangles with the mouse.  All of these actions work only on the Desktop. Here is a demo:    I'm using the Xorg session with nVidia proprietary drivers. I also noticed that Nautilus seems to hang when I try to copy, paste or cut a file...  EDIT 1: I solved the problem for the slow copy/paste by disabling the clipboard sync plugin of KDEConnect. I also discovered that if I open Nautilus as root, I can drag and drop or select whatever I want... How do I know if food left at room temperature is still safe to eat? Unable to mount /dev/loop0 during install I'm runing 15.04 on a dell xps 13 bluetooth recognises devices when i  try to add them but won't let me connect to them Here is the results from my terminal.  ~ $ uname -a; lspci -nnk | grep -iA2 net; lsusb; dmesg | grep -i bluetooth; dmesg | grep -i firmware; lsmod | grep bluetooth  Linux aaron-XPS-13 3.19.0-15-generic #15-Ubuntu SMP Thu Apr 16 23:32:37 UTC 2015 x86_64 x86_64 x86_64 GNU/Linux 02:00.0 Network controller [0280]: Broadcom Corporation BCM4352 802.11ac Wireless Network Adapter [14e4:43b1] (rev 03)     Subsystem: Dell Device [1028:0019]     Kernel driver in use: wl Bus 003 Device 002: ID 8087:8001 Intel Corp.  Bus 003 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub Bus 002 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub Bus 001 Device 003: ID 0bda:5682 Realtek Semiconductor Corp.  Bus 001 Device 002: ID 0a5c:216f Broadcom Corp.  Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub [    8.164048] Bluetooth: Core ver 2.20 [    8.164065] Bluetooth: HCI device and connection manager initialized [    8.164069] Bluetooth: HCI socket layer initialized [    8.164073] Bluetooth: L2CAP socket layer initialized [    8.164079] Bluetooth: SCO socket layer initialized [    8.353160] bluetooth hci0: Direct firmware load for brcm/BCM20702A0-0a5c-216f.hcd failed with error -2 [    8.353166] Bluetooth: hci0: BCM: patch brcm/BCM20702A0-0a5c-216f.hcd not found [   20.289452] Bluetooth: BNEP (Ethernet Emulation) ver 1.3 [   20.289455] Bluetooth: BNEP filters: protocol multicast [   20.289459] Bluetooth: BNEP socket layer initialized [   20.310897] Bluetooth: RFCOMM TTY layer initialized [   20.310907] Bluetooth: RFCOMM socket layer initialized [   20.310912] Bluetooth: RFCOMM ver 1.11 [  886.399085] Bluetooth: hci0 urb ffff8800d8c15e40 failed to resubmit (2) [  895.471190] Bluetooth: hci0: BCM: patching hci_ver=06 hci_rev=1000 lmp_ver=06 lmp_subver=220e [  896.113983] Bluetooth: hci0: BCM: firmware hci_ver=06 hci_rev=1624 lmp_ver=06 lmp_subver=220e [    8.353160] bluetooth hci0: Direct firmware load for brcm/BCM20702A0-0a5c-216f.hcd failed with error -2 [  896.113983] Bluetooth: hci0: BCM: firmware hci_ver=06 hci_rev=1624 lmp_ver=06 lmp_subver=220e bluetooth             491520  22 bnep,btusb,rfcomm ~ $ Drawing/Sketching Tool for elaborating questions More often than not I need to elaborate my question put up on Stack Overflow with a custom sketch, UML class diagram, flow chart.    It is in these times I have to open up a custom paint software, factor out some diagrams, export it as an image, attach it to Stack Overflow. I wouldn't know how complicated it is to invest in having such a sketching or drawing tool integrated, It could even be a basic pen stripped off all the advanced features leaving it a bare minimum.  Such a tool if incorporated into the Stack Overflow "ask question" UI would be certainly helpful.  As of Today this Question has been visited around 170 times and 7 answers, This was meant to be the voice of Stack Overflow users. Would you need a Drawing Tool for you on the Stack Overflow site, would it help you to express you questions and answers better? Sadly, only 2, or 3 answers are in the context of the question. The bounty was meant to be a bait and even that ends tomorrow. Hope you'll get the will and the zest to comment on this question today and in the future . Is it the case that for all sets $A, B, C,$ and $D$, $(A \times B) \cup (C \times D) = (A \cup B) \times (C \cup D)$? I think I have managed to work this out, however there is no solution provided with the question so I thought it best to check.   My working:  Let $(x,y) \in (A \times B) \cup (C \times D)$  $\Rightarrow x \in (A$ or $C)$ and $y \in (B$ or $D)$  $\Rightarrow (x, y) \in (A \cup C) \times (B \cup D)$  $\Rightarrow (A \times B) \cup (C \times D) \subseteq (A \cup C) \times (B \cup D)$  Now let $(x,y) \in (A \cup C) \times (B \cup D)$  $\Rightarrow x \in (A$ or $C) $ and $y \in (B$ or $D)$  $\Rightarrow (x, y ) \in (A \times B) \cup (A \times D) \cup (C \times B) \cup (C \times D)$  $\Rightarrow (A \cup C) \times (B \cup D) \nsubseteq (A \times B) \cup (C \times D)$  $\Rightarrow (A \times B) \cup (C \times D) \not= (A \cup C) \times (B \cup D)$  Is this correct?  Thank you. Is it possible to set a DNS record to redirect all example.com/* traffic to www.example.com/*?  I'm running a  app on Heroku's .  I set up , and the documentation discusses . I also read about how to do this with . However, I'm wondering if there's a way to do this via DNS, i.e., without hitting my app. "need to do" vs "need do" Consider:  I need to do this. I need do this.  My English grammar knowledge tells me that &quot;need&quot; doesn't have the same status as the modal verbs &quot;may&quot;, &quot;can&quot;, &quot;should&quot; and what not. Hence the second usage where two verbs appear consecutively is incorrect. But yesterday, my native English speaking friends (Americans) told me that &quot;I need compute this.&quot; is a perfectly grammatical sentence, and one is simply omitting the &quot;to&quot;. How can this be? Is it a colloquial usage but grammatically incorrect, or is it grammatically correct? If it is grammatically correct, is it because &quot;need&quot; is a semi-modal verb? EDIT: in particular, is it okay to use &quot;need compute&quot; in a scientific paper? EDIT2: the exact phrase that raised the question was &quot;The advantage of this representation is that we need only compute sums and products&quot; How to search text throughout entire file system? An example of a lattice that's not totally ordered Dragging files into blender Why does list(my_list) modify the object? How to get a drive formatted with exfat working? In Ubuntu 13.04 there was an option to use the PPA by Relan in order to get ExFat functionality. Seeing that in Ubuntu this functionality is now available from the repositories without the PPA I tried this but failed to make it work.  So my question is how do I enable exfat support? How to Create a Half-Turn Staircase? I would like to create a half-turn staircase without a landing. Is there an easy way to accomplish this without having to manually calculate and create each step individually?  Here’s an image similar to what I would like to achive:    I have found the Archimesh add-on including . While I can bend the created stairs, I haven’t found any way to get anywhere close to the image above. My stairs just always look out of shape and I don’t know how to get the outline of the staircase into a square.  I should mention that I only have very little experience with Blender modeling, so it’s well possible that I’m just missing some curve modification basics. Perhaps Archimesh is also the wrong approach for this in the first place? Cancelling special & general relativistic effects We know that for a GPS we need to make a correction for both general and special relativity: general relativity predicts that clocks go slower in a higher gravitational field (the clock aboard a GPS satellite moves faster than a clock down on Earth), while special Relativity predicts that a moving clock is slower than the stationary one (slow the clock compared to the one down on Earth).  My question is this: is it possible, in theory, to set up an orbit so that these two effects cancel each other out, allowing a clock on board a GPS satellite to tick as if it were on Earth? Is there a distance at which the special and general effects cancel?  Sorry if this is a stupid question - I'm still not entirely confident with the theory of general relativity. How do I use regular expressions in bash scripts? I want to check if a variable has a valid year using a regular expression. Reading the  I understand I could use the operator =~  Looking at the example below, I would expect to see "not OK" but I see "OK". What am I doing wrong?  i="test" if [ $i=~"200[78]" ] then   echo "OK" else   echo "not OK" fi Question: If $(1+x)^n=\binom{n}{0}+\binom{n}{1}x+\binom{n}{2}x^2+\dotsm+\binom{n}{n}x^n$, prove that $\binom{n}{1}-2\binom{n}{2}+3\binom{n}{3}-\dotsm+(-1)^{n-1}n\binom{n}{n}=0$  My attempt:  I wrote the expression for $\binom{n}{k}$ for each term in the L.H.S and then tried to simplify but could not reach the R.H.S.  Please help. I have no idea on how to begin. I am not allowed to use calculus.