let P$_n$ be the following statement
Induction problem: "if the group has at least one player who is better than Messi, then all the members of the group are better than Messi"
How to move Ubuntu to an SSD My current situation is:   One hard disk Dual boot Ubuntu 11.04 and Windows 7. Partitions:  100MB Windows System thingy 144GB Main Windows 160GB Ubuntu 4GB Swap 12GB System Restore stuff    Now I want to install an 80GB SSD and move Ubuntu to it. AFAIK I need to:   Shrink the 160GB Ubuntu partition to 80GB Copy it over to the SSD Change fstab to mount the SSD as /   How do I do the second? And what do I need to do about Grub? iOS 9 Screen Recording in El Capitan I used to record iOS devices through QuickTime, however now it's only recording audio (not sure is this linked to OS X 10.11 or iOS 9).  How can I fix this (without third party sofrware)? What is the value of $i^{i^{i^\ldots}}$? What is the value of $i^{i^{i^\ldots}}$?   My effort is the following: If $z, \alpha \in \mathbb{C}$ with $z \neq 0$ then we can write $z^{\alpha}=e^{\alpha \log z} = e^{\alpha [ \log |z|+i \text{ Arg z} + 2 \pi i m]}$ where $ m=0, \pm 1, \pm 2, \ldots$  and Arg z is the principle argument of the complex number $z$. But in above expression we don't have the finite no of exponents, so I am not sure how should I use this formula to the solve above problem. Thanks and Regards! Find all entire functions $f(z)$ such that $|f(z)|=1$ for $|z|=1$ how to use \input{file.tex} correctly? Suppose I have two latex files file1 and file2 with the same preamble and so on. Then I want to create a file called bigfile which just puts the two files together. This is not working for some reason. Therefore I first tried to include just file1, this is what I have done:  \documentclass .... %% same as file1 ... same preamble as file1 \begin{document} \input{file1} \end{document}   The result is that I not only get file1, but also the preamble and so on. This is my first experience with putting files together in 1 file. Kindly provide me a solution :) Functional Analysis: The rank of an operator detemines if it's a compact operator. Where did they go / do they went? Where did they go?   Where do they went?   Can you please advise which of above forms is correct?  I'm pretty sure that first one is fine but wondering about second one.   Can I use a second form as well or it's incorrect? How is the ability of a person who gained physical access to your computer to get root with those steps in any way secure?   When grub2 menu opens press  e  to edit the Linux start options Change:   "linux   /vmlinuz-2.6.35-23-generic root=UUID=e7f1e48d-0015-485f-be7d-836217a31312 ro   quiet splash"    to:  "linux   /vmlinuz-2.6.35-23-generic root=UUID=e7f1e48d-0015-485f-be7d-836217a31312 ro init=/bin/bash"  Now you have root access just do:   mount -o remount,rw / passwd user mount -o remount,ro /  sync  reboot the computer and you win.   My question is, how is being able to break into any Linux machine through grub2 secure? I don't understand that fact about Linux, thank you for your answers. Are the LIGO observations proof of a black hole merger, and what happened to the black holes? Recent reports claim that the gravitational waves detected by LIGO match up with the signal expected from two black holes merging as predicted by general relativity.  Additionally, the masses of both black holes were estimated. Questions:  How certain are we that the detected of gravitational waves are necessarily from two black holes merging?  Since supermassive black holes are typically at the center of a host galaxy, what happened to the galaxies that contained the two merging black holes?  For example, did their host galaxies merge?    Edit After reading the answers, I understand that the signals detected by LIGO are proof of the validity of gravitational wave generational artifacts as predicted by general relativity.  When additionally gravitational waves, caused by the merger of the supermassive black holes (those which ARE indeed located in the centers of the merging galaxies) will be detected, since mergers of galaxies could be observed by the methods independent of gravitational waves such as registering the fact of the quasar appearance (). Additional questions:  Could someone offer me the historical ASTRONOMY precedent when the second degree of inference (from the mathematical model, being associated with the theory of Physics) was accepted as the discovery of the astronomical object?  Could someone give a reference to trustable scientific publication, with the subject of study being discussion of requirements satisfying claim of astronomical discovery of an astronomical object?  Have independent scientific sources (outside of members of the LIGO team) analyzed methodology and results of the LIGO signal detection, and published their conclusions with regards of what was actually discovered? Render not showing UV texture $(K[x,y,z]/(x^2+y^3+z^7))_{(x,y,z)}$ is a UFD. Wifi hotspot software package other than ap-hotspot? I have tried using ap-hotspot to create a wifi-hotspot but it gives me some problem every time I use it . I just want to ask is there any other software  package that create a wifi-hotspot othen than ap-hotspot ? Stop inserting hard line-wraps in blockquotes! When you use the markdown editor's blockquote feature (the quote button / Ctrl+Q), it inserts hard line-wraps in the markdown source automatically for you. That is, it transforms text like this:  Hindus regard it as an earthly manifestation of the goddess Tulsi, a consort of the god Vishnu.   The offering of its leaves is mandatory in ritualistic worship of Vishnu and his forms like Krishna and Vithoba.   Into text like this:  &gt; Hindus regard it as an earthly manifestation of the goddess Tulsi, a &gt; consort of the god Vishnu.  &gt;  &gt; The offering of its leaves is mandatory in ritualistic worship of &gt; Vishnu and his forms like Krishna and Vithoba.   The editor should instead transform it into this:  &gt; Hindus regard it as an earthly manifestation of the goddess Tulsi, a consort of the god Vishnu.  &gt;  &gt; The offering of its leaves is mandatory in ritualistic worship of Vishnu and his forms like Krishna and Vithoba.   That is, without adding any newlines.   Why on earth does it insert hard line-wraps!? Both these forms look the same when rendered, but the current way makes it more difficult for us to go back and edit the blockquoted text later if need be.   This is particularly objectionable functionality for sites that use MathJax - while the hard line-wraps don't impact the rendered output, the additional &gt; that are inserted do (they manifest as greater-than signs if they get inserted within MathJax $$...$$). See this post on Meta.Math.SE for more details: .    I found  that this behavior is apparently :      The "reflow the text when you click blockquote" is a deliberate feature, intended to improve the readability on quoted text.   Seriously? Are there any browsers that don't soft-linewrap textareas anymore? How is hard-wrapping at 70(?) characters better than soft-wrapping at $textareawidth? If readability is the concern here, then why not hard-wrap all non-code upon post submission? Escaping regex string "Nikki's and Alice's X" vs. "Nikki and Alice's X" Which option is grammatical?        There will be readings from Nikki Giovanni’s and Alice Walker’s writings.   There will be readings from Nikki Giovanni and Alice Walker's writings.      Saying it out loud the latter sounds right, but looking at it the former looks better. Review filter appears to be broken When browsing questions for a given tag, a review indicator has recently started showing up that links to the open review tasks for that tag.  For example, this is what I see when viewing :    The number 187 in the screenshot above would link to    However, clicking on that often opens review tasks that do not have the tag in question.  For example, it opened the following on successive attempts:   (c)   (java)  It seems that the filters are broken.  A sample screenshot (note the mention of the filter on the review page): That's a lot of ___ vs. those are a lot of ___ That's a lot of cars!   Those are a lot of cars!      The context is when a someone sees many objects (in this example, cars) and makes the exclamation.   According to , lot can handle either singular or plural verbs.  I agree with the author who states that that's sounds better, but the post doesn't seem definitive either way.     Are both grammatically correct and do they have the same meaning? This week we rolled out a series of changes to  of the question close workflow.  You can read more about the details of these changes .    For context, the overall effort to improve the question close experience will be optimized for Stack Overflow. Given Stack Overflow’s scale, many of the pain points we hear about with question closing and reopening are unique to Stack Overflow and won’t make sense for other network sites. However some  changes are general improvements that should improve usability and guidance overall. Wherever possible, we plan to roll these changes out network wide as well. Any time we roll out a change network wide, we’ll make sure to cross-post here. This first phase is being rolled out to the network and is why I’m posting today.  Let us know if you run into any issues or have questions regarding the network here. What is a good book to learn number theory? What would be a good book to learn basic number theory? If possible a book which also has a collection of practice problems? Thanks. Live USB data gets lost on Restart I am crawling some data using Apache Nutch and storing it on my USB Drive. The OS itself is Ubuntu Live Boot OS. But for every restart or shutdown I am losing my data. I also tried suspending my Ubuntu user still data was not visible when I reinserted my live USB.  Is there any way I can keep the data intact and does not loose and application settings installations when I do restart Ubuntu.  Used USB installer provided by pendrivelinux.com at