Just got a new iPAD air 2, iOS 9.1. It says I should update it to iOS 9.3.1.  I might be interested to jailbreak it later on, so I'd like to preserve that option for me possible.  I hear jailbreak for 9.3.1 is not available yet, and on the other hand, apple stopped signing iOS 9.1 and it is impossible to install or downgrade to iOS 9.1. I want to know how I can back up the current state with iOS 9.1, and later after I updated the iOS, when ever I wanted I could restore to the iOS 9.1.  I know that I should backup shsh blobs using Tiny Umbrella. but I cannot find the official download file in their website. Also I don't know how to backup APTicket.  Thanks
I'm trying to downgrade my iPhone from the current iOS to an older one, as per .  But every time I try, I always receive this error:     The iPhone could not be restored. This device isn't eligible for the requested build.     I have tried many times with and without DFU mode. Any ideas regarding this?
When does function composition commute? I've read that function composition "generally does not commute."  Not counting compositions involving the identity function, and compositions of a function and its inverse, are there examples of functions on the reals (for example) $f, g$ where $fg = gf$ outside of these cases? I try to download a file with wget and curl and it is rejected with a 403 error (forbidden).  I can view the file using the web browser on the same machine.  I try again with my browser's user agent, obtained by . I do this:  wget -U 'Mozilla/5.0 (X11; Linux x86_64; rv:30.0) Gecko/20100101 Firefox/30.0' http://...   and  curl -A 'Mozilla/5.0 (X11; Linux x86_64; rv:30.0) Gecko/20100101 Firefox/30.0' http://...   but it is still forbidden. What other reasons might there be for the 403, and what ways can I alter the wget and curl commands to overcome them?  (this is not about being able to get the file - I know I can just save it from my browser; it's about understanding why the command-line tools work differently)  update  Thanks to all the excellent answers given to this question. The specific problem I had encountered was that the server was checking the referrer. By adding this to the command-line I could get the file using curl and wget.  The server that checked the referrer bounced through a 302 to another location that performed no checks at all, so a curl or wget of that site worked cleanly.  If anyone is interested, this came about because I was reading  page to learn about embedded CSS and was trying to look at the site's css for an example. The actual URL I was getting trouble with was  and the curl I ended up with is  curl -L -H 'Referer: http://css-tricks.com/forums/topic/font-face-in-base64-is-cross-browser-compatible/' http://cloud.typography.com/610186/691184/css/fonts.css   and the wget is   wget --referer='http://css-tricks.com/forums/topic/font-face-in-base64-is-cross-browser-compatible/' http://cloud.typography.com/610186/691184/css/fonts.css   Very interesting. How to pronounce fractions with denominators larger than 20 where the last digit of the denominator is 1 or 2? eg 4/31 Disclaimer: I speak British English.  I've noticed a lot of differences between the way Americans and Brits pronounce numbers.1  Since the question concerns this, I thought it might be appropriate to draw attention to it case we inadvertently confuse each other.  My question is not about these differences, I just wish to highlight them in case they cause confusion.  1. You seem to happily call a quarter "a fourth" sometimes, we always call 131 "one hundred and thirty one", we pronounce double digits in phone numbers like 12449 as "one two double four nine", and I think we are much more likely to use expressions like "thirteen hundred" to mean 1300.    Question  When talking about fractions, I have frequently heard  1/2    a half 1/3    a third 1/4    a quarter 1/8    an eighth 1/64   a sixty fourth 1/56   a fifty sixth   etc.  Essentially the rule seems to be that, except for "a whole", "a half", and "a quarter", the word matches the ordinal number; that is to say:      Numeral       Ordinal         Fractional     one           first           whole     two           second          half     three         third           third     four          fourth          quarter     five          fifth           fifth     six           sixth           sixth     fifty-seven   fifty-seventh   fifty-seventh  Even though 1/4 is a quarter, 1/64 is a sixty-fourth.  So what’s 1/62?  A  sixty-twoth?  A sixty-second? Surely not a sixty-half!  I know that simply saying one over sixty-two can usually work, but I'm asking specifically for the word itself, i.e.  if I divide a huge pizza into 21 pieces, what are the pieces?  Other than baker’s twentieths.  Summary: Can anyone point me to any sources (whether style guides or common usage studies or anything else) that discuss the pronunciation of fractions; specifically one that discusses this separately from ordinal numbers, rather than how to form ordinal numbers in the first place. I have been playing with Ubuntu for a few weeks now, and I'd like to revert my computer back to it's original - factory - defaults.   On the computer I have a recovery partition (it's a netbook). I went through the process of recovery and everything seemed fine. However, when I restart the computer I'm presented with   grub rescue &gt;   Now, my understanding is that when I installed Ubuntu "side by side" it replaced the MBR or something like it, with GRUB.   I've read on a slew of forums, that I need to use a Windows Recovery Disk.   Here are my issues:   a) I don't have a recovery disk, I have a recovery partition - it's a netbook. b) I don't have an external cd drive.   What I do have is a USB key that has about 1gb of space on it.   Thanks in advance. I think my MacBook Pro battery was replaced by Apple's service team. How do I check that? How do I prove if $\sup\{ (n!)^{1/n} | n \in\Bbb N\} = +\infty$?  I don't know how to properly explain it Splitting all polygon features in a shapefile into smaller equal width polygons I have a shapefile of thousands of polygon features, that i would like to break up into smaller pieces (i.e. break a square into 8 equal pieces). I have read all over these boards for the right solution and haven't found one yet unfortunately. I've tried parcel editor but that only allows you to manually edit one feature at a time, and I've tried fishnet but that doesn't run through each individual feature it just processes across the entire extent of the shapefile. I have the full license for ArcGIS so all options are game. Ultimately I would like to be able to split this initial shapefile of features into a specified amount of equal width slots that each would be their own feature in the resulting shapefile.  Any thoughts? I started thinking about the number of associative (binary) operations on a set with $n$ elements today.  Looking online I found  which indicates only $113$ of the possible $19,683$ operations on a three-element set satisfy association.  So, $50\%$ of binary operations on a two-element set satisfy association, and less than $0.6\%$ of all binary operations on a three element set satisfy association.  For an $n$-element set, where $n$ denotes a natural number, is the ratio $R_{n}=A_{n}/B_{n}$, of the number of associative binary operations $A_{n}$ to the number of all binary operations $B_{n}$, in general small?  I don't mean the following questions as equivalent, but since they seem more concretely answerable in principle, does   $$ \lim_{n \to +\infty} \frac{A_{n}}{B_{n}} = 0 ? $$       Also, is $F : n \to R_{n}$ a monotonically decreasing function?  Some Background of the Question: In his Linear Algebra Problem Book 1995 on p. 6 Paul Halmos writes "The commonly accepted attitudes toward the commutative law and the associative law are different.  Many real life operations fail to commute; the mathematical community has learned to live with that fact and even to enjoy it.  Violations of the associative law, on the other hand, are usually considered by specialists only."  For all I know, Halmos might only have written that to motivate the study of Linear Algebra and doesn't quite literally mean what he appears to say.  But, if he means what he appears to say, and if $F : n \to R_{n}$ is monotonically decreasing, or $R_{n}$ is generally small, I think there's something amiss with what Halmos says, since non-associative operations seem so common that one may as well enjoy them. There is an exercise in Humphreys's An Introduction to Lie Algebras and Representation Theory: "Any nilpotent Lie algebra contains a codimension 1 ideal".  The proof I am thinking of is the following.  Suppose the Lie algebra $L$ satisfies $L\neq[L,L]$. Then $\pi\colon L\to L/[L,L]$ is a projection onto an abelian algebra. Choose a codimension 1 subspace $I\subset L/[L,L]$. Then $I$ is an ideal and its preimage $\pi^{-1}(I)$ is necessarily an ideal in $L$, because any subspace containing the derived algebra is an ideal. Moreover, $\pi^{-1}(I)$ has codimension 1. $\square$  The only condition on $L$ is that $L\neq[L,L]$, which holds for solvable Lie algebras as well. Is this proof correct? How come Humphreys didn't set the exercise with "nilpotent" replaced by "solvable"? View progress towards Announcer, Booster, and Publicist badges I shared a link to a question and now I am wondering whether I am almost going to get an announcer badge.  Can I somehow see which links I shared and how many clicks were on it for the last days?  Update:  Maybe this would be a nice feature. Next to any question you can see who has promoted it the most (number of fresh hits from a referer link) and also the amount of new ip's through search engine's and other referring sites.  Note the progress feature should include the Announcer, Booster, and Publicist badges. Give each site a parallel site for polling, recommendations and subjective-ish stuff Stuff like polls, recommendations based on subjective constraints, puzzles, webcomics etc. do not belong on the serious main SE sites, where professionals should be considered at work and having just a few spare minutes ("code's compiling") to answer questions, so they should not be distracted by such things. However, I'd also like to have a home for these things still using the SE engine. For the reason I mentioned before, this needs to be a separate place though. Let's call it four.[sitename-here].com. Verbatim Environment in Figure Caption I've already read The Hobbit and The Lord of the Rings, which I assume would be the best start in any case. I also got about halfway through The Silmarillion several years ago and am quite familiar with the legendarium as a whole, but for the sake of argument let's assume I'm starting from scratch.  What is the best order for a budding scholar of Middle-earth to read Tolkien's books? Or does it even matter once you've covered the core novels? Chronological order clearly isn't the most logical approach here, and even publication date isn't necessarily best.   The Hobbit The Lord of the Rings The Silmarillion The Children of Hurin The History of Middle-earth Unfinished Tales The Letters of J.R.R. Tolkien Anything else   Note: After asking this question I found  on Reddit. It covers even more material and in more detail than my original question or any answers here. I'm working on an exercise from functional analysis.  Let $E$ be a vector space and $\|\cdot\|_1$ and $\|\cdot\|_2$ be two complete norms on $E$. Now suppose that $E$ satisfies the following property:  $\bullet$ if $(x_n)$ is a sequence in $E$ and $x,y\in E$ such that $\|x_n-x\|_1\to 0$ and $\|x_n-y\|_2\to 0$, then $x=y$.  Now we want to show that the norms $\|\cdot\|_1$ and $\|\cdot\|_2$ are equivalent.  My idea is as follows: If for any $n&gt;0$, there is an element $x_n\in E$ such that $\|x_n\|_1&gt;n\|x_n\|_2$. Then consider $(\frac{x_n}{\|x_n\|_1})_{n\geq 1}$. Clearly, $(\frac{x_n}{\|x_n\|_1})_{n\geq 1}$ converges to $0$. However, I cann't get a contradicition from this. Maybe my idea is wrong.   In fact, I even don't konw how to show that a Cauchy sequence in norm $\|\cdot\|_1$ is also a Cauchy sequence in norm $\|\cdot\|_2$.   Anyone can give me some hints or a counter example? Thank you very much. Automatically determine tags while writing a question Can we modify "Ask question" to automatically suggests tags based on your question content.   So instead that user needs to type "team-foundation-server" or "TFS" or "TeamFoundationServer" he will see list of tags auto-populated with ajax which he (or she) can then select and it will be associated with the question. So basically only thing we need is code which will cross-match question content with list of known tags while user is typing and display results in some nice ajax-enabled list/cloud/whatever UI control. This should be separate control for tags suggestions so user still has option to use standard tag list input to type-in tags.  In this case, instead of three (or more) tag variations we would have only one tag for Team-Foundation-Server. I am looking for one word to describe someone who always does what he loves.   Loving means enjoying something very much, free-spirited means not restrained by convention. Is there a hybrid word?   I mean a word that describes someone who is independent and always does what he loves. Please also try to not make the word too esoteric. Also, the word needs to be positive.  How will it be used?  I am submitting an application for college, and they require me to supply a word to describe myself. I have always done what I love. So, I require a word to describe someone who loves what they want. There is no sentence, in particular, just a prompt asking me to describe myself in one word. Different mechanics of \hyperlink vs. \hyperref I am fiddling around with the hyperref package to build a hypertext structure into my pdf. At first glance, hyperref provides two similar macros to put links between parts of my document: \hyperlink{target}{text} and \hyperref[target]{text}. You might notice their slightly different syntax. What really interests me is their different working mechanics. I will illustrate this by the following example: \documentclass{article}  \usepackage{pdfpages} \usepackage[]{hyperref} \usepackage{mwe}  \begin{document}  \section{Section Heading} \label{sectionheading}  \includepdf[link=true, linkname=pdfpage]{example-image}   Link to section works with \hyperref[sectionheading]{hyperref} and with \hyperlink{sectionheading}{hyperlink} (but with slightly different targets on the page).  Link to pdf works with \hyperlink{pdfpage.1}{hyperlink} but not with \hyperref[pdfpage.1]{hyperref} (and not this way, either: \hyperref[pdfpage]{hyperref}).  \end{document}  To link to the labeled section heading, I may use both commands. While \hyperref directs my pdf viewer directly to the linked section, \hyperlink directs me somewhere slightly different, so I can see more context. To link to the \includepdf of pdfpages however, I may only use \hyperlink. \hyperref does not work at all. I suspect this is because of a subtle difference in their working mechanisms. While checking the aux file, I found a line \newlabel{sectionheading}{{1}{1}{Section Heading}{section.1}{}} which \hyperref seems to use as a target. However, I did not find any similar target for the included pdf. My question: I suspect, I understand the workings of \label and \ref very well. \hyperref seems to work quite similarly with the added clickability. Could you please explain to me how \hyperlink does work differently and how it is implemented? E.g. what mechanics explain the difference when clicked on the link and where and how are the link targets stored in the first place? How to prove that the set $A = \left\{ {p:{p^2} < 2,p \in {\Bbb Q^+}} \right\}$ has no greatest element? More specifically, I have to find a $q$ in $A$ such that $q$ is larger than any $p$ in $A$.  The only thing I can think of is using (${2 - {p^2}}$) somehow, or ${(p+x)^2}&lt;2$, but other than that I don't know how to proceed. This exercise is taken from the very first chapter of Walter Rudin's Principles of Mathematical Analysis. Quoting the exercise:     To do this, we associate with each rational $p &gt; 0$ the number:     $$q = p - \frac{{{p^2} - 2}}{{p + 2}} = \frac{{2p + 2}}{{p + 2}}$$   But he didn't explain how he came up with that number.   The only thing I've thought of is the following procedure:  $$\eqalign{   &amp; {p^2} + (2 - {p^2}) = 2 \Rightarrow {p^2} + (\frac{{2 - {p^2}}}{2}) &lt; 2,{\text{ and since }}2 - {p^2}{\text{ is always positive,}}  \cr    &amp; {p^2} &lt; \left[ {{p^2} + (\frac{{2 - {p^2}}}{2})} \right] &lt; 2  \cr    &amp; {\text{Therefore, let }}q = \sqrt {{p^2} + (\frac{{2 - {p^2}}}{2})} ,{\text{ then:}}  \cr    &amp; p &lt; q &lt; \sqrt 2  \cr} $$  However, my result doesn't necessarily belong to ${\Bbb Q}$. I wonder how did he obtain the value of $q$ in the book.  EDIT: Feel free to point out if there are more appropriate tags for this question. I have always argued adamantly, as long as the issue has been around, that gift should never be used as a verb. However, someone whose English knowledge I quite respect disagrees.  I’ve done some searching and I haven’t found a consensus; should gifting be shunned? How do I set environment variables from Java?