I can't figure out how to download a book to my iPhone 7 iOS 13.6 that's currently stored in iCloud. How can I download the book so that I can read it offline later?
There is something strange going on with Books on iPad and iPhone. It keeps deleting some books locally, keeping them in the cloud.  It's frustrating because it happens when I'm offline and I simply lose the access to them.  Why is this happening at all? And how can I stop it?  I enabled syncing things over iCloud Drive and everything, but I can't see an option to disable such optimizations.    PS: the same thing happens with Photos, Numbers and Pages. The Photos app has an optimize storage option. But there doesn’t seem to be such an option for Books, Numbers and Pages.   A clear example: just a few hours I was reading a book on Books, I took a nap, and when I opened the Books app, the book was not available offline anymore. Since I don’t have internet right now, it’s simply impossible to access the document.
Show that $\left(1+\frac xk\right)^k$ is monotonically increasing In set theory, if natural numbers are represented by nested sets that include the empty set, how are the rest of the real numbers represented as sets?    Thanks for the answers. Several answers basically said for irrational numbers that  A Dedekind cut is a pair of sets of rational numbers $\{L, R\}$. The set of real numbers is defined to be the set of all Dedekind cuts, where a Dedekind cut is a pair of sets of rational numbers $\{L, R\}$ which have no elements in common, and where all the elements of $L$ are less than any element of $R$.  Each Dedekind cut is a real number. This is where I have a problem - surely that can’t be correct. The set $L$ is a set of all rationals, and there must be a rational in the set $L$ that is greater than all other rationals in that set, even if we have no method of determining it. And similarly, there must be a rational in the set $R$ that is less than all other rationals in that set, even if we have no method of determining it. If every irrational number has a corresponding set $L$, then each irrational number has some such corresponding largest element of that set $L$, and then each irrational number has some corresponding rational number. And that would mean that the irrational numbers are countable. So, with Dedekind cuts,  the only conclusion is that there must be irrational numbers $x$ which are either greater or lesser than some irrational cut $y$ of the rationals, and between $x$ and $y$ there is no rational number.  But that is impossible, so that the Dedekind cuts cannot be the correct representation of the real numbers.  Surely the problem with Dedekind cuts is in using sets of rationals that include all rationals up to a certain rational. But there is an alternative method of representing irrationals can be defined in terms of infinite sets of rational numbers. For example, in binary notation, the non-integer part of $\pi$ is $.00100100\ 00111111\ 01101010\ 10001$. You define a set by: if the nth digit is a $1$, then  the natural number $n$ is in the set. And then we have that, for the real numbers between $0$ and $1$, that the set of real numbers is simply the set of all subsets of natural numbers. Each subset corresponds to some real number between $0$ and $1$.  And in this way, all real numbers can be considered to be some set based only on nested sets of the empty set.  But I still haven’t got a satisfactory answer for how negative numbers can be represented in terms only of sets containing the empty set. Any ideas? Can someone pgfplots the following picture concerning confidence intervals? I've been trying to use the following code to produce it, but have no idea how to shade in the tails I am interested in. By the way, the line pointing the (100-C/2)% can be an arrow, does not have to be squiggly as depicted in the picture.   \begin{tikzpicture}[ every pin edge/.style={&lt;-}, every pin/.style={fill=yellow!50,rectangle,rounded corners=3pt,font=\small}] \begin{axis}[every axis plot post/.append style={   mark=none,domain=-3:3,samples=50,smooth}, clip=false, axis y line=none, axis x line*=bottom, ymin=0, xtick=\empty, ] \addplot {\gauss{0}{0.5}}; \addplot {\gauss{0}{1}}; \node[pin=70:{$\hat{\theta}_1$}] at (axis cs:0.57,0.5) {}; \node[pin=270:{$E(\hat{\theta} = 0$}] at (axis cs:0,0) {}; \draw[dashed] (axis description cs:0.5,0) -- (axis description cs:0.5,0.92); \end{axis} \end{tikzpicture} Ways to prove Euler's formula for $\zeta(2n)$ Showing that if the center of a group is trivial, then the center of its automorphism group is trivial Why does Blender use so much memory for large textures? Get list of ALL offers from Amazon Product Advertising API Let $f(z)=\frac{1}{(z-1)(z-2)}$ and $g(z)=\frac{z}{(z-1)(z-2)}$. Let $\gamma$ be the circle of radius 4 centered at the origin and traveled once in the counterclockwise direction. Let $A=\{ z \in \mathbb{C}: |z|&gt;3 \}$  1) I need to show there is no analytic function $G: A \to \mathbb{C}$ such that $G'(z)=g(z)$ for all $z$ in $A$.   2) I also need to show that there is an analytic function $F:A \to \mathbb{C}$ such that $F'(z)=f(z)$ for all $z$ in $A$.  Do I have to integrate to find such function? I'm new to both JavaScript and . In YUI library examples, you can find many uses of this construct:  (function() {     var Dom = YAHOO.util.Dom,     Event = YAHOO.util.Event,     layout = null,         ... })();   I think the last couple of parentheses are to execute the function just after the declaration.  ... But what about the previous set of parentheses surrounding the function declaration?  I think it is a matter of scope; that's to hide inside variables to outside functions and possibly global objects. Is it? More generally, what are the mechanics of those parentheses? From the :   -exec command ;     There are unavoidable security problems     surrounding use of the -exec action; you should use the     -execdir option instead.  -execdir command {} +     Like -exec, but the specified command is run from the     subdirectory containing the matched file, which is not     normally the directory in which you started find.  This a much     more secure method for invoking commands, as it avoids race     conditions during resolution of the paths to the matched     files.    What does this mean? Why are there race conditions with running it from the starting directory? And how are these security risks? The question asks to compute:   $$\sum_{k=0}^{n-1}\dfrac{\alpha_k}{2-\alpha_k}$$   where $\alpha_0, \alpha_1, \ldots, \alpha_{n-1}$ are the $n$-th roots of unity.   I started off by simplifiyng and got it as:  $$=-n+2\left(\sum_{k=0}^{n-1} \dfrac{1}{2-\alpha_k}\right)$$  Now I was stuck. I can rationalise the denominator, but we know $\alpha_k$ has both real and complex components, so it can't be simplified by rationalising. What else can be done? How to copy the filename quickly in windows I agree that every page in a site should have a unique TITLE, and that every page should have one and only one H1 element, but should the text of each H1 be completely unique too?  Instinctively one would think so, but there are potentially many cases where (IMHO) mind this doesn't make sense and attempting to do so will impair the user experience &amp; presentation of the page - for example, where pages are part of a closely related cluster, e.g. a multi-step process/tool/wizard.  Surely the process name should go in the H1 (e.g. "Pregnancy Planner"), and the current step you're on should be marked up as a H2 (e.g. "Step 1 - Trying for a baby"), rather than shoehorning both into a single H1 together (e.g. "Pregnancy Planner - Step 1 - Trying for a baby")?  Not only does this make the H1 rather long and potentially impact the presentation of the page, I would argue that in combining both into one you also lose semantic goodness, as the page is surely semantically richer by keeping parent (process) and child (step) as separate, nested headings?  Furthermore, the current proposal I have read is that on the first page the H1 should be the name of the process and the first step an H2, but on subsequent pages the same text should not be a H1 at all (just text styled exactly the same as an H1) and the current step should become the H1 instead. For me this is introducing unnecessary complexity to the page authoring/production process, and inconsistency in the semantic structure of the pages within the stepped process.  So it all comes back to the basic assertion that each H1 must be completely unique, which I question. Can you convince me that this should be so and that the cost/complexity of implementing this (especially in situations such as that above) is worth it?  Your thoughts please... How to restrict some websites in Ubuntu 14.04 Strange Recurrence: What is it asymptotic to? So I have the following recurrence relation for the growth rate of an algorithm:  $T(n)$ = time taken by algorithm to solve problem of size n:  $$T(n) = T(n-1) + T(\lceil(n/2)\rceil)$$  Clearly this does not obey any polynomial law but now my question is what does it obey?  I merely want an asymptotic equivalence.  My guess is subexponential since this is faster than polynomial but clearly slower than any exponential form.  What though is the question.... What pins on a nRF51822 do I connect to a STM32 programmer? I want to be able to program a  with  but I'm not sure what pins on the actual chip I should use, and all the guides seemed to be using a different chip Is it possible to smooth or generalize a polygon in QGIS, perhaps by using a plugin like the generalizer-plugin for lines?  I could convert my polygons to lines, smooth them and convert them back to polygons but this is not working for my polygons because of several reasons. $R^2$ of 1 but RMSE > 0 su command + authentication failure I am having problems with the su command. I know my password and I am typing it correctly but su indicates authentication failure.  So I checked on the internet and then went into recovery mode and changed my username's password to what I was entering before.  Even now entering the same password on su gives me authentication failure.  Please suggest what am I doing wrong?? ViewPager as a circular queue / wrapping