I have rEFInd installed on the EFI partition of my 2015 MacBook Air. Every time I update macOS, it ends up taking over the bootloader and resetting it to using the macOS operating system. Afterwards, if I hold the option key while booting up my mac, there is no boot option for rEFInd that I can select. The only way I can bring rEFInd back is to boot up into recovery mode, manually mount my system partition with Disk Utility (as it is encrypted using FileVault), then open Terminal and reinstall rEFInd. It's quite a hassle.  Is there any better way to handle macOS updates?  I have read the section of the rEFInd manual named "Recovering from a Coup Using MacOS" but I didn't find any information in there that was pertinent to my situation. Note that I cannot disable System Integrity Protection (which one of the solutions there requires) as I need to keep it enabled for the software development I do on this system.  Below is the output from the command diskutil list disk0.  /dev/disk0 (internal, physical):    #:                       TYPE NAME                    SIZE       IDENTIFIER    0:      GUID_partition_scheme                        *121.3 GB   disk0    1:                        EFI EFI                     209.7 MB   disk0s1    2:                 Apple_APFS Container disk1         121.1 GB   disk0s2   I have Windows, Linux, and macOS 10.15 beta installed to an external drive, so my MacBook's internal drive just has macOS.
I use a macbook pro 2015 with macOS High Sierra. I installed windows 10 using bootcamp, which resized the macOS partition and created a 80GB windows partition. The machine boots into windows just fine.  Unfortunately I can't go back to macOS because the macOS partition is not selectable as a boot source in bootcamp and "boot into X" boots into windows again. When I start from recovery (ctrl+R) I can see both partitions in diskutil. I tried to repair the macOS partiton but it had no effect.  How can i resurrect the macOS partion so I can choose which OS to start?  Update: I can start macOS by booting with option/alt pressed and chose the mac partition.  diskutil list output:  Capsicum:~$ diskutil list /dev/disk0 (internal, physical):    #:                       TYPE NAME                    SIZE       IDENTIFIER    0:      GUID_partition_scheme                        *251.0 GB   disk0    1:                        EFI EFI                     209.7 MB   disk0s1    2:                 Apple_APFS Container disk1         170.0 GB   disk0s2    3:       Microsoft Basic Data BOOTCAMP                80.3 GB    disk0s3    4:           Windows Recovery                         503.3 MB   disk0s4  /dev/disk1 (synthesized):    #:                       TYPE NAME                    SIZE       IDENTIFIER    0:      APFS Container Scheme -                      +170.0 GB   disk1                                  Physical Store disk0s2    1:                APFS Volume Macintosh HD            101.3 GB   disk1s1    2:                APFS Volume Preboot                 20.2 MB    disk1s2    3:                APFS Volume Recovery                506.6 MB   disk1s3    4:                APFS Volume VM                      2.1 GB     disk1s4  /dev/disk2 (external, physical):    #:                       TYPE NAME                    SIZE       IDENTIFIER    0:     FDisk_partition_scheme                        *2.0 TB     disk2    1:                  Apple_HFS Passport                2.0 TB     disk2s1   thanks a lot for any clarification what is wrong!
What are the costs of books and materials in Harry Potter? In the first book, Harry sees his Gringotts vault for the first time.  (Quotes thanks to Slytherincess!)     Griphook unlocked the door. A lot of green smoke came billowing out, and as it cleared, Harry gasped. Inside were mounds of gold coins. Columns of silver. Heaps of little bronze Knuts.      "All yours," smiled Hagrid.      All Harry's -- it was incredible. The Dursleys couldn't have known about this or they'd have had it from him faster than blinking. How often had they complained how much Harry cost them to keep? And all the time there had been a small fortune belonging to him, buried deep under London.      Hagrid helped Harry pile some of it into a bag. "The gold ones are Galleons," he explained. "Seventeen silver Sickles to a Galleon and twenty-nine Knuts to a Sickle, it's easy enough. Right, that should be enough fer a couple o' terms, we'll keep the rest safe for yeh."      Harry Potter and the Sorcerer's Stone - pages 58-59 - US Hardcover Edition   Jk Rowling posts in the Harry Potter Lexicon      JKR has stated in an interview (Comic Relief 2001) that she estimates the value of one Galleon to be "about five pounds," which works out to around US$9.75 (the exchange rate at the time of the interview was US$7.33). In the introduction to both QA and FB, US$250-million is stated to be the equivelent of 34 million Galleons. That also works out to a value of £5 to the Galleon, at the exchange rate of the time. The price listed on the back of the books, however, is not correct, since US$3.99 would equal less than half a British pound, or 8 sickles and 15 knuts. The book instead incorrectly lists US$3.99 as being equal to 14 sickles and 3 knuts. (Unfortunately, CNN.com uses this incorrect value for their Knuts-to-dollars converter.)      This gives us approximate values as follows:      1 bronze Knut = £0.01 (US about 2 cents)      1 silver Sickle = £0.29 (about US$0.57)      1 Galleon = £5.00 (more or less US$9.75)      These rates vary as the exchange rate fluctuates - see the Wizarding World Currency Converter for the current rate.   Now looking at the quote      Hagrid helped Harry pile some of it into a bag.   and     Right, that should be enough fer a couple o' terms, we'll keep the rest safe for yeh.   Obviously "some" is unspecified, but presuming the costs of ...     Typical elementary-school textbooks cost more than $100 each   He would be carrying at least 10 galleons for each school book, and going by the list of books just for his first year,  (Thanks Ibid!)     COURSE BOOKS      All students should have a copy of each of the following:         The Standard Book of Spells (Grade 1) by Miranda Goshawk   A History of Magic by Bathilda Bagshot   Magical Theory by Adalbert Waffling   A Beginners’ Guide to Transfiguration by Emeric Switch   One Thousand Magical Herbs and Fungi by Phyllida Spore   Magical Drafts and Potions by Arsenius Jigger   Fantastic Beasts and Where to Find Them by Newt Scamander   The Dark Forces: A Guide to Self-Protection by Quentin Trimble         (Harry Potter and Philospher's Stone, Chapter 5)   That's 80 Galleons just for books. This does not include the list of other expenses Harry has for his school years (wand, potion reagents, etc.)  How many Galleons is "some" or is Diagon Alley selling supplies for third world prices?  Sidenote, is this just a case of bad JK maths? In other words, can I do something like  for() {     for {        for {        }     } }   Except N times? In other words, when the method creating the loops is called, it is given some parameter N, and the method would then create N of these loops nested one in another?  Of course, the idea is that there should be an "easy" or "the usual" way of doing it. I already have an idea for a very complicated one. I have always recommended pressing ALT+F2 and typing for example gksu nautilus or gksudo nautilus both are equivalent; to run graphical programs with root privileges.  However, I have just installed raring on a test system and this no longer works.  gksu and gksudo are not installed as part of a default raring install; though they are in the repositories. In 12.04 at least gksudo was just a symbolic link to gksu  The reasons I have always done this are because while it is often safe to use sudo under some circumstances it can cause problems with graphical applications because gksu has you running the program as root while with sudo you are running as yourself but with elevated privileges.  This can mean you inadvertently change the owner of critical system files.  This can cause problems.  This reasoning is explained better here:         Why was command removed from a fresh install and what should we be using instead? Why do Harry and Dumbledore need to get the memory from Slughorn? In Harry Potter and the Half-Blood Prince, Dumbledore orders Harry to retrieve the memory about the talk with Tom Riddle/Voldemort from Slughorn. The memory is said to be needed because it contains valuable information that is needed to defeat him. The result is that they know that Voldemort uses Horcruxes.  Why do they not know this before? If the knowledge about Horcruxes is present in school books (albeit forbidden section) and teachers, then surely some magical academics will already have guessed that Voldemort would try to use them?  Also, if I recall correctly, there is a hint in the first book, "some thought that he was no longer alive enough to be able to really die" which hints a lot at the split soul as a price you pay for being immortal.  Why does Slughorn's memory seem so crucial to Dumbledore? Let $X,Y,Z$ be subspaces of $V$ so that $X$ is a subspace of $Y$. Prove that $Y\cap (X+Z)=X+(Y\cap Z)$ On finding polynomials that approximate a function and its derivative (extensions of Stone-Weierstrass?) The Stone-Weierstrass Theorem tells us that we can approximate any continuous $f:\mathbb{R}^n\to\mathbb{R}$ arbitrary well on a compact subset of $\mathbb{R}^n$ by some polynomial. Suppose that $f$ is continuously differentiable, under what conditions can we guarantee we can find a polynomial $p$ such that $p$ approximates arbitrarily well $f$ and the partial derivatives approximate of $p$ arbitrarily well those of $f$ (on a compact subset of $\mathbb{R}^n$)? References are welcome. See below for my (probably naive) approach to the question.    It is straightforward to find conditions if $n=1$: Let $K:=[a,b]\subseteq\mathbb{R}$ and let $K_+$ denote some open cover of $K$. Suppose that $f:K_+\to\mathbb{R}$ is continuously differentiable and let $f'$ denote its derivative. Then, by Weierstrass's approximation Theorem we have that there exists a polynomial $q$ such that   $$||f'(x)-q(x)||\leq \varepsilon$$  for all $x\in K$. Choose some $y\in K$. For any $x\in K$ define  $$p(x):=f(y)+\int_y^xq(t)dt.\quad\quad(*)$$  By the Fundamental Theorem of calculus we have that $p'=q$. So for any $x\in K$  $$||f(x)-p(x)||=\left|\left|\int_y^x (f'(t)-q(t))dt\right|\right|\leq \int_y^x ||f'(t)-q(t)||dt\leq \varepsilon||x-y||\leq \varepsilon (a-b).$$  However, the above argument doesn't work in higher dimensions because the analogue of $(*)$ does not imply that $\nabla p = q$ (since not every vector of polynomials spans a gradient field). Can anyone suggest a way around this? That is, a way to to show that for continuously differentiable $f:\mathbb{R}^n\to\mathbb{R}$ and for any $\varepsilon&gt;0$, we can always find a polynomial $p$ such that   $$||f(x)-p(x)||+||\nabla f(x)-\nabla p(x)||\leq \varepsilon$$  for all $x$ in some compact set $K$? Feel free to add extra conditions on $K$, if it makes life easier. Are there any differences between insmod and modprobe? "Naturally occurring" non-Hausdorff spaces? I am using ArcGIS Desktop 10.1.   I am trying to find the location of the highest value pixel in my Direct Solar Radiation Raster. I can see the extent of the data in my raster but don't know where the highest value pertains to.   Is there a way to simply select pixel with highest value or create a point at highest value? How much hard disk space should be needed for Xbox 360? I want to get a 360 and don't know wether to get the bigger (250GB), newer, more expensive Elite, or get one of the older, smaller (120GB), last gen ones. I know the arcade is going to be too small to save anything useful  How much hard disk space is recommend? What else is stored besides games? Sum with parameter convergence How do I transfer my Pokemon Go account to another device (Android to Android)? I was having trouble playing the game on my android so I downloaded it to my wife's phone (Galaxy S6). I read some posts on how to get it running on my android and it worked but, my level 7 account is on my wife's phone.  How do I get it back to my android? When I sign out and back in it doesn't ask for any sign in info. I've tried deleting the app's data and even uninstalling and re-installing, but it still doesn't ask for sign-in info. Prove the equality: $\det\left[\begin{smallmatrix} -2a &a+b &a+c \\ b+a&-2b &b+c \\ c+a&c+b &-2c \end{smallmatrix}\right] = 4(a+b)(b+c)(c+a)$ i have to prove:   $$\begin{vmatrix} -2a &amp;a+b  &amp;a+c \\   b+a&amp;-2b  &amp;b+c \\   c+a&amp;c+b  &amp;-2c  \end{vmatrix} = 4(a+b)(b+c)(c+a)$$   I have tried many calculations between the rows and columns of the determinant to get to the answer i want to solve the exercise however none of them gave me something right. Can someone help? How are self-replicating mines supposed to work? How does one prove that the Klein bottle cannot be embedded in $R^3$? I'm talking about smooth embeddings. Show the title character limit when writing a title I just ran into this while writing .  [I originally wrote:     you need a minimum of X reputation to comment on questions that are not your own, and on answers that are not to your own questions   But had to shorten it to:     you need a minimum of X reputation to comment]   First, it didn't tell me that I'd gone over the character limit for the title until after I had already tabbed out of the title field.  Second, it didn't tell me how much I'd gone over or anything. I had to copy-paste the text I'd written into my text editor in order to get some real-time feedback on the exact character count, to help figure out how to best shorten it. Double dual mappings How can I blow out the background when shooting down for clothing on the ground? What happens to a lens when you turn the focus ring during AF mode? What happens to a lens when you turn the focus ring during AF mode?  I have read that this causes damage, or can cause damage. But what is actually happening? I've done this recently with my Canon EF 50mm 1.8 lens.  Is a lens damaged after doing this once or does it have to happen multiple times? Jamaica Inn episode 5 from BBC learning English drama section:  The dialogue says:     Mary: My aunt is in bed.   She doesn't say -      My aunt is in the bed.   That section is for teaching English.  Are they using incorrect English?