AMD-Action:downloadProduct:SP error on clean install I'm getting the AMD-Action:downloadProduct:SP error when trying to reinstall macOS, it doesn't even get to the option to sign in with an apple ID.  I've tried the solutions below but it's still not working:      I've also tried creating a bootable usb using transmac starting by making a GPT partition but it doesn't get discovered as a boot device.  iMac Late 2013
How can I recover from a "AMD-Action:downloadProduct:SP" during installation of macOS? Just wiped my hard drive on my MacBook Pro from 2013. Went to install a new copy of MacOS Sierra. I get the following error:  AMD-Action:downloadProduct:SP   I looked online and tried change the date using the Utility Terminal and the following command:  date mmddHHMMyy   Then did   csrutil enable csrutil clear   Then I tried clearing the NVRAM using command + option + P + R on startup.  Still no luck. Still getting the same error message. Apple support told me to go to a "computer repair store".  Any advice?
How to prove the inequality $2\sqrt{n + 1} − 2 \le 1 +\frac 1 {\sqrt 2}+\frac 1 {\sqrt 3}+ \dots +\frac 1 {\sqrt n} \le 2\sqrt n − 1$? Prove that for any positive integer $n$, $$2\sqrt{n + 1} − 2 \le 1 +\frac 1 {\sqrt 2}+\frac 1 {\sqrt 3}+ \dots +\frac 1 {\sqrt n} \le 2\sqrt n − 1$$ Progress I think Riemann sum should be used for the middle term. I got the limit as $n\to \infty$ of the function inside using Riemann sum but what I cannot get are the lower and upper bound. How do I rename all folders and files to lowercase on Linux? Let $X$ be any distribution with defined mean, $\mu$, and standard deviation, $\sigma$.  The central limit theorem says that  $$ \sqrt{n}\frac{\bar{X} - \mu}{\sigma}  $$ converges in distribution to a standard normal distribution.  If we replace $\sigma$ by the sample standard deviation $S$, is there a theorem stating that  $$ \sqrt{n}\frac{\bar{X} - \mu}{S}  $$ converges in distribution to a t-distribution?  Since for large $n$ a t-distribution approaches a normal, the theorem, if it exists, may state that the limit is a standard normal distribution.  Hence, it would seem to me that t-distributions are not very useful - that they are useful only when $X$ is roughly a normal.  Is this the case?    If it is possible, would you indicate references that containing a proof of this CLT when $\sigma$ is replace by $S$?  Such a reference could preferably use measure theory concepts.  But anything would be great to me at this point. Show that no application $f: \mathbb{R}^2 \rightarrow \mathbb{R}$, of $C^k$ class, $k \geq 1$ can be injective How can I proof this:     Show that no application $f: \mathbb{R}^2 \rightarrow \mathbb{R}$, of $C^k$ class, $k \geq 1$ can be injective, i.e., there are $A,B \in \mathbb{R}^2$ such that $A \neq B$ and $f(A) = f(B)$ (Hint: show that given $(a,b) \in \mathbb{R}^2$ in every open neighbourhood of $(a,b)$ there are points $(c,d),(c_1,d_1)$ where ${\partial}_1f(c,d) \neq 0$ or ${\partial}_1f(c_1,d_1) \neq 0$).   The problem is that I have no idea how to use the hint.  Thanks for all your comments. I'd like to "add to" an existing command by writing something like  \renewcommand{\somecommand}{\begin{something}\somecommand\end{something}}   but (not surprisingly) I get errors about being "too deeply nested".  Is there a way to take an existing command, add to it (by appending or prepending additional commands or text), and then have that "augmented" command replace the existing command? Intuitive Bernoulli numbers Sort order issue I'm having an issue sorting data in ascending order.   Right now the sort order is: 1.0.0  10.0.0 10.0.1 11.0.0 2.0.0 2.0.1 3.0.0 3.0.1 3.1.0  What I want is: 1.0.0 2.0.0 2.0.1 3.0.0 3.0.1 3.1.0 10.0.0 10.0.1 11.0.0  How can I achieve this? The datatype can't be number or currency because of the 2 decimals, so I used text-field. How to `bundle install` when your Gemfile requires an older version of bundler? Can't move/snap Nautilus window to occupy left or right half of the 1366x768 screen - is it just me? How does carbon dioxide or water vapour absorb thermal infra red radiation from the sun? We are all told at school water vapour and carbon dioxide are the top two greenhouse gases, and that they absorb thermal infra red radiation, trap heat and warm up the Earth. My question is how do they do that? Why can't Oxygen or Nitrogen or any other gas not absorb infra red radiation as well as water vapour or CO2? Find all $x$ such that $$x^6=(x+1)^6.$$   So far, I have found the real solution $x= -\frac{1}{2}$, and the complex solution $x = -\sqrt[3]{-1}$.  Are there more, and if so what/how would be the most efficient find all the solutions to this problem? I am struggling to find the rest of the solutions. When updating, I get the following error message:   W: The repository 'http://ppa.launchpad.net/mc3man/trusty-media/ubuntu xenial Release' does not have a Release file.   Here, I find another statement on this error:   This recommends removing certain PPAs; and, I'm not sure if I should do that since it might mean not getting the updates that I need.    Is this what I should do? Currently questions are added in a rapid pace to SO, so that new questions disappear very quickly from the homepage. It I want to see questions from my areas of interest I can do either:   Go to the tagged/my tags page, but then I will see the questions only according to the votes Supply a list of tags "x or y or z", but it seems the list is limited to 15 or 20 tags.   What I suggest is to have categories as grouping of tags - the .net category , java category , web development category , etc. It can also help new users to locate questions from their area of expertise they can answer. We can decide that a category can contain between 5 and 20  tags in order no to have too narrow or too broad categories (numbers were given just for the sake of argument) Avoid synchronized(this) in Java? Whenever a question pops up on SO about Java synchronization, some people are very eager to point out that synchronized(this) should be avoided. Instead, they claim, a lock on a private reference is to be preferred.  Some of the given reasons are:    (very popular this one, also has an "accidentally" variant)     Other people, including me, argue that synchronized(this) is an idiom that is used a lot (also in Java libraries), is safe and well understood. It should not be avoided because you have a bug and you don't have a clue of what is going on in your multithreaded program. In other words: if it is applicable, then use it.  I am interested in seeing some real-world examples (no foobar stuff) where avoiding a lock on this is preferable when synchronized(this) would also do the job.  Therefore: should you always avoid synchronized(this) and replace it with a lock on a private reference?      Some further info (updated as answers are given):   we are talking about instance synchronization both implicit (synchronized methods) and explicit form of synchronized(this) are considered if you quote Bloch or other authorities on the subject, don't leave out the parts you don't like (e.g. Effective Java, item on Thread Safety: Typically it is the lock on the instance itself, but there are exceptions.) if you need granularity in your locking other than synchronized(this) provides, then synchronized(this) is not applicable so that's not the issue Proving that, $|f'(x)-f'(y)|\le k|x-y| \implies (f'(x))^2< 2 kf(x) $ Let $f:\Bbb R\to (0,\infty)$ be a differentiable function such that for some constant $k$ we have, $$|f'(x)-f'(y)|\le k|x-y|$$   for all $x,y \in\Bbb R.$ Then prove that, $$(f'(x))^2&lt;2 kf(x).$$   Due to lack of arguments I could not proof this inequality. But rather I proved that is true for the particular function,   $$f(x) =\cos^2(x)+1\implies f'(x) = -\sin(2x).$$ And we readily have,$$|\sin(2x)-\sin(2y)| = \left|\int_{2x}^{2y}\cos t dt\right|\le 2|x-y|$$ as well   $$(f'(x))^2 = 4 \sin^2 x\cos^2x &lt; 4(\cos^2x +1) = 4f(x).$$  It is also true for the function $x\mapsto \sin^2x +1.$   From these example I don't see how to prove the general case. Any hint will be welcome. I read  and thought that would easily be solved (not that it isn't solvable without) if one could write:   @Override public String toString() {     return super.super.toString(); }   I'm not sure if it is useful in many cases, but I wonder why it isn't and if something like this exists in other languages.  What do you guys think?  EDIT: To clarify: yes I know, that's impossible in Java and I don't really miss it. This is nothing I expected to work and was surprised getting a compiler error. I just had the idea and like to discuss it. Key Derivation Functions vs. Password Hashing Schemes Key derivation functions, such as HKDF (standardized in ), are meant to stretch some initial keying material having enough entropy, like a Diffie-Hellman shared value, into one or more strong cryptographic secret keys.   Password-hashing schemes, such as the  winner , are meant to hash usually low-entropy passwords with the goal of making the hash digest inversion as costly as possible for an adversary with respect to CPU and memory consumption, as well as parallelization.  Is it exact to consider that password-hashing schemes are actually key derivation functions specialized for low-entropy inputs? Or is there any other essential difference of theoretical nature between these two types of cryptographic schemes? I want to better understand why the construction something + [adjective] makes grammatical sense. Background: I was recently reading a Washington Post article and came across the following sentence.  So if you fall in that category, [the movie] feels more like magic than repetitive.  (Note: I've copied the relevant spoiler-free sentence above; following the link to the article will open you up to movie spoilers! ) The phrase more like magic than repetitive struck me as odd, presumably because it was non-parallel (more like [noun] than [adjective]). I would have expected &quot;...more like magic than something repetitive.&quot; (Actually, that needs to be rewritten to flow better, but the point is that at least it appears to be grammatical.) Thus, one would have the noun phrase &quot;something repetitive,&quot; of the form &quot;[noun] [adjective].&quot; This got me to thinking about the use of adjectives after nouns. There is a great Stack Exchange article  that involves the characteristics of the adjective that indicate it should come after the noun. But I haven't been able to find examples of how the word &quot;something&quot; requires a postponed adjective. Consider the following sentences:  I want to buy something red. I am looking for something sweet to eat.  You cannot say:  *I want to buy red something. *I am looking for sweet something to eat.  But you can say:  I want to buy something (that is) red. I am looking for something (that is) sweet to eat.  So, my question:  Do the above examples mean that the &quot;something [adjective]&quot; construction is an example of the ellipsis of &quot;that is&quot;?  Is there something special about the word &quot;something&quot; that requires the postponed adjective? Note that I am NOT looking for details about adjectives that are postponed; I'm interested in the word that precedes the adjective (either &quot;something&quot; or similar words).   By the way, I am not interested in the following constructions, which are different:  I want to paint the house red. I tried to build the brick house taller.  Thanks in advance! Why do wet objects become darker? How to grep a specific line _and_ the first line of a file?