Every time I plug my iPhone into one of my computers to charge it, it prompts me to trust or don't trust. How do I force it to remember he don't trust setting? I don't want this specific computer to ever be trusted, and I don't want it to ask me every time.  All searches I've found relate to how to reset the warning dialog in case you've chosen the wrong option by mistake.  It's running iOS 10.3.3
I have a 2015 MBP for work, which I connect my iPhone (6 plus, iOS 10) to charge, and I don't want to trust the computer, ever. However, I must click "Don't Trust" every single time I connect for charging. This is asymmetric to the "Trust" selection, which remembers my decision.  Does anyone know if it's possible to stop the 'Trust/Don't Trust' modal from appearing every time, and have the machine not be trusted?  If possible, can you please tell me how? If not possible, can you please provide proof or evidence that lead you to this conclusion?  Finally, I am not concerned with arguments or opinions about this feature. Only what is outline above.
Compactness of $\operatorname{Spec}(A)$ In an exercise in Atiyah-Macdonald it asks to prove that the prime spectrum $\operatorname{Spec}(A)$ of a commutative ring $A$ as a topological space $X$ (with the Zariski Topology) is compact.   Now because the basic open sets $X_f = \{\mathfrak{p} \in \operatorname{Spec} (A) : \{f\} \not\subseteq \mathfrak{p} \}$ form a basis for the Zariski Topology it suffices to consider the case when   $$X = \bigcup_{i \in I} X_{f_i}$$   where $I$ is some index set. Then taking the complement on both sides we get that   $$\emptyset = \bigcap_{i \in I} X_{f_i}^c$$  so there is no prime ideal $\mathfrak{p}$ of $A$ such that all the $f_i$'s are in $\mathfrak{p}$. Now from here I am able to show that the ideal generated by the $f_i$'s is the whole ring as follows. Since there is no prime ideal $\mathfrak{p}$ such that all the $f_i \in \mathfrak{p}$, it is clear that there is no $\mathfrak{p}$ such that $(f_i) \subseteq \mathfrak{p}$ for all $i \in I.$ Taking a sum over all the $i$ then gives $$\sum_{i \in I} (f_i) = (1).$$  Now here's the problem:          How do I show from here that there is an equation of the form $1 = \sum_{i \in J} f_ig_i,$ where $g_i \in A$ and $J$ some finite subset of $I$?       This part has been giving me a headache. I am not sure if the finiteness bit has to do with algebra, topology or the fact that we are dealing with prime ideals.  This is not a homework problem but rather for self-study.  $\textbf{Edit:}$ I have posted my answer below after the discussion with Dylan and Pierre. Why does turning Caps Lock off take such a long time to work? This is my biggest issue with Linux and the main reason I don't use it as my main working OS.  Whenever I use caps lock to write something in upper case and disable it in order to keep writing the next letter AFTER I've disabled it is written in upper case.  So, my text comes out weird, as SOMETHING *L*ike this  I've tried Linux Mint, Fedora ... and the issue keeps happening.  Searching Google I've found some very rare persons have the same issue, but I was unable to find any solution.  Is there any way to solve this or am I DOOMED *F*or life?  BTW, whenever I ask this question someone suggest I should learn to use shift, instead of caps lock. I know, that's the right way, but I'm used to use caps lock and, well, it should work. How to convert coordinates from vertex to world-space? How do I convert from object-space to world-space?  I suspect it is:  vert_os = obj.vertices[foo] vert_ws = vert_os.getPositionFromMatrix(obj.matrixWorld)   but does the matrix also handle translations, or do I need to handle that separately?  Can someone link to the relevant documentation? How to calculate the limit of $\frac{a_n}{n^2}$ for the sequence $a_{n+1}=a_n+\frac{2 a_{n-1}}{n+1}$? Assume $\{a_n\}$is a sequence which  satisfies the following recursion formula: $$a_{n+1}=a_n+\frac{2a_{n-1}}{n+1}~(n\geqslant 1).$$ and $a_0=\pi,a_1=\pi^2 $. How to compute $\displaystyle\lim_{n\to \infty}\frac{a_n}{n^2}$? I am in the process of completing some homework and have come across a question that says: "What is the steady-state current?" It is asking in reference to a circuit that includes two capacitors in parrallel and a DC source of 24V and an AC source given by $\epsilon = 20 \cos(120 \pi t)\ \text{V}$, where $t$ is in seconds. I assume that it is asking when the current is constant. Because naturally the current is not constant due to the AC source, would I just consider the DC source for this? Restart my graphics card without rebooting? Questions on "All Horse are the Same Color" Proof by Complete Induction Desktop shows a white or black background instead of wallpapers I hope it is alright to ask something like this here, I am having trouble keeping up with all the special cases and my book is being kind of vague.  I know how to do the standard method of finding diagonal matrices, but I know that triangular matrices are special and my book makes a connection, but it is hard to tell what it is.  Thanks. android expandablelistview how to set space between groups items What does 'synchronized' mean? Integrating radial free fall in Newtonian gravity How can I specify a long list of math operators? The preambles of my LaTeX documents often include many many lines of \DeclareMathOperator instructions, e.g.  \DeclareMathOperator{\Rep}{Rep} \DeclareMathOperator{\Tet}{Tet} \DeclareMathOperator{\Maps}{Maps} \DeclareMathOperator{\Diff}{Diff}   Is there a nice way to map some macro over a list, so I could do this more concisely, and with less copying and pasting when I add a new math operator? Deployed web parts don't show up in Web Part Gallery Grammatical number agreement in a complex phrase using singular "they" another question, I used the following phrase:     Your reader is [...], but they are a busy person.   I have two difficulties here:   In the first phrase, a reader, being singular noun, certainly implies is; In the second phrase, they, being a plural pronoun (regardless that it refers a single person), still requires are, but are implies the plural for busy persons which sounds awkward (a reader &lrarr; persons);   Obviously, if I used "...but he is a busy person", everything works fine, but I'm trying to use a gender-agnostic form.  What is the proper number agreement here? How to format a disk/sdcard as FAT32 in windows 10 Is it possible to to take a screenshot of a webpage with JavaScript and then submit that back to the server?  I'm not so concerned with browser security issues. etc. as the implementation would be for . But is it possible? This is about a step in a derivation of the expression for the relativistic Doppler effect.  Consider a source receding from an observer at a velocity $v$ along the line joining the two. Light is emitted at frequency $f_s$ and wavelength $\lambda_s$. The frequency $f_0$ and wavelength $\lambda_0$ received by the observer will be different.  Some textbooks now argue that the wavelength received by the observer is given by $\lambda_0=(c+u)T_0$, where $T_0$ is the time period of the wave in the observers frame. The argument given is that the successive "crests" will be an extra distance $uT_0$ apart due to movement of the source. Upon relativistically transforming the time period in the source frame to the observer frame, the correct result $f_0=f_s\sqrt{\frac{c-u}{c+u}}$ is obtained.  But the argument for the wavelength seems reminiscent of the classical Doppler effect for sound. Is it really applicable here through this argument? And is there a way to show the same result for $\lambda_0$ mathematically? Organize uploads by year, month and day How to stack three relations