pip got corrupted after uninstalling python packages
pip: AttributeError: 'module' object has no attribute 'SSL_ST_INIT'
I changed permissions of a file (chmod g+w testfile) and running ls -l testfile gives:  -rwxrwxr-x 1 user1 user1 0 2011-01-24 20:36 testfile   I then added a user to that group ("/etc/group" has user1:x:1000:user2 line), but am failing to edit that file as user2. Why is this so? The square roots of different primes are linearly independent over the field of rationals I need to find a way of proving that the square roots of a finite set    of different primes are linearly independent over the field of    rationals.    I've tried to solve the problem using elementary algebra  and also using the theory of field extensions, without success. To  prove linear independence of two primes is easy but then my problems  arise. I would be very thankful for an answer to this question. I am considering purchasing a Mac for my godson who will be using it to run Blender 2.8.  I know very little about this program.  All I can find are requirements for a Mac that will run earlier versions of Blender.  Would someone please recommend a list of requirements for a Mac (or a link to a list of requirements) that I could use to find a model that can run 2.8?  Thank you in advance for all your help! Sincerely, M. Lap Why does subsurf modifier cause weird deformation at the end of a cylinder? My problem is simple. I think that the strange deformations on the top are there because there are so many vertices in one face. How do I fix this while maintaining nice topology?  Although I triangulated the top polygon, the problem still persists. I usually use "at a company" but I have encountered some articles using "in a company", "in XYZ firm" or "in an organization".  Which one is right? How to ignore everything in the document environment? What are weapon damage dice? Following discussion , what constitutes a weapon damage die?  Is it any damage die dealt by the weapon? For example, consider a  longsword.     While the sword is ablaze, it deals an extra 2d6 fire damage to any target it hits.   What are the weapon damage dice? Just the 1d8 from the longsword? Or do the 2d6 Fire damage also count? What is the difference between Gödel's completeness and incompleteness theorems? How do I convert old Pages documents to Pages '13? I have a document I created with an old Pages version. When I try to open it in Pages '13, I get the message :     This document is too old. Please open and save with Pages '09   I don't have Pages '09 and I don't know where that old version of Pages is and if it will run on Mac OS 10.9.   Is there an easy way to convert the document? If there is no easy way, is there a way to at least extract the text from the document? Show that $\lim_{n\to\infty} \sqrt[n]{a^{n} + b^{n}} = \max(a, b)$ Prove that:  $$\lim_{n\to\infty} \sqrt[n]{a^{n} + b^{n}} = \max(a, b)$$  I don't have a clue even how to start the proof here. Any hint is appreciated! Visiting the US after overstaying as a minor 13 years ago? Is it OK to borrow a ground wire from a different circuit? I've got a circuit in the basement carrying a handful of outlets.  This circuit has no ground wire.  I want to add a couple of outlets and want them to be grounded.  I may even want gfci outlets on them in the future.  I have no reasonable way of getting a ground wire to the panel but I do have easy access to another circuit that does have a ground wire.  Is it acceptable to borrow or share a ground wire between circuits?  If not, why not?  Both circuits are 20A with 12 AWG wire. I have Ubuntu 16.04 with GNOME shell. I set ctrl+shift for the "Modifiers-only switch to next source" option.   This shortcut conflicts with apps hot-keys. I can't use ctrl+shift+i to open devtools in Chrome, it just switches the layout. In VS code IDE if I press shortcuts with ctrl+shift (for example ctrl+shift+f), shortcuts work but always switch a keyboard layout. When I used Windows this problem didn't exist.  Can I set the ctrl+shift shortcut in such a way that it causes a switch action only after the keys are released and only if this 2 keys were pressed (without additional keys)? Contour integral of $\sqrt{z^2-1}$ on $|z| = 2$ I've been wrestling with this problem (available  ):  Evaluate the integral of $f(z) = \sqrt{z^2-1}$ around the circle $\{z: |z| = 2\}$, where the branch of the square root function is chosen so that $\sqrt{2^2-1} &gt; 0$.  I came up with the answer $$\int\limits_{|z| = 2} \sqrt{z^2-1} dz = \pi i$$ using the following argument, which seems a little like voodoo to me.  You notice that there are two points, at $z \pm 1$, where you might have to pick a branch of $log()$ to define the square root. Then, I convinced myself that as long as you exclude from your domain the real interval $-1 \le x \le 1$, the function $f(z)$ can be continuously defined (maybe the two branches somehow cancel?), and so is analytic on its domain.  Therefore you can shrink the contour of integration continuously using the Cauchy Closed Curve Integral Theorem, so that you wind up reducing it to the real integral $$2\int_{-1}^1 \sqrt{x^2-1} dx = \pi i$$  I'm not really sure the answer is correct, and I'm even less certain about the way I got it. I had a hard time convincing myself that $\sqrt{z^2-1}$ was not multi-valued on the domain. To try to get at that I tried $\sqrt{z^2-1} = \sqrt{z+1} \sqrt{z-1}$ and reasoned that the product makes the discontinuity disappear, using $$e^{\frac{\pi}{2}i}\cdot e^{\frac{\pi}{2}i} = -1 = e^{-\frac{\pi}{2}i}\cdot e^{-\frac{\pi}{2}i} $$ for the different branches of $log()$ you can choose.  I'd appreciate any input that would help me get a a better way to look at this.  Thanks!    EDIT  An attempt to use the Residue at infinity:  By substituting $z = 1/w$ you get \begin{eqnarray} \int\limits_{|z| = 2} \sqrt{z^2-1} dz &amp;=&amp; \int\limits_{|w| = 1/2} \frac{1}{w^2}\sqrt{\frac{1}{w^2}-1} dw \\ &amp;=&amp; \int\limits_{|w| = 1/2} \frac{1}{w^2}\sqrt{\frac{1-w^2}{w^2}} dw \\ &amp;=&amp; \int\limits_{|w| = 1/2} \frac{1}{w^3}\sqrt{1-w^2} dw \end{eqnarray} The integrand is analytic in $|w| \le 1/2$ except at $w = 0$, so we can apply the Residue Theorem. Near $w = 0$, $\sqrt{1-w^2} = 1 - \frac{1}{2}w^2 + \dots$, so the residue of $\frac{1}{w^3}\sqrt{1-w^2} $ at $w = 0$ is $-\frac{1}{2}$. Then the integral is $$\int\limits_{|z| = 2} \sqrt{z^2-1} dz = 2\pi i \cdot (-1/2) = -\pi i$$ Some of you might insist that it was not a murder, as we know that a rebounding spell had hit Ariana, as shown in .  However, a death in such a well known family would not go uninvestigated, I presume. Were the Dumbledore brothers investigated? How did they get away with their sister suddenly dropping dead?  I'd think that Ministry of Magic has means to recognize a death caused by magical means. That's how we know that Tom Riddle Snr. was killed by Avada Kedavra. So Ariana's failing health might be a poor excuse. How to store and preserve lots of data? I have many DVDs with movies and games, they are getting old and dusty, some of them are damaged. And I have more than 300 GB of general files in my PC. I want to store and preserve all of my data and keep them for a long long time.  I want to know what is the best and more reliable storage media that I should use and... I can buy. I will copy all of my DVDs to a new media and throw all of my DVDs away. It will take a very smaller physical space.  I think that everything that I need to store is currently 800 GB.  I do not like optical discs, because they are fragile and I have lost many CDs and DVDs. Hard drives would be good, but they can suddenly stop working, and it is very expensive to recover data from a broken hard drive.  Other questions: How often will I have to copy the files to a new storage media? Is it good idea to have another copy of each file stored in another storage media?  Edit: If I put all of the movies and games in a HDD, if the HDD stops working, I will lose everything. This is how valuable they are for me: If I lose 10% of them, I will not cry, because I can get new ones, but if I lose 90%, it will be a disaster.  Edit 2: I do not think that that online storage is reliable even if I pay for it, because they may be closed or may get bankrupt. They are not from my country and it would be difficult to get the files back. I want to prove  \begin{equation*} \tan A  + \tan B + \tan C = \tan A\tan B\tan C \quad\text{when } A+B+C = 180^\circ \end{equation*}  We know that   \begin{equation*} \tan(A+B) = \frac{\tan A+\tan B}{1-\tan A\tan B}~\text{and that}~A+B = 180^\circ-C. \end{equation*}  Therefore $\tan(A+B) = -\tan C.$ From here, I get stuck. Please help. What happens when I connect a 2 amp charger instead of the 0.7 amp charger provided? Possible Duplicate:             I have a phone with 0.7 amp charger. I also have a Galaxy Nexus with a 2 amp charger.  If I connect the 2 amp charger into my phone, will my phone blow up? How does this wiring work? I have a Trane XV90 and XL 14i. The wiring looks a little strange as in the picture bellow.                    _____________                   |           |   BK W2  W1   R  G  Y  B/C  YLO O     |___||   |__|  ||   |          |   |     ||   |_____>|----------|         |   |     ||_________>|other wire|         |   |     |           ------------         V   V     V     ---------------     |thermostat   |     ---------------  The R and G are jumpered together and the G wire is connected on the board  but is actually not connecting to the thermostat on the other end. So people told me that means the furnace fan is always on! (In my diagram above, I switched the location of Y and B/C to make diagram easier to draw. You can refer to the photo added below to see the details) My questions are the following  is the jumper between O and Y doing anything? I don't think I have heat pump I need to install Honeywell wifi thermostat and I am thinking of doing either one of the following:   remove jumper between R and G, and use G to connect B/C and then to thermostat C and put jumper between G and Y  leave jumper between R and G, and use G to connect B/C and then to thermostat C and put jumper between G and Y  remove jumper between R and G, connect G on control board to thermostat G, and finally have the spare wire to connect B/C and then thermostat C  leave jumper between R and G, does not connect G to thermostat,  and just use a spare wire to connect B/C on board to thermostat C   Can anyone comment on those plans? Thanks a lot! Is it possible to interrupt spellcasting? As  suggests, there seems to be a hole in the D&amp;D Basic rules.  Maybe.  The rules for readying an action state:     When the trigger occurs, you can either take your reaction right after the trigger finishes or ignore the trigger.   This seems to imply that it is impossible to interrupt a spell in 5e.  If you set your trigger to be "I attack the Wizard when he casts a spell", then you make the attack after the spell has been cast.  Does this mean that spells can no longer be interrupted in combat like they could be in previous editions?