"sudo start mysql" results in an error
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The exercise is: Prove that $-(-v)=v$ for every $v \in V$  Proof Suppose  $v \in V$ and $V$ is a vector space. Then $-(-v) \in V$ as result of the scalar multiplication property and $-(-v)=-(-1\cdot v)=-1 \cdot(-1\cdot v) =(-1 \cdot-1)\cdot v = 1 \cdot v = v $ The desired result $-(-v)=v$ holds.  The solution manual gives the proof:  Proof   I just wanted to make sure that the way I did the proof isn't missing anything?Thanks Difference between "I have got" and "I have gotten" Last semester I picked up an algebra course at my university, which unfortunately was scheduled during my exams of my major (I'm a computer science major). So I had to self study the material, however, the self written syllabus was not self study friendly (good syllabus overall though).  The course was split up into 3 parts, group theory, ring theory and field theory. As a computer science major we only had to study the first 2.  Now that I passed the exam for this course I want to study the field theory part ( which covers Galois theory, etc).  So, now I want to ask whether any of you know any good books on abstract algebra, which lift off at basic ring theory and continue to more advanced ring theory and to finite fields, Galois theory, ...  Please keep in mind that I am not a math major, and that I would like books which are suited for self study (thus a lot of examples and intuition).  Thanks in advance! How can I get around giving my mobile phone number to Google? What are the pros and cons of adding a vapor barrier behind shower backer board? How to install TeX on Android phones? I used  app in my Android phone. But this app does not support XeLaTeX and requires an internet connection to be used.  Is there any distribution of TeX for Android? How I can install TeX on my Android phone? link new object to scene with python in 2.8 In Python 2.8, I would like to create copies of the object 'CubeTemplate' but am having no luck.  I have reviewed every blender.stackexchange post on this subject (, ,  and ) but cannot get them to work - either they don't apply or the sample code throws errors (perhaps because it was pre 2.8).  The code below throws this error:       AttributeError: 'bpy_prop_collection' object has no attribute 'link'   for x in range(1, 3):     bpy.data.objects['CubeTemplate'].select_set(True)     bpy.context.view_layer.objects.active = bpy.data.objects['CubeTemplate']     me = bpy.context.object.data # use current object's data     me_copy = me.copy()     ob = bpy.data.objects.new('CubeCopy'+str(x), me_copy)     ob.location = (0, 0, x)     scene = bpy.context.scene     scene.objects.link(ob)     scene.update() How can I bind arguments to a Python method to store a nullary functor for later invocation?  Similar to C++'s boost::bind.  For example:  def add(x, y):     return x + y  add_5 = magic_function(add, 5) assert add_5(3) == 8 Is there an app that will notify me (in notifications center) if a process is using up a high percentage of CPU for a specified amount of time? The other day, I was sitting in a coffee shop working, when I looked down to find that 25% of my battery was left.   I looked at my Activity Monitor and saw that the time machine process was going at 90% for a while (as long as I was watching it).   Are there any apps that can notify me if a process is at a certain level for a certain amount of time? What does the function f: x ↦ y mean? I am doing , and am having a few problems with function notation. I understand the form f(x).  What does the form f: x ↦ y mean? Could you also give one or two examples?  And, if possible, state your source. Thank you. How to do joins in LINQ on multiple fields in single join I need to do a LINQ2DataSet query that does a join on more than one field (as  var result = from x in entity join y in entity2         on x.field1 = y.field1  and            x.field2 = y.field2   I have yet found a suitable solution (I can add the extra constraints to a where clause, but this is far from a suitable solution, or use  solution, but that assumes an equijoin).  Is it possible in LINQ to join on multiple fields in a single join?  EDIT  var result = from x in entity              join y in entity2              on new { x.field1, x.field2 } equals new { y.field1, y.field2 }   is the solution I referenced as assuming an equijoin above.  Further EDIT  To answer criticism that my original example was an equijoin, I do acknowledge that, My current requirement is for an equijoin and I have already employed the solution I referenced above.  I am, however, trying to understand what possibilities and best practices I have / should employ with LINQ. I am going to need to do a Date range query join with a table ID soon, and was just pre-empting that issue, It looks like I shall have to add the date range in the where clause.  Thanks, as always, for all suggestions and comments given Lost passport with Schengen visa VirtualBox 5.0.40 crashes the whole host since update to kernel 4.13.0-26-generic How to flag a typo question I came across  today. In reading the answer and the comments it turns out that the issue was just a simple typo that the OP made. So that being the case I decided that this question probably needs to be closed since this will not be helpful to any future vistors. However, in looking at the flag reasons (I don't have the close ability yet), I don't see a flag that would be appropriate.   I know some of these options might still be influx because of the . However, until a different off-topic flag description is created, how should this be flagged? Or should this not be flagged at all and just allowed to live on or wait for a user with close votes to use a custom off-topic close option? n tasks assigned to n computers, what is the EX value of a computer getting 5 or more tasks? Say a central server assigns each of n tasks uniformly and independently at random to n computers connected to it on a network. Say a computer is ‘overloaded’ if it receives 5 or more tasks.  Q: Calculate the expected number of overloaded computers.  I thought of doing [1 - Pr(a computer is not overloaded)] but that leads me to a complicated expression of: $$1 - PR(NotOver) = 1 - \sum_{i=0}^4  \left( \frac{1}{n} \right)^{i} { \left( \frac{n-1}{n} \right)}^{n-i}$$ multiplying this by n would(hopefully) give the Expected value. But the answer seems not very elegant atall, is there something I'm missing or an easier way to tackle this? Thanks! Exercise $1.8$ of chapter one in Hartshorne. Does a subsequent charm effect override a previous one? In a recent session, I was confused about how multiple charm effects would interact with each other:  A vampire used its 'Charm' ability to charm a PC. It reads (paraphrased):     The target must succeed on a saving throw or be charmed by the vampire. It takes the vampire's requests in the most favourable way it can. It can repeat the saving throw if the vampire or its companions harm it. Otherwise, the effect last 24 hours or until the vampire is destroyed, is on another plane of existence, or takes a bonus action to end the effect.   Another PC then decided to attempt to wrest control back from the vampire by casting crown of madness on their friend. it reads (paraphrased):     The creature must succeed on a saving throw or be charmed. The charmed target must use its action before moving on each of its turn to make a melee attack against a creature other than itself that you mentally choose. The target can act normally on its turn if you choose no creature, or none are within its reach.   At the time, I ruled that both effects would take place simultaneously. This meant that Crown of Madness took effect first, and the vampire's charm afterwards.  Was this the correct ruling? Can a creature be charmed twice? Or does one charm effect override the other? Is there to make the login screen appear on the external display in 18.04? Why aren't people voting for questions? Can a function be differentiable at the end points of its (closed interval) domain? Assume $f$ has a domain of $[a,b]$. Is it possible that $f$ is differentiable on the closed interval $[a,b]$, or must the maximal domain for $f'$ be $(a,b)$?