X/Ubuntu 20.10 on Asus ROG Strix G17 has no sound
No sound ALC294 Asus ROG Strix 512 Ubuntu 20.04.01
Fields - Proof that every multiple of zero equals zero This is one of my first proofs about fields. Please feed back and criticise in every way (including style and details).  Let $(F, +, \cdot)$ be a field. Non-trivially, $\textit{associativity}$ implies that any parentheses are meaningless. Therefore, we will not use parentheses. Therefore, we will not use $\textit{associativity}$ explicitly.  By $\textit{identity element}$, $F \ne \emptyset$. Now, let $a \in F$. It remains to prove that $0a = 0$. \begin{equation*} \begin{split} 0a &amp;=  0a +  0      &amp;&amp; \quad \text{by }\textit{identity element }(+    ) \\    &amp;=  0a +  a + -a &amp;&amp; \quad \text{by }\textit{inverse element  }(+    ) \\    &amp;=  0a + 1a + -a &amp;&amp; \quad \text{by }\textit{identity element }(\cdot) \\    &amp;= (0 + 1)a + -a &amp;&amp; \quad \text{by }\textit{distributivity   }        \\    &amp;= (1 + 0)a + -a &amp;&amp; \quad \text{by }\textit{commutativity    }(+    ) \\    &amp;=      1 a + -a &amp;&amp; \quad \text{by }\textit{identity element }(+    ) \\    &amp;=        a + -a &amp;&amp; \quad \text{by }\textit{identity element }(\cdot) \\    &amp;=  0            &amp;&amp; \quad \text{by }\textit{inverse element  }(+    ) \end{split} \end{equation*} QED  PS: Is "Let $(F, +, \cdot)$ be a field." ok? Besides, I would not want to call $F$ a field, because $F$ is just a set. Also, what do you think about using adverbs like "Now"? How would you have said the associativity-thing? I'd like to know your opinion on citations in abstracts. At my university, there is no rule on that matter so it's basically a question of preference.  Do you think it's okay to have citations in an abstract or do you  personally prefer to have the abstract be a ``stand-alone'' piece of  work? How to Set Firefox 4 to only store History for a set period of time, i.e. one day? I want to setup Firefox 4 to only store my history for 1 day (or some other set period of time), but I can't seem to find an option to do that in the options dialog, all I can see is "Remember History", "Never Remember History" and "Custom History Settings". "Custom History Settings" only lets me select what to keep, not for how long.  Is there anyway I can do this? What graduation gown should a PhD-holder wear when later receiving a Master's in another field? Looking for the name of a card-battle cartoon show Looking for a show about a group of three kids/teens who, using cards to change into monsters, fight and recover relics. I believe there are two or three other groups of three also trying to get the relics.  In the main group there are two boys and a girl. The boys were both white, one is from a farm and I don't know where the other is from. The girl was dark skinned and either black or blue hair. The three travelled around the world using a red plane.  I think they only use one monster primarily. The girl uses a monster created from gas and at one point is green. One of the boys uses a metal robot most of the time and at one point is given another better version of that card to use. I believe the episode for this was called something like green with envy.  All I'm getting from the internet is that it may be Chaotic, but that isn't the right show.  I also believe the girl's name was Mai and one of the boys were Ky, but I may be wrong. Using Apple Script to Manage Sound Output Selection I am brand new here and I have an additional clarification or need additional help for an issue from this thread -   In my preference pane, in addition to Headphones and Digital out, I also have 2 apple monitors and would like the option of selecting one of them as out put (namely the first one in the list).   Basically I need help with adjust his solution to be able to select the third row or first monitor as sound output.  Or a way to accomplish this without knowing how to edit AppleScript for a different setup. Subquery in SQL Server Compact Edition When does function composition commute? I've read that function composition "generally does not commute."  Not counting compositions involving the identity function, and compositions of a function and its inverse, are there examples of functions on the reals (for example) $f, g$ where $fg = gf$ outside of these cases? I'll be generous and say it might be reasonable to assume that nature would tend to minimize, or maybe even maximize, the integral over time of $T-V$.  Okay, fine.  You write down the action functional, require that it be a minimum (or maximum), and arrive at the Euler-Lagrange equations.  Great.  But now you want these Euler-Lagrange equations to not just be derivable from the Principle of Least Action, but you want it to be equivalent to the Principle of Least Action.  After thinking about it for awhile, you realize that this implies that the Principle of Least Action isn't really the Principle of Least Action at all:  it's the "Principle of Stationary Action".  Maybe this is just me, but as generous as I may be, I will not grant you that it is "natural" to assume that nature tends to choose the path that is stationary point of the action functional.  Not to mention, it isn't even obvious that there is such a path, or if there is one, that it is unique.  But the problems don't stop there.  Even if you grant the "Principle of Stationary Action" as fundamentally and universally true, you realize that not all the equations of motions that you would like to have are derivable from this if you restrict yourself to a Lagrangian of the form $T-V$.  As far as I can tell, from here it's a matter of playing around until you get a Lagrangian that produces the equations of motion you want.  From my (perhaps naive point of view), there is nothing at all particularly natural (although I will admit, it is quite useful) about the formulation of classical mechanics this way.  Of course, this wouldn't be such a big deal if these classical ideas stayed with the classical physics, but these ideas are absolutely fundamental to how we think about things as modern as quantum field theory.  Could someone please convince me that there is something natural about the choice of the Lagrangian formulation of classical mechanics (I don't mean in comparison with the Hamiltonian formulation; I mean period), and in fact, that it is so natural that we would not even dare abandon these ideas? In the Final Battle, when you remove doom tokens for rolling successes against an Ancient One do you stop counting successes for that roll? In Arkham Horror you have to roll a cumulative number of successes equal to the number of players to knock off a doom token from the Elder God's health. If you reach the number of players worth of successes do you then stop counting for the player and move on or do you count the extra successes against the next doom token?  We played it so that you kept on adding them but it meant that we turned Nyalothotep into mince meat quite quickly (One Character was blessed had a fight of 6 a shotgun and Fight +1 skill card though) How can I verify the following statement?     The image of a morphism $f : A \longrightarrow B$ is defined as $\text{Im}(f) = \text{Ke}r(\text{coke}r f)$ whenever it exists (e.g., in every abelian category). The morphism $f : A \longrightarrow B$ factors   uniquely through $\text{Im} f \longrightarrow B$ whenever $\text{Im} f$ exists, and $A \longrightarrow \text{Im} f$ is an epimorphism and a cokernel of ker $f \longrightarrow A$ in every abelian category. the structure "like for somebody to do something" Prove that $\omega + \omega_1 = \omega \cdot \omega_1 = \omega^{\omega_1} = \omega_1$ I am assuming already that a) the union of countably many countable sets is countable and  b) $\omega_1$ is the least uncountable ordinal, so $x &lt; \omega_1$ if and only if $x$ is a countable ordinal.   I'm not sure if it is relevant but this question also allows The Axiom of Choice.   Thanks I had created the xml document with xml version="1.0".  In that document I need to use the greater than symbol &gt; and less than symbol &lt;.  How should I include those symbols? It's not working.  &amp;gt; and &amp;lt; are not working for me.  Is there any special encoder for this? MySQL cartesian product between two SELECT statements How Do I Allow A Standard User to Install Programs? How do I install an individual package on a Linux system? I need to install a new TeX/LaTeX/ConTeXt package on my computer.  I'm running Ubuntu/Fedora/Slackware/Some-Version-Of Linux.  What are the possible ways to do this?    Note:&nbsp;&nbsp; We get a number of questions that essentially reduce to this one; it was felt a good idea to have one question-and-answer that can cover all the standard methods.  See  for the discussion.  The question-and-answer are CW so that more information can be easily added.  If you have information to add, please do so.  If you are unsure, leave a comment here or (preferably) in .  Comments on the question and answer will be periodically removed to ensure that the information is clear. Allow converting comments to answers Allow converting comments to answers, so they can become accepted answers.  I asked a question. Someone commented on it, and it was an awesome comment that fully answered the question. As the original questioner, I would like to convert that comment to an answer in order to accept it.  Or, if you prefer, I would be okay with being able to simply mark the comment as accepted. How do I find packages to install via apt-get What is the meaning of this senctence:Excellent answer. Delusions of grandeur. Folks have been institutionalised for less Can an atheist at least agree that existence is a mystery that is bigger than all of us?                                                       You’ve got it backwards. It’s religious people who try to fill the mysteries of the universe with beliefs based on nothing emprical. Where atheists say “I don’t know” religious people say “It’s God.” Atheists are comfortable with not knowing everything. They know humans are infinitesimal specks in the universe. Religious people think the entire universe was created for and about them. Talk about grandiosity. Comment:Delusions of grandeur. Folks have been institutionalised for less lol