Which one of three styles is the most correct?
Analysis's output vs analysis output vs output of the analysis
Human vs. alien to avoid extinction by omnipotent being What is the difference between 'su -' , 'sudo bash' and 'sudo sh'? I would like to know what is the difference between    su - sudo bash sudo sh   I cannot login as root while doing su - because I do not have the root password - I mean I have my user password with which I can sudo "command"  but this password does not work for su - I can log in as root with sudo bash with my user password and I can login while doing sudo sh but then I get a command prompt in this form # Not every boolean function is constructed from $\wedge$ (and) and $\vee$ (or) Let $a,b,c\in \Bbb R^+$ such that $(1+a+b+c)(1+\frac{1}{a}+\frac{1}{b}+\frac{1}{c})=16$. Find $(a+b+c)$ Cardinality of a set that consists of all existing cardinalities I'm using an HP laptop running Windows 7 Home Edition.  The moment I reach the login screen the computer automatically types "ppppppppp" in the password place, luckily I have fingerprint login to counter that.  The moment I login, it keeps acting as if I'm typing 'p' repeatedly. I tried removing the button and cleaning under it but it was no use. I've tried restarting, uninstalling the keyboard driver, but it was no use.  I can't go to Control Panel because the moment I get there, it starts typing "pppppp" in the search field and I'm unable to find anything.  I'm typing this from my phone because going anywhere on my laptop seems impossible. Calculating the eigenvalues of a matrix "The train will leave" vs. "is going to leave" vs. "leaves" vs. "is leaving" Recently I encountered a problem (the first exercise from chapter four of Atiyah &amp; McDonald's Introduction to Commutative Algebra) stating that if $\mathfrak{a}$ is a decomposable ideal of $A$ (a commutative ring with unity), then the prime spectrum of $A/ \mathfrak{a}$ has finitely many irreducible components. This follows easily from the recognition that the maximal irreducible subspaces of $\textrm{ Spec } (A / \mathfrak{a})$ are precisely the "zero loci" of the minimal prime ideals of $A /\mathfrak{a}$.   I'm curious about the converse - the proof isn't easily reversed since the notion of minimal ideals of $\mathfrak{a} $ doesn't make sense before we know what we are trying to prove. My intuition says that it is false based on the general premise that images are badly-behaved (and the fact that it isn't part of the exercise.) However, I've had some difficulty constructing a counterexample, so that the main purpose of this post is to ask for a reasonable procedure or heuristic for doing so (or, of course, proof that my intuition is false.)   If it helps, if $\textrm{Spec }(A / \mathfrak{a})$ is irreducible then the nilradical $\mathcal{R}_{A /\mathfrak{a}}$ is prime so that $r(\mathfrak{a}) = \rho^{-1} ( \mathcal{R}_{A / \mathfrak{a}} ) = \displaystyle\cap_{i=1}^n \rho^{-1} (p_i),$ where $p_i$ are the minimal prime ideals of $A /\mathfrak{a}$ and $\rho $ is the associated projection, is also prime. Thanks! What is the sum of this series: $\displaystyle\sum_{n=0}^{\infty} \dfrac{a^n}{(3n)!}$ I tried getting it into a closed form but failed. Could someone help me out?  $$\sum_{n=0}^{\infty} \dfrac{a^n}{(3n)!}$$ Does commutativity imply Associativity? Explicitly calling a default method in Java Short story from many years ago: the ancient, brilliant, cruel race was Earthlings $P_n(x):=1+ \sum_{m=1}^n\dfrac{x^m}{m!}$ has no real root for even $n$ and exactly one real root for odd $n$ I know this issue has been addressed before with different software, but how do I do it with Shapely?  I have a polygon with a very small gap on the interior of the shape:    Here is a close up:    The polygon is valid so I can't use the buffer trick, and simplifying the polygon also doesn't work. 14.04 microphone noice buzzing sounds My Microphone started acting up badly this morning has a loud buzz, it has got to be software it was working fine last night installed updates and shutdown last night and boom here we are, oh and i have a Microphone jack microphone and a internal mic, both are acting up... Please help  PLEASE help i need to use skype.  Dafull97 Let $(a_n)$ be a strictly increasing sequence of positive integers such that: $a_2 = 2$, $a_{mn} = a_m a_n$ for $m, n$ relatively prime. Let $(a_n)$ be a strictly increasing sequence of positive integers such   that: $a_2 = 2$ and $a_{mn} = a_m a_n$ for $m, n$ relatively prime. Show that $a_n = n$, for every positive integer $n$.   This is a result apparently due to Paul Erdős, and  has a proof by induction.  I tried like this, $a_{10}=a_2a_5$. After this what we can do?    [Editor's comment] Possibly due to the apparent simplicity of the conditions it may be difficult to appreciate the subtleties of this question. If we try and construct a counterexample like $a_3=4$, $a_4=5$, $a_5=6$, then the requirements dictate $a_6=8$, $a_{10}=12$, $a_{15}=24$. At this point we realize that we have been speeding. For monotonicity forces $a_9\le 11$, and therefore $a_{18}\le22&lt;a_{15}$, violating the requirements. It is not obvious why something similar ruins all the modifications to the sequence $a_n=n$. [/comment, JL] What do you do in Dungeon World when someone wants to perform an action they don't have a move for? So in Dungeon World, everything breaks down to 'moves'.  What about situations where a move is not available, but a check of some sort is called for, such as in the case of a non-fighter who wants to kick down the door?  What mechanism do you use to resolve that situation? Is there the equivalent of a skill check? Problem in notation: $(\vec{v}\cdot\vec{\nabla})\vec{v}$ versus $L_v(\vec{v})$ Are security.ubuntu.com updates eventually merged into normal updates? Upon my observation, seems new packages will first appear in security.ubuntu.com, but if you upgrade later, they will appear in XX.archive.ubuntu.com (depends on your config),  Was that true ?