I just realized I can't unrar .rar files on my Ubuntu machine!
I just realized I can't unrar .rar files on my Ubuntu machine!  What's the easiest way to accomplish this fundamental task? If possible I'd love something like 7Zip that I can just right Click, and extract and have the program worry about how to do it regardless if it's a .zip, a .rar or a .foo compressed file.
Given a subset $A$ of $\mathbb{R}^{n}$, a point $x \in \mathbb{R}^{n}$ is said to be in the boundary of A if and only if for every open rectangle $B\subseteq\mathbb{R}^{n}$ with $x\in B$, $B$ contains both a point of $A$ and a point of $\mathbb{R}^{n}\setminus A$.  My question is from Spivak's Calculus on Manifolds: Construct a set $A \subseteq [0,1]\times [0,1]$ such that $A$ contains at most one point on each horizontal and vertical line but has boundary equal to $[0,1]\times[0,1]$. How to prove $\vdash\neg P\to (P\to Q)$? I am trying to prove,  $$\vdash\neg P\to (P\to Q)$$  where $P$ and $Q$ are arbitrary but otherwise fixed formulas. The only axioms and rule of inference that I can use are,  $\color{crimson}{\text{Axiom 1.}}\  P\to (Q\to P)$ $\color{crimson}{\text{Axiom 2.}}\  (S\to (P\to Q))\to((S\to P)\to (S\to Q))$ $\color{crimson}{\text{Axiom 3.}}\  (\neg Q\to\neg P)\to(P\to Q)$ $\color{crimson}{\text{Rule of Inference.}}$ .  I know that in Angelo Margaris's book First Order Mathematical Logic there is a proof (page 53) but as I have mentioned , the dot notation seems very confusing and translating them to the nested parentheses notation seems very difficult to me. So, I am trying on my own to prove the result. Can anyone help? Сanonical form of a quadratic form by Lagrange's method This is just an eg. to understand how to solve it.  There is a quadratic form as below we need to bring to canonical form using Lagrange's method and find the coordinate transformation.   Then find the positive &amp; negative indexes, rank of the quadratic form. Finnally, to investigate sign-definiteness of the quadratic form by two ways: according to it's canonical form and the criterion of Sylvester: $4x_{1}^2+2x_{2}^2+10x_{3}^2-4x_{1}x_{2}-12x_{1}x_{3}-8x_{2}x_{3}$  Any clarification on how to do it are very welcomed. What is the origin of non-conservative force? My understanding about  is a force that its work is independent of path such that we can construct another form of the work called potential to make our life easier.  For friction, if I start from microscopic point of view, it should be the macroscopic effect of the electric force or gravity which are both conservative force.  Why do we initially have description by conservative forces (electric/gravity force) but end up with a macroscopic description of nonconservative force(friction)? Label equations arbitrarily Jutifying: irrational + rational = irrational I am not sure how to show this. This is what I tried.   Proposition: If x is rational number and y is an irrational number then x+y is an irrational number.  Logically speaking this is  P=x is rational  Q= Y is irrational  R= x+y is irrational  $P\wedge Q \rightarrow R$  Explanation: What I did  $x=\frac{p}{q}$ P and Q integer  Y cannot be written as the a rational by definition  So therefore  $x+y=\frac{p}{q}+y$  Will not be a rational number as there cannot be a common denominator. How do you handle the varying sizes of filters in your kit? I have a variety of Nikon DX lenses that take differently sized filters. Most take 52mm filters, but there are a few that take larger 67mm or 77mm filters. The advice I've read most commonly online is to buy one filter size and get filter conversion rings to step up to that size filter. In my case, the largest size appears to be 77mm.  So, I walked into a couple local photo shops and asked about 52mm-77mm filter conversion rings and they looked at me like I had two heads. One guy suggested I stack a 52mm-67m and a 67mm-77mm. I have found 52mm-77mm rings online, so I know they exist.  Is this not a common thing to do? How does the stack exchange community handle the varying sizes of filters in their kit?  Thanks, PaulH How do I SSH to machine A via B in one command? Deep in my families history (1600's or there abouts) our family split in two. About three or four generations later two distant cousins got married creating a split / rejoin.                G.G.G.Parents A        +---------+---------------------------+     G.G.Grand Parent                      G.G.Grand Parent        |                                     |     G.Grand Parent                        G.Grand Parent        |                                     |     Grand Parent                          Grand Parent        |                                     | +------+-------+                     +-------+-------+ Aunt       Parent A - - -+- - - Parent B         Uncle                          |                   +------+------+                Child A        Child B                  ...           ...   So in this small example, the family splits in two at G.G.Grandparents and then rejoins later when Parent A and Parent B marry.  About 8 years ago I tried to find a software package which could model this and failed. Has anything happened in the intervening time?  Sorry I'm just asking in SE without doing much research, but I spent a lot of effort last time without any success and I am sure there is someone out there who can point me to an excellent package!    @ColeValleyGirl: I'm looking for a piece of software that is able to print out such a tree/DAG (thanks @ACProctor) in high enough quality to display/frame. All software I tried before didn't seem to be able to display this as they seemed to support mainly variations of Ancestors / Descendants rather than an output of all the people that had been inputed.  @AdrianB38: Essentially, I want to see "everyone". The tree I have was put together by my grandfather, who probably had a lot more data/people, but I've only got the hand written tree which highlights this split. It's essentially a tree of my grandparents ancestors (including this split which is joined at a common ancestor) and descendants (me + my family). I'd like to reproduce this in the computer (there is about 400 years - hundreds of people).  @AdrianB38: Re your point about generations, yes, I have that issue. I think it's only one generation, might be two - i've not looked at the tree in a while. The split between families happened over about 150-200 years iirc.  I can write an SVG generator if I really need to (I'm a Software Engineer) albeit I'm aware such a "loop"/"dependency" is painful to program for, but I was hoping that there was something which could handle this. Auto-fit TextView for Android Does a creature with Lifelink provide lifegain equal to its power, or the defender's toughness? Are $(\mathbb{R},+)$ and $(\mathbb{C},+)$ isomorphic as additive groups?  I know that there is a bijection between $\mathbb{R}$  and $\mathbb{C}$, and  asks whether they are isomorphic as abelian groups, are they referring to the additive abelian group? If so is there any simple isomorphism I can find? I know nothing about Hamel basis. Thanks. A colleague and I recently submitted a paper to a journal with an impressive-sounding name, the "International Journal of Artificial Intelligence and Computational Research". According to ,      IJAICR is a referred [sic] journal in the field of computer science, artificial intelligence and soft computing methods.   It was accepted two days after we submitted it. That's too fast. We were suspicious. Although the journal said that all papers are peer-reviewed, we could not see how that was done in two days. Plus, we received no comments from the reviewers. Also, the submission guidelines didn't ask for a "blind" copy (without our names or any references to who we were).   But wait, there's more.  The acceptance letter asked us to send them US$300 to publish it. We did not. We've withdrawn our submission and will submit a new version of the paper to a more reputable journal in the coming months.  How might we make a better choice of respectable journals before we submit next time? How to trigger Ajax forms machinery I'm working on ajaxifying a form which uses Hierarchical Select widget. I need to update a text field based on the value of HS and a couple of other fields. I want to use Drupal forms Ajax API. I followed the . Now the form is updated when user fills in the text fields. But I can't cope with HS.   I was told  HS doesn't support regular Drupal #ajax mechanism. I can easily attach the handler to HS update event. So all I need now is to manually trigger Drupal Ajax machinery from my own handler. How it's best to be done?   I see there is a global Drupal.ajax object but can't figure out how to make use of it. How to generate random points on a sphere? Let $F : X → X$ be continuous. Prove that the set $\{x ∈ X : F(x) = x\}$ of fixed points of F is closed in X Here X is a Hausdorff Space.  I know that singleton sets, {x}, are closed in a Hausdorff space. Although Im not sure if thats how to use the Hausdorff property.   Should I investigate $h=F(x)-x$?  Can anyone give a hint Does the series $\sum\limits_{n=1}^\infty \frac{1}{n^3 \sin^2n}$ converge or diverge? I have this series given by $$\sum\limits_{n=1}^\infty \frac{1}{n^3 \sin^2n}.$$ I know that the terms are all nonnegative. Can I get a subsequence of $\frac{1}{n^3 \sin^2n}$ such that its sum diverges to $+\infty$? Lisp Executable I've just started learning Lisp and I can't figure out how to compile and link lisp code to an executable.  I'm using clisp and clisp -c produces two files:   .fas .lib   What do I do next to get an executable? Converting Raw HTTP Request into HTTPWebRequest Object $a+b+c = 3$, prove that :$a\sqrt{a+3}+b\sqrt{b+3}+c\sqrt{c+3} \geq 6$ $a, b,c $ are positive real numbers such that $a+b+c = 3$, prove that :$a\sqrt{a+3}+b\sqrt{b+3}+c\sqrt{c+3} \geq 6$  Any ideas ?