I've downloaded and installed Android Studio and also added the path to my .bashrc  export PATH="~/android-studio/bin/:$PATH"   What I'm looking at now is that one command which will launch android studio from anywhere in the Ubuntu file system. For example if I type subl or atom anywhere it opens up the respective editor. Can something like that be done here?
I'd like to know if there is a way to run  program/shell script without typing full path:  /opt/idea/bin/idea.sh
So, I have proven already that every open set in $\mathbb{R}$ can be written as a countable union of disjoint open intervals; i.e., that $\mathcal{O} = \bigcup_{i=1}^\infty (a_{x_i}, b_{x_i})$.  Now, consider the closed interval $\left [ a + \frac{1}{n}, b - \frac{1}{n}\right ] \subset (a, b)$.  Since the midpoint of $(a,b)$ is $\frac{b-a}{2}$, we need $\displaystyle n &gt; \frac{2}{b-a}$.  Otherwise, $\displaystyle a + \frac{b-a}{2} = a + \frac{1}{ \frac{2}{b-a}} = b - \frac{1}{ \frac{2}{b-a}} = b - \frac{b-a}{2}$, and our interval will be degenerate.  Note that $\forall (a,b) \in \mathcal{O}$,   $\displaystyle \bigcup_{n = \frac{b-a}{2}+1}^{\infty} \left[ a + \frac{1}{n}, b - \frac{1}{n} \right] = (a,b)$.  So, we have $\displaystyle \mathcal{O} = \bigcup_{i=1}^\infty \left ( \bigcup_{n = \frac{b-a}{2} + 1}^\infty \left[ a_{x_i}+\frac{1}{n}, b_{x_i}-\frac{1}{n} \right] \right)$.  But, I don't like this. It looks like I'm still just taking a union of open sets.  Please help me get this to look like the union of closed sets.  (For unbounded intervals, I know what to do - it should follow from this relatively easily). Inspired by :  In my answer, I had stated that Patronuses appear to not be physical beings because they have no effect on anything other than Dementors.     They don't cause leaves to stir in the movies. They passed straight through the tent. They don't appear to be bound by normal laws pf physics and can travel great distances almost immediately (Shacklebolt was presumably in London when his Patronus issued the warning). They can apparently walk across water without sinking (as they did in The Prisoner of Azkaban). They can jump, walk, and float in mid-air (as seen in the Room of Requirement in the movie version of The Order of the Phoenix). They make no footprints in lightly powdered snow (The Deathly Hallows Chapter 19) and make no sound of crunching snow as Harry does (further down the same page in Chapter 19).   I stated incorrectly that the only place in canon where there is an exception is with Dementors, where the Patronus physically fends them off with its horns.  A Dementor is clearly a physical being, if it prised Dudley's mouth open and (in the movie anyway) physically slid open the train door.)   Based on comments and further thought, I can think of at least two other examples when a Patronus interacts physically with a physical being.   As pointed out by Slytherincess, a Patronus can fend off a Lethifold (Living Shroud). When training, the Patonus took form against a Boggart, which had taken the form of a Dementor.   All three of these things have, AFAIK, only three things in common (but I may be off).   They are evil They are magical They are, indeed, physical beings.   So the question is, why can a Patronus interact with all three of these, but seems to have no physical effect on everyday things? Earlier today my 2009 iMac emitted I/O errors trying to copy files. So I ran disk utility, verify disk to see if anything was amiss. It was. But as it's my startup disk I couldn't repair it, so I tried safe mode. Safe mode worked the very first time, but when I rebooted it shows the progress bar filling up, before halting. Every time I turn it on now, the same progress bar then crash happens. Booting in verbose mode reveals fsck is failing with signal 8.  Using single-user mode, as that's as far as I'm aware the only way I can get any access to the system, I've been running fsck_hfs. However, it always fails. Below is the output from fsck_hfs -d /dev/disk0s2.  ** /dev/rdisk0s2         Using cacheBlockSize=32K cacheTotalBlock=65536 cacheSize=2097152K. ** Root file system    Executing fsck_hfs (version diskdev_cmds-491.6~3). ** Verifying volume when it is mounted with write access. ** Checking Journaled HFT Plus volume. ** Checking extents overflow file. ** Checking catalog file.    Missing thread record (id = 9931104)    Missing thread record (id = 16434146)    Missing thread record (id = 19370458) disk0s2: I/O error hfs_swap_BTNode: offsets 10 and 11 out of order (0x0000, 0x0000)    Invalid node structure (4, 115897) ** The volume Macintosh HD could not be verified completely.         volume check failed with error 7         volume type is pure HFS+         primary MDB is at block 0 0x00         alternate MDB is at block 0 0x00         primary VHB is at block 2 0x02         alternate VHB is at block 1952491198 0x74622d5e         sector size = 512 0x200         VolumeObject flags = 0x07         total sectors for volume = 1952591200 0x74622d60         total sectors for embedded volume = 0 0x00   I absolutely need to be able to boot to use it as an external monitor. Intuitive understanding of the derivatives of $\sin x$ and $\cos x$ One of the first things ever taught in a differential calculus class:   The derivative of $\sin x$ is $\cos x$. The derivative of $\cos x$ is $-\sin x$.   This leads to a rather neat (and convenient?) chain of derivatives:   sin(x) cos(x) -sin(x) -cos(x) sin(x) ...   An analysis of the shape of their graphs confirms some points; for example, when $\sin x$ is at a maximum, $\cos x$ is zero and moving downwards; when $\cos x$  is at a maximum, $\sin x$ is zero and moving upwards.  But these "matching points" only work for multiples of $\pi/4$.  Let us move back towards the original definition(s) of sine and cosine:  At the most basic level, $\sin x$ is defined as -- for a right triangle with internal angle $x$ -- the length of the side opposite of the angle divided by the hypotenuse of the triangle.  To generalize this to the domain of all real numbers, $\sin x$ was then defined as the Y-coordinate of a point on the unit circle that is an angle $x$ from the positive X-axis.  The definition of $\cos x$ was then made the same way, but with adj/hyp and the X-coordinate, as we all know.  Is there anything about this basic definition that allows someone to look at these definitions, alone, and think, "Hey, the derivative of the sine function with respect to angle is the cosine function!"  That is, from the unit circle definition alone.  Or, even more amazingly, the right triangle definition alone.  Ignoring graphical analysis of their plot.  In essence, I am asking, essentially, "Intuitively why is the derivative of the sine the cosine?" Right-hand sidebar covers the footer on the "ask question" page and markdown help page I have noticed that while asking questions and scrolling to the bottom of the page, the right sidebar containing recent questions covers the footer partially. Also, a part of it goes beyond the browser's boundary. It may not be a big problem but it still doesn't look good.    This also happens on the  page Truncated trivariate normal - conditional expectation How to interpret Mean Decrease in Accuracy and Mean Decrease GINI in Random Forest models Using beamer \visible command inside a table, without adding vertical space When using the beamer \visible command inside a tabular environment, beamer adds an extra vertical space before the text. For example, in the following code, beamer adds an empty line before the word World in the second row. Can this be avoided?  \documentclass{beamer} \begin{document} \begin{frame}   \begin{tabular}{|p{1cm}|p{1cm}|}     \hline     1 &amp; Hello World \\     \hline     2 &amp; \visible&lt;2-&gt;{Hello World} \\     \hline   \end{tabular} \end{frame} \end{document} ¿Can you help me with axiom of regularity? I understand that if we define a set such that $A=\{A\}$ we have then a contradiction because of regularity axiom, thus, a set can not be a member of itself. My question is; how can it be so, if I define a set $A=\{A,b\}$ ($b$ disjoint from $A$)?  Thanks. Are C++ enums signed or unsigned? And by extension is it safe to validate an input by checking that it is &lt;= your max value, and leave out >= your min value (assuming you started at 0 and incremented by 1)? I read this quite a while back, part of my parents library (they're in their 50s now) I think the book was probably published in the 70s or 80s, my copy was paperback. I don't recall the cover art, but I have vague recollections of a satellite on the cover and maybe blue with grid-lines below it?  I've made concerted efforts to find it again but to no avail. My parents don't remember it either, but mum's an avowed book-aholic and buys a lot of books, reads them once and forgets about them, so that's not so surprising.  The key parts I remember:   Both the Soviets and Americans were working on psychic techniques and technologies, with real and tangible results including Remote Viewing. MK-ULTRA was explicitly namedropped in relation to the American psychic program. The Soviets and Americans both had orbiting superweapons, One was a microwave laser (or something very similar) and the other used slivers of the brains of psychics to blow people's brains up in a wide area. A super-psychic (male) took offence to the state of the cold-war and took control over the orbital weapons by manipulating the onboard computers psychically. There's a gruesome description of a psychic weapon being tested on monkeys in a lab, the POV character throws up afterwards in horror. I think there might have been more than one POV character. There's an extended description of the psychic orbital weapon as experienced by people in its area of effect. Similar to the monkeys, it builds up, starting with alzheimer-esque hand-shaking and building up to seizures and screaming before their brain liquifies fully and either comes out the nose and ears or outright blows the skull open. (this is one of the more vivid recollections I have of the book) I remember that the super-psychic was working wholly alone and did most of his psychic stuff from motels halfway around the world from events. I believe the super-psychic also killed other psychics explicitly. The weapon satellites had code-names Both weapons were used on cities in the course of the story I vaguely recall an office building getting targeted specifically at one point. How would I connect to a proxy on Ubuntu Studio? So I am running Ubuntu Studio on my laptop and what do I do to connect to a proxy? I search for proxy and in network settings their is no PROXY tab. What are key words in the tabs to look for? Recurrence relation for number of ternary strings that contain two consecutive zeros The question is: Find a recurrence relation for number of ternary strings of length n that contain two consecutive zeros.    I know for ternary strings with length one, there are 0. For a length of 2, there is just 1 (00), and for a length of 3, there are 5 (000,001,002,100,200).    I did a similar problem, finding a relation for the number of bit strings of length n with two consecutive zeros: $$a_n = a_{n-1} + a_{n-2} + 2^{n-2}$$    Since you can add "1" to the end of all the $a_{n-1}$ strings, "10" to all the $a_{n-2}$ strings, and "00" any string of size $n-2$.    For the ternary string problem, I'm pretty sure you would replace the $2^{n-2}$ with $3^{n-2}$, but confused about the other terms of the relation. My guess is that it would have the coefficient $2$ in front of the other terms, since you can add either $1$ or $2$ to the end of $a_{n-1}$ and either $01$ or $02$ at the end of $a_{n-1}$.    So I believe the answer for the relation is: $$a_n = 2a_{n-1} + 2a_{n-2} + 3^{n-2}$$    How does that look? Is Checksum to file back decoding possible? So, I was having this weird thought. If the checksums(MD5 or SHA...) are unique to any file and are modified if any part of the file is edited, why cant the checksums be decoded back to get the original file? That is if I want to send a large(say 700MB) video, instead I could send just the hash and the file be decoded locally in my friend's computer. I know the thought is stupid, but is it possible by any chance? Or am I missing some thing here? And forgive me if I'm wrong, I ain't a professional. Exclude from * in command line Submodule of free module over a p.i.d. is free even when the module is not finitely generated? What does the word "SARGable" really mean? Is there any way to script Windows 10's "color filter" feature programmatically? About free quarks and confinement What does a resistor do? OK, very basic question here.  I read lots of books, searched quite a bit, and every description I read seemed to talk about the flow of electrons and right away go too deep in theory for me to grasp the basic principle of their use.  I understand a resistor limits the "flow", so that an LED doesn't blow up for example. But I fail to understand exactly what a resistor does to current and voltage...  Do resistors affect both current and voltage? In what manner?