We know the computer on Starfleet ships has very advanced AI to interact with the crew, but also it can produce very complex simulations in the holodeck with person-to-AI interaction.  So did Starfleet ever design a fully AI vessel for research / combat?  (I would prefer canon-only answers.)
Computers on board Starfleet vessels are quite primitive compared to on board computers such as . At their best, they can decipher requests such as "Computer, delete that last sentence" and utter things such as "That crewman is no longer on board this vessel". Even real life computers will be capable of this within a decade or so (by some estimates). Even computers such as HAL 9000 are likely to be available within a few decades.  So, in a genre where intelligent computers are abound, why this strange absence? Did the Federation run into some Battlestar-Galactica-like problem with AI in the past and decide to keep on board computers decentralized?  But if that is the case, how can one explain Data and highly intelligent holographic characters? The technology and programming constructs clearly exist, yet Starfleet vessels continue to be manned by hundreds of people standing in front of consoles.
Showing that if a subset of a complete metric space is closed, it is also complete Let $(X, d(x,y))$ be a complete metric space. Prove that if $A\subseteq X$ is a closed set, then $A$ is also complete.  My attempt: I tried to prove that every Cauchy sequence $(b_n)$ of points of $A$ converges to a point $b\in A$. However could not figure out the exit way. Maybe I am on the wrong track. Could you please help me?  edit: More from my attempt:  Suppose $A$ is a closed set and let $(x_n)$ be a sequence of points $A$ such that $\lim_n x_n\to b$.  Suppose now that $A$ has the property that $b\in A$, whenever $x_n$ converges to $b$. We know that every element of $x_n$ which is convergent in $X$ also converges to a point in $A$. Since $x_n$ is a Cauchy sequence in $A$, it must converge to a point $y\in A$. But the limit of a convergent sequence is unique.   Take $x\in A$ and select an appropriate $n$, which enables $x_n$ to converge to a point $x$ in $X$. Since the limit is unique, it must follow that $x=y$. Thus $x\in A$ and $A$ is closed.   If $A$ is a closed subset of $X$, then any Cauchy sequence of a point in $A$ is convergent in $X$ and hence converges to a point in $A$. Thus $A$ is complete. Implicit Differentiation Help I have to use implicit differentiation to find $\frac{dy}{dx}$ given:  $$x^2 \cos(y) + \sin(2y) = xy$$  I don't even know where to begin, I missed the class where we went over implicit differentiation, and because of that, I am completely stuck.   Thank you everyone.  Edit: I don't know how to make the equation look all nice and whatnot, so sorry about that Is the proof of these identities possible, only using elementary differential and integral calculus? If it is, can anyone direct me to the proofs? ( or give a hint for the solution )  1)$$\int_0^\infty { e^{-x^2} \ln x }\,dx = -\tfrac14(\gamma+2 \ln 2) \sqrt{\pi} $$  2)$$\int_0^\infty { e^{-x} \ln^2 x }\,dx = \gamma^2 + \frac{\pi^2}{6} $$  3) $$\gamma = \int_0^1 \frac{1}{1+x} \sum_{n=1}^\infty x^{2^n-1} \, dx$$  and lastly,  4) $$\zeta(s) = \frac{e^{(\log(2\pi)-1-\gamma/2)s}}{2(s-1)\Gamma(1+s/2)} \prod_\rho \left(1 - \frac{s}{\rho} \right) e^{s/\rho}\!$$  I personally think the last is obtained from a simple use of the Weierstrass factorization theorem. I'm unsure as to what substitution is used.  $\gamma$ is the Euler-Mascheroni constant and $\zeta(s)$ is the Riemannian Zeta function.  Thanks in advance. I'd love your help with finding the sign of the following integral: $\int_{0}^{2 \pi}\frac{\sin x}{x} dx$,I know that computing it is impossible.  I tried to use integration by parts and maybe to learn about the sign of each part and conclude something but It didn't work for me.  Any suggestions? SharePoint Current User View using JavaScript Laptop water damage repair procedure I'd love some advice in repairing a water-damaged laptop.  My girlfriend spilled a glass of water on her Sony Vaio and now it doesn't turn on...at all...dead! What steps should I go through to work out where the problem is and which part(s) I'll need to replace?  I can't seem to find out what has happened by just looking at the circuit boards. I'm new to electronics but could buy relevant volt-meters etc. I'm just looking for a decent trouble-shooting guide. How Can I prove (a+b) mod m = (a mod m) + (b mod m)) mod m? modular arithmetic  How Can I prove (a+b) mod m = (a mod m) + (b mod m)) mod m ? Is there a way to merge to two bars in GNOME 3? Best case scenario would be to have one single bottom or top bar that has all the symbols on the left side and the rest like the time indicator, connections, on/off button, etc. on the right side.  Is that possible in any way? Why doesn't the Moon fall onto the Earth? Custom Edit control inside a ExtJS Editor grid Why doesn't archive.ubuntu.com use HTTPS? I always see instructions for adding the Universe and Multiverse repositories that look something like the following:  sudo add-apt-repository -y "deb http://archive.ubuntu.com/ubuntu $(lsb_release -sc) main universe restricted multiverse"   Recently I tried editing this to use HTTPS instead and was dismayed to find that archive.ubuntu.com doesn't appear to respond to HTTPS. Now I wonder how feasible it would be, or what damage could be done, if an attacker were to successfully perform a man-in-the-middle attack here?  Am I being too paranoid, considering the role these repositories perform on a system? The Definitive C++ Book Guide and List This question attempts to collect the few pearls among the dozens of bad C++ books that are published every year. Unlike many other programming languages, which are often picked up on the go from tutorials found on the Internet, few are able to quickly pick up C++ without studying a well-written C++ book. It is way too big and complex for doing this. In fact, it is so big and complex, that there are very many very bad C++ books out there. And we are not talking about bad style, but things like sporting glaringly obvious factual errors and promoting abysmally bad programming styles. Please edit the accepted answer to provide quality books and an approximate skill level — preferably after discussing your addition in . (The regulars might mercilessly undo your work if they disagree with a recommendation.) Add a short blurb/description about each book that you have personally read/benefited from. Feel free to debate quality, headings, etc. Books that meet the criteria will be added to the list.  Books that have reviews by the Association of C and C++ Users (ACCU) have links to the review. *Note: FAQs and other resources can be found in the  and under . Difference between var = {} and var = []? This question has come up    ( ), but I'm finding the answers to be generally incomplete. The general question is "Why does/doesn't my job get killed when I exit/kill ssh?", and here's what I've found.  The first question is:  How general is the following information?  The following seems to be true for modern Debian linux, but I am missing some bits; and what do others need to know?   All child processes, backgrounded or not of a shell opened over an ssh connection are killed with SIGHUP when the ssh connection is closed only if the huponexit option is set: run shopt huponexit to see if this is true. If huponexit is true, then you can use nohup or disown to dissociate the process from the shell so it does not get killed when you exit.  Or, run things with screen. If huponexit is false, which is the default on at least some linuxes these days, then backgrounded jobs will not be killed on normal logout. But even if huponexit is false, then if the ssh connection gets killed, or drops (different than normal logout), then backgrounded processes will still get killed.  This can be avoided by disown or nohup as in (2). There is some distinction between (a) processes whose parent process is the terminal and (b) processes that have stdin, stdout, or stderr .  I don't know what happens to processes that are (a) and not (b), or vice versa.   Final question: How can I avoid behavior (3)?  In other words, by default in Debian backgrounded processes run along merrily by themselves after logout but not after the ssh connection is killed.  I'd like the same thing to happen to processes regardless of whether the connection was closed normally or killed.  Or, is this a bad idea?  Edit: Another, important way to keep jobs of being killed, that works (?) in either case is to run them through .  But, the question is more about understanding when things get killed and when they don't: sometimes people want the jobs to be killed on logout, for instance.  More threads: -  -  -  -  -  -  -  - It seems that Mac OS X 10.6.1 Snow Leopard has a tendency to leave some windows off-screen at times, especially when I disconnect an external monitor from my MacBook. How can I move the window back on-screen when it's not possible to grab the title bar and drag it back onto the screen?   recommends adjusting your screen resolution downward to have off-screen windows "snap back into view" and then adjust your screen resolution back to its original setting. In OS X 10.4 Tiger, I had a script that brought all off-screen windows back on-screen, but in my upgrades to Leopard and now Snow Leopard, I don't seem to have that script.  Any better solutions out there? For any smooth manifold, is it true that for any two points on the manifold, there exists a chart that covers the two points? How to show $f'(0)$ exist and is equal to $1$? pc ram memory 2x1GB or 1x2GB I don't know if it's the right place to ask but can somebody advise me for buying a ram memory for my computer.  I have a Dell Vostro 200 with 1GB of RAM and 667MHz. (2 x 512MB)  I want to buy raise the amount of RAM but I'm confused whether to buy 1 x 2GB or 2 x 1GB  I know it's the same for the available amount of memory but is ther a difference maybe in the clock speed so that 2 x 667MHz will be better than 1 x 667MHz. or maybe accessing one single memory slot will be faster and better than accessing two slots.  Please anyone helps. I understand that the alphabet for the English language is not strictly English as languages such as French, Dutch and many more use the same alphabet, with few additions in other languages. Is Roman alphabet the common term to refer to this set of symbols for writing texts? How do I install the latest OpenOffice?