How to input integer value to an array, based preceeding row + column values?
How to input integer value to an array, based preceeding row + column values?
Possible Duplicate:        My Windows 7 is 64-bit, and I thought that means it can use the full 4GB of RAM installed on the computer.  But I just saw this on my computer's properties: (So only 3.25GB is usable??) Make terminal use pageup/pagedown instead of shift-pageup/shift-pagedown? I've grown quite weary of shift-pgup to page up in gnome terminal, the command line, terminator, and guake, etc.  Any way to easily make these apps use the straight page-up and page-down keys for paging around? Access: Making a Pivot Table with Multiple, Same Values as Columns How to make beveled 90 degree corners on a curve better? I know the title is a mouthful, but this is the problem: I made a curve with 90 degree corners, like so:  I then beveled it, and this was the result:  As you can imagine, this isn't very pretty. I'm looking for something like this:  How can I achieve this look? Can Button[] generate output without using Print[]? What happens to Bucky's arm at the end of Infinity War? Bucky (Winter Soldier) has a metal arm (possibly made from vibranium?) but it's an attachment to his body as far as I understand. Why, when Thanos destroys half of the universe at the end of Infinity War, does his metallic arm also disappear with him? Shouldn't it be left behind as his gun did? I am creating a type of adventure map. Once you enter the map, you step on some pressure plates that are supposed to seamlessly close the wall behind you. For some reason this command does not work when in a command block or just in text. Here is the command:  /fill -17 4 -109 -18 5 109 minecraft:light_gray_concrete   The output it gives me is "That position is not loaded". I am on a singleplayer superflat world in 1.14.3. Any help would be very appreciated! Prove that if $V$ is an inner product space, then $|\langle x,y\rangle| = \Vert x \Vert\Vert y\Vert$ if and only if one of the vectors $x$ or $y$ is a multiple of the other.  I am given a hint to let $a= \frac{\langle x,y\rangle}{\|y\|^2}$, and let $z = x - ay$, then prove $y$ and $z$ are orthogonal and $|a|= \frac{\|x\|}{\|y\|}$. I don't know how they come up with this, what was the original idea? Which is correct, "you and I" or "you and me"? When the phrase is used as an object, why so many native speakers are saying "you and I" instead of "you and me"? I'm not a native speaker but I thought "you and me" is correct. Not sure if this falls into the same category, but "Just between you and me" sounds more natural than "Just between you and I". explicit formula for recurrence relation $a_{n+1}=2a_n+\frac{1}{a_n}$ For $n\in\mathbb N$, $$a_{n+1}=2a_n+\frac{1}{a_n},\quad a_1=1. $$ Can any one give an explicit formula for all $a_n$? If such an explicit general formula doesn't exist, please explain it. I've tried to figure out the $n$-iterated function $f^{(n)}$ where $f(x)=2x+1/x$ or even $f(\tan(t))$. But in either cases, I failed.Since the recurrence isn't linear nor homogeneous,the generating function method doesn't apply here. I wanted a list of sub-domains of Stack Exchange that are not mentioned over here   Some of the sub-domains I found which were not mentioned are       Are there any other which are not mentioned?    Mentions by , ,             Other mentions below which are not mentioned in "All Sites" but are mentioned in the drop down menu on the top left of the Stack Exchange website         Any other website that's left out ? What defines a PC's consciousness of self, memories and knowledge? Why does speed of light have to be constant? My question is not about why speed of light has a particular constant value which has been sufficiently addressed in other questions on SE already. I want to know whether the fact that speed of light has to be constant is a consequence of other fundamental laws of Universe, or is it just a fundamental law itself.  My motivation for asking this question is thinking about Special Theory of Relativity. One way of understanding why time dilation and length contraction happen is to look at it from the perspective of constancy of speed of light. Alice who is on the moving source of light and Bob, a fixed observer see the speed of light as constant. In order for Alice to see the speed of light as a constant value, time slows down and length expands (in forward direction) thus keeping the speed constant.   In the  I'm doing, the Professor tells that this constancy of speed of light could be more generally referred to as, "Principle of wave constancy". That is, the speed of any wave is a property of the medium (and thus it remains constant). So, the speed of a wave in water, for example, remains constant even if the source of the waves (say a paddle keeps moving). Frequency and wavelength may change but the speed remains constant. In a similar fashion, light is an electromagnetic wave and thus its speed is constant. And the constant speed is defined by the medium (which happens to be vaccum i.e., no medium for light).   My questions are twofold now -    Is the above reasoning correct to explain why speed of light is constant? (i.e., thinking of it as constancy of any wave in general) Theoretically, could there be other waves that could travel through vaccum at a different speed? If yes, time dilation and length contraction will have to be different.   I'd appreciate it if the answer is kept non-technical (essential math is okay). More importantly, I request you to try and explain without using General Theory of Relativity. Because I'm thinking how the scientific understanding by 1905 had already knew that speed of light has to be constant. Mobile site says "your answer couldn't.." when submitting a question edit that creates a new tag Noticed this on Bicycles, but I presume it affects any Stack Exchange site   Write question Edit question, write a new tag Submit edit   When performing the above steps, I properly get an error message, but it says "answer" instead of "question" or "edit". Equal simple field extensions? I have a question about simple field extensions.  For a field $F$, if $[F(a):F]$ is odd, then why is $F(a)=F(a^2)$? This is the first part of the first half of the a proof in the Axiom of Choice. The proof that the Axiom of Choice is equivalent to the choice function. REsources: Keith Devlin's Joy of Sets: pg. 58. F.R. Drake and Singh Intermediate Set Theory: pg. 110).   I am confused on proving disjointness and will ask further questions of proof once I get this first part v. clear for myself.   AC1: Let $\mathcal F$ be a family of pairwise disjoint, non-empty sets. Then there is a set $\mathcal M$ that consists of precised one element from each member of $\mathcal F$  AC2: For every family $\mathcal F$ of non-empty sets, there is a choice function $\mathcal f$. (I.e. $\mathcal f(X)$ is a member of X, for each X in $\mathcal F$.   Disjointness: Two sets are disjoin if Q $\cap$ R = $\emptyset$. Meaning that they have zero elements in common. These sets do not overlap.   Show: AC1 $\leftrightarrow$ AC2   (1) ($\rightarrow$) Let $\mathcal F$ be a set of nonempty sets.   (2)For each X $\in$ $\mathcal F$, let $X^*$ = (X $\times$ {X}) = {(x, X) | x $\in$ X})  (3) Show Disjointness.  An outline of how book proves  disjointness:  (a) if u = {(X $\times$ {X}) | x $\in$ X} then u is of the form $\lt  z, t \gt$ where z = X and t=x, i.e. x $\in$ X.   (b) then if u $\in$ ({X} $\times$ x) $\cap$ ({Y} $\times$ Y) $\rightarrow$ u = $\lt z, t \gt$ with z = X and z=Y, i.e. X=Y. Which means ({X} $\times$ x) = ({Y} $\times$ y).  Questions: (1) Apparently we cannot prove disjointness in $\mathcal F$ but must prove in a different set. If so, why is that?  (2) why is the case that if u $\in$ ({X} $\times$ X) $\cap$ ({Y} $\times$ Y) then z =X and z=Y? I am not following that step at all.   (3) why does the axiom of choice have to do with ordered pairs? Why are we setting X $\in$ $\mathcal F$, let $X^*$ = (X $\times$ {X})?    Thank you! sir, problem about a host file sir, over department created a host file to run over office program in windows, but they give us dell system having operating system ubuntu 16.4 now my question is that how this add file in ubuntu to run the program. the windows command is given below  TO ACCESS FIORI - Please Follow the Instructions in this Video  Path:- C:\Windows\System32\drivers\etc  Copy attached Hosts File in the above path.  Fiori Link to access SAP in Google Chrome: Java - Splitting a CSV file into an Array In terms of purely set theory, the axiom of choice says that for any set $A$, its power set (with empty set removed) has a choice function, i.e. there exists a function $f\colon \mathcal{P}^*(A)\rightarrow A$ such that for any subset $S$ of $A$, $f(S)\in S.$ Is this correct?  My question then is about proving this fact, so that we do not need to put it as an axiom. Now as per the research done on this single object- Axiom of Choice, I believe here that there should be some falsity in my argument. I do not find the mistake.  For any $S\in \mathcal{P}^*(A)$, since $S\neq \emptyset$, $\exists s\in S$. Define $f(S)=s$. Then $f$ is a choice function.  This was showing me that the axiom of choice is proved, but then why it had been put as an axiom? For example, in  book, the author asserts that      It is a metatheorem of mathematical logic that it is impossible to specify the function that assigns to each non-empty subset of $\mathbb{R}$, an element of itself.     There are several notes and books on axiom of choice, but here I am trying to understand through doing some argument for some problem, where problem actually arises. What is $P(X > 0 \mid X + Y > 0)$ given that $X, Y$ are i.i.d standard normal?