When I'm doing an interating sum over a double precision value:      REAL*8 :: a     INTEGER :: p      a = 0.0d0     DO p = 1,10     a = a + 1d-04        END DO   I get the following answer:      p =1 - a = 1.000000000000000D-004     p =2 - a = 2.000000000000000D-004     p =3 - a = 3.000000000000000D-004     p =4 - a = 4.000000000000000D-004     p =5 - a = 5.000000000000000D-004     p =6 - a = 6.000000000000001D-004   Why in interation p=6 I get the number 1 in the end of the variable 'a'?
Consider the following code:   0.1 + 0.2 == 0.3  -&gt;  false   0.1 + 0.2         -&gt;  0.30000000000000004   Why do these inaccuracies happen?
So a couple of weeks ago my network manager icon stopped appearing; I still get automatically connected to my saved networks and the internet works fine, etc. If I go into System Settings and look at the Network settings I can still see all the networks, only the icon that's normal in the top bar is missing.  I have no idea what caused this, I don't remember installing anything. I think it just happened after a regular update.  I tried these commands to make sure I was properly up-to-date, (which I found on another forum post):  sudo apt-get -f install sudo apt-get update sudo apt-get upgrade   That didn't do it so I found this post:  and I followed the instructions in those answers:  sudo apt-get purge network-manager-gnome &amp;&amp; \ sudo apt-get install network-manager-gnome   And, quoted from an answer there:     Add nm-applet to the Startup Applications (which may be found by   entering "Startup Applications" in the Dash).   I restarted and then saw no Unity interface at all! So I tried those 3 commands above to update again and thankfully that fixed Unity but I still don't have my network manager.  If I try the command nm-applet in a terminal it says:  nm-applet-Message: using fallback from indicator to GtkStatusIcon   So.... I'm pretty much stumped. Any help would be appreciated. Random integer in VB.NET I need to generate a random integer between 1 and n (where n is a positive whole number) to use for a unit test. I don't need something overly complicated to ensure true randomness - just an old-fashioned random number.  How would I do that? Let $(A,+,\cdot)$ be a unity ring with the property that if $x \in A$ and $x^2=0$ then $x=0$. Consider the set $M=\{a\in A | a^3=a\}$. Prove that:      a) $2a\in Z(A)$, $\forall a\in M$, where $Z(A)$ denotes the centre of the ring $A$;   b) $ab=ba$, $\forall a,b\in M$.   My attempts revolved around the fact that an idempotent element in a reduced ring is central. So, since for $a\in M$ we have that $(a^2)^2=a^2$, it follows that $a^2\in Z(A)$, $\forall a\in M$. The next thing I wanted to use in order to solve a) was that $Z(A)$ is a subring of $A$, so if I had proved that $(a+1)^2 \in Z(A)$, $\forall a\in M$, then we would have reached the desired conclusion. However, I couldn't prove this and I honestly doubt that it is true. Another idea that I had was to prove that $M$ is a subring of $A$. Of course, this didn't work out because I cannot even prove that $M$ is closed under addition. Again, I don't know if this is true and it most likely isn't. As for b), I think that a) should be of use, but I don't know how. It is a well-known problem that a ring with $x^3=x$ for any $x$ in that ring is commutative, but since $(M,+,\cdot)$ is almost definitely not a ring, this doesn't help. EDIT: Is there any chance that this question is simply wrong? I tended to believe this before asking it here too, but since nobody has made any progress on it until now I am even more inclined to think so. When using the xhtml1-transitional.dtd doctype, collecting a credit card number with the following HTML  &lt;input type="text" id="cardNumber" name="cardNumber" autocomplete='off'/&gt;   will flag a warning on the W3C validator:     there is no attribute "autocomplete".   Is there a W3C / standards way to disable browser auto-complete on sensitive fields in a form? RF Energy Harvesting Why can energy invested in RF radiation not be harvested fully? What are the main factors that affect this? Is there any significant research nowadays that fully describes this process? I stand on the conclusion: "Energy moves from one form to another.", but in this case why can it not be harvested in that quantity to use it for powering low-power devices or store it in significant quantities in some batteries for later use? Why is it not profitable nowadays and why is it not used today like energy from water, wind and other energy sources? How to ignore accent in SQLite query (Android) How to vertically align underbraces I am trying to balance underbraces in the equation below, how can I ensure that both underbraces at the same depth?  \begin{equation} y = \underbrace{ \left [ x^2 + r^2 (a^2+\frac{a^{0.3}}{b}) \right]}_\text{growth rate} \times  \underbrace{ C_0}_\text{initial} \end{equation} Thought Experiment - Poking a stick across a Black Hole's Event Horizon How do I show that $x$ is a root of $p(x)$ in $F[x]/\langle p(x)\rangle$? Let $F$ be a field, and $p(x)$ an irreducible polynomial in $F[X]$. Define $K=F[X]/\langle p(x)\rangle$. For every $a\in F$, denote $\bar{a}=\left&lt;p(x)\right&gt;+a$. How do I show that $\bar{x}\in K$ is a root of $p(x)$?. Is it consistent with ZF for there to exist a set $S$ such that the power set $P(S)$ is countable? If so, what is the weakest form of the axiom of choice needed to prove that no such set exists? Show that a ring is commutative if it has the property that ab = ca implies b = c when $a\neq 0$.   This is my proof to show that a ring is commutative if it has the property that ab = ca implies b = c.  We need to show that if x, y ∈ R then xy = yx. Let a = x, b = yx and c = xy. Then ab = x(yx) = (xy)x = ca. Thus, by the hypothesis, b = c, or xy = yx. Thus, for x, y ∈ R we have xy = yx.   How would I show when $a\neq 0$? Also how do LEFT JOIN, RIGHT JOIN and FULL JOIN fit in? Would a fast interstellar spaceship benefit from an aerodynamic shape? Some (generous) assumptions:   We have a spaceship that can reach a reasonable fraction of light speed. The ship is able to withstand the high energies of matter impacting at that speed.   Given the amount of matter in inter-stellar space, at high speed, would it encounter enough of it and frequently enough that an aerodynamic shape would significantly reduce its drag (and thus save fuel)? Can I visit the USA as a VWP tourist immediately prior to entry on non-tourist visa? Here's my situation: I'm a UK citizen. I have an H-1B visa to work in the US as of 1 August. I also have a valid ESTA.  I would like to go to the US in July for a holiday, immediately prior to beginning my work. The holiday would be at the other end of the country from my work.  I can't enter with the H-1B as I can only enter the US on that visa 10 days prior to starting work.  Specific question: Would it be possible to visit the US in early July on the VWP, visit Canada/Mexico for a few days in late July, and re-enter the US with my H-1B visa?  General question: Is it possible to visit the US on the VWP, leave briefly, and re-enter on a different status (e.g. H, F, J, K, etc), without ever returning to one's home country?  I have posted this in Travel rather than Expatriates because, although in my specific case I have an H-1B visa, my question is more generally about VWP and travel, and I believe that it is applicable to travellers with non-immigrant visas.  There's a similar question , although that's about going to the US and before having the H-1B visa. Need help identifying short story about retired military colonel who fought war at end of time I read this story in an anthology in the eighties or early nineties.  It was about an old man who lived outside a western-like town, though that might have just been how I imagined it.  He goes to town and some ex-military thugs are there causing problems.  Flaunting some odd interdimensional military tech of some sort.  He doesn't want to intervene as doing so would be bad but in the end he must.     By intervening, his military identity is revealed and that causes him (some paradox or causality law) to have to go back and fight the war again.   The war is at the end of time or the universe.  The man is maybe a colonel of the sky something... Not much to go on; I have been searching my collection and wracking my brain for years trying to recall the story. Why is sum of squared residuals non-increasing when adding explanatory variable? In my econometric textbook(Introductory Econometrics) covering OLS, the author write, "SSR must fall when another explanatory variable is added."  Why is it? how many ways can the letters in ARRANGEMENT can be arranged Dwellers return automatically after finding a low amount of items in Wasteland How to end paragraph text in an inverted pyramid shape? In many old books, the final paragraphs of chapters end in an inverted pyramid shape, like this:    I think this is beautiful, so I would like to imitate this for my book. I've found the code for a triangle in this post   \documentclass{article} \usepackage{microtype,shapepar}  \def\triangleupshape{% {0}% {0}b{0}\\% {8.66}t{-5}{10}\\% {17.32}t{-10}{20}\\% {17.32}e{0}% }      \begin{document} \shapepar{\triangleupshape}A ipsum dolor sit amet, consectetuer    adipiscing elit, sed diam nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat. Ut wisi enim ad minim veniam, quis nostrud exerci tation ullamcorper suscipit lobortis nisl ut aliquip ex ea commodo consequat. Duis autem vel eum iriure dolor in hendrerit in vulputate velit esse molestie consequat, vel illum dolore eu feugiat nulla facilisis at vero eros et accumsan et iusto odio dignissim qui blandit praesent luptatum zzril delenit augue duis dolore te feugait nulla facilisi. Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat. \par \end{document}   Which results in this:    But I'd like it to be inverted and the first part of the paragraph need to be full line width. Only the last few lines should end in an inverted pyramid like in the example above.  Is there a way to do this? Thanks in advance for your help. The Riemann zeta function $ζ(s)$ is defined for all complex numbers $s ≠ 1$ with a simple pole at $s = 1$. It has zeros at the negative even integers, i.e., at $s = −2, −4, −6, ...$.   My question: How one can obtain these roots.