I know there are some truncating issues or kind of rounding issues in float. but truncation for any value should be same. but here Can anyone explain. why outputs for 4.2 5.2 etc are extracting 19 as decimal part while 1.2, 2.2 etc as 20.  By the way the program is trying to represent pattern as follows  1.23 => 100 and 23  4.2 => 400 and 20 etc..  I guess in my machine 4.2 is stored as 4.1999998092651367187500000000000000000000000000000000000 while 1.2 as 1.2000000476837158203125000000000000000000000000000000000 But why ? whats differs from 1.2 and 4.2.  #include &lt;stdio.h&gt;  int main(void) {     for ( float value = 1.2 ; value &lt; 100; value++){     printf("Obtained value : %f real part : %d decimal part : %f \n", value, (int)value * 100, (value - (int) value) * 100);     }     return 0; }
Consider the following code:   0.1 + 0.2 == 0.3  -&gt;  false   0.1 + 0.2         -&gt;  0.30000000000000004   Why do these inaccuracies happen?
I want to do a survey of textbooks in set theory. Amazon returns 3582 books for the keywords "set theory". A small somewhat random selection with number of references in Google scholar is the following.   Two questions:    What textbooks in set-theory are considered standard?  What is a good place to aggregate standard references (of textbooks)?    (I'm only interested in text-books, which as a format already provide a kind of standardization)  Textbooks on set theory (author: title (year) #Google Scholar citations )   Thomas J. Jech: Set Theory 3rd Edition (1978) #2441  Kenneth Kunen: Set Theory (1980) #1881  P. R. Halmos: Naive Set Theory (1974) #1079 AA Fraenkel, Y Bar-Hillel, A Levy: Foundations of set theory (1973) #696 K Kuratowski, A Mostowski, M Mączyński: Set theory (1976) #609 Suppes: Axiomatic set theory  (1972) #589 Quine: Set theory and its logic (1969) #442 A Levy: Basic set theory (1979) #442 Herbert B. Enderton: Elements of Set Theory (1977) #349 Karel Hrbacek, Thomas J. Jech: Introduction to set theory (1999) #284 RR Stoll: Set theory and logic (1979) #281  N. Bourbaki: theory of sets (1970) #211 K Devlin: The joy of sets: fundamentals of contemporary set theory (1994) #182 Ciesielski: Set theory for the working mathematician (1997) #156 YN Moschovakis: Notes on set theory (1994) #138 FW Lawvere: Sets for mathematics (2003) #118 G Takeuti, WM Zaring: Introduction to axiomatic set theory (1982) #106 Kaplansky: Set Theory and Metric Spaces (2001) #103 Potter: Set Theory and Its Philosophy: A Critical Introduction (2004) #91 PT Johnstone: Notes on logic and set theory (1987) #87 Judith Roitman: Introduction to Modern Set Theory (1990) #47 Derek Goldrei: Set Theory: For Guided Independent Study (1996) #31 Basic set theory: A Shen, NK Vereshchagin (2002) #14 Ralf Schindler: Set Theory (2014) #13 Foreman, Kanamori: Handbook of Set Theory (2009) #38   Note:  Please feel free to add textbooks to the list, as long as they are not just on a smaller subset of set theory. (Some of the dates might not be the first published edition.) I committed and joined  in private beta. As per private beta privilege page casting close and reopen votes requires only 1 reputation. So anyone is able to access close votes and reopen votes review queues. But there is no link of the review page in the top bar or anywhere. So I thought I am not able to access any review queue. I opened the review page by typing the URL manually (to see review statistics for curiosity). But I found that I can access close &amp; reopen votes review queues.        Probably I won't be able to access any review queue if I have less than 350 and the site goes to public beta. But during private beta off topics, unclear, or closable questions are likely to come. So it is very important to close/reopen them during private beta.  So can we please add the "review" link in the top bar if I am able to review some queues? If two vectors $a$ and $b$ make angle $\alpha$ and $\beta$ with the $x$-axis, prove, using vectors, that:   $$\cos(\beta - \alpha) = \cos \alpha \cos\beta + \sin\alpha \sin\beta$$   I tried taking components of each vector along the plane, but that didn't get me anywhere. I tried taking component of vector $b$ along vector $a$, but I also got stuck there. Can anyone point me in the right direction? Show that if $\sqrt{a}+\sqrt{b}\neq 0$, then $\mathbb{Q}(\sqrt{a}+\sqrt{b}) = \mathbb{Q}(\sqrt{a},\sqrt{b}), \forall a,b\in\mathbb{Q}$ What is the importance of the Diophantine inequality $\frac{1}{p} + \frac{1}{q} + \frac{1}{r} > 1$? In Humphreys' book  Introduction to Lie algebras and Representation Theory(3rd printing, p.62), the Diophantine inequality $$\frac{1}{p} + \frac{1}{q} + \frac{1}{r} &gt; 1$$ appeared while classifying all Coxeter graphs of irreducible root systems. Under the assumption $p \geq q \geq r \geq 2 $, the possible triples turn out to be $(p,2,2), (3,3,2),(4,3,2),(5,3,2)$, which correspond to the Coxeter graph $\text{D}_{p+2}, \text{E}_6, \text{E}_7, \text{E}_8$, respectively.  It seems quite straightforward to solve the inequality in positive integers, but Humphreys said that      This inequality, by the way, has a long mathematical history.   without further comment. So I want to know if this Diophantine inequality has any important significance, or if it has appeared in other context (maybe relevant history) before. Feature Request: Could 7.5K users have the privilege of proposing synonyms without the 5 upvotes per tag requirement?  (in other words unrestricted synonym suggestion)  Background: I would like to be able to suggest tag synonym suggestions.  I do not however, have the required , but someday I will.  Yet many 2.5K users do not have the requisite 5 upvotes in each tag in order to propose synonyms.  I realize that this  for low-rep users.  But could it be made available to users with 7,500 rep?  At this level, they've clearly demonstrated an understanding of the Stack Exchange site.  Note: I'm not requesting the ability to create synonyms -- merely synonym suggestions.  I believe this privilege is currently only available to moderators? (and  )  Lastly, please note that  clearly demonstrates the breadth of simple synonym suggestions which could be made (almost every Stack Exchange site has some), but many haven't even been suggested yet. I've been trying to understand how the second order derivative "formula" works:  $$\lim_{h\to0} \frac{f(x+h) - 2f(x) + f(x-h)}{h^2}$$  So, the rate of change of the rate of change for an arbitrary continuous function. It basically feels right, since it samples "the after $x+h$ and the before $x-h$" and the $h^2$ is there (due to the expected /h/h -> /h*h), but I'm having trouble finding the equation on my own.  It's is basically a derivative of a derivative, right? Newtonian notation declares as $f''$ and Leibniz's as $\frac{\partial^2{y}}{\partial{x}^2}$ which dissolves into:  $$(f')'$$ and $$\frac{\partial{}}{\partial{x}}\frac{\partial{f}}{\partial{x}}$$  So, first derivation shows the rate of change of a function's value relative to input. The second derivative shows the rate of change of the actual rate of change, suggesting information relating to how frequenly it changes.  The original one is rather straightforward:  $$\frac{\Delta y}{\Delta x} = \lim_{h\to0} \frac{f(x+h) - f(x)}{x + h - x} = \lim_{h\to0} \frac{f(x+h) - f(x)}{h}$$  And can easily be shown that $f'(x) = nx^{n-1} + \dots$ is correct for the more forthcoming of polynomial functions. So, my logic suggests that to get the derivative of a derivative, one only needs to send the derivative function as input to finding the new derivative. I'll drop the $\lim_{h\to0}$ for simplicity:  $$f'(x) = \frac{f(x+h) - f(x)}{h}$$  So, the derivative of the derivative should be:  $$f''(x) = \lim_{h\to0} \frac{f'(x+h) - f'(x)}{h}$$  $$f''(x) = \lim_{h\to0} \frac{  \frac{ f(x+2h) - f(x+h)}{h} - \frac{ f(x+h) - f(x)}{h}  }{h}$$  $$f''(x) = \lim_{h\to0} \frac{  \frac{ f(x+2h) - f(x+h) - f(x+h) + f(x)}{h}  }{h}$$  $$f''(x) = \lim_{h\to0} \frac{  f(x+2h) - f(x+h) - f(x+h) + f(x)  }{h^2}$$  $$f''(x) = \lim_{h\to0} \frac{  f(x+2h) - 2f(x+h) + f(x)  }{h^2}$$  What am I doing wrong? Perhaps it is the mess of it all, but I just can't see it. Please help. Let $a,b,c&gt; 0$ be three real numbers such that $a+b+c=1$. I want to prove that   $$\frac{a}{a^2+b^3+c^3}+\frac{b}{b^2+a^3+c^3}+\frac{c}{c^2+a^3+b^3}\le\frac{1}{5abc}.$$  My attempt: Using AM-GM on each denominator gives (here, LHS denotes the left-hand side) $$LHS\le\frac{1}{3a^{\frac12}bc}+\frac{1}{3b^{\frac12}ac}+\frac{1}{3c^{\frac12}ab}.$$  However, I think that my attempt doesn't work because the last expression can get larger than $\frac{1}{5abc}$. In fact, if we multiply with $3abc$ then the original inequality is: $$\sqrt a+\sqrt b+\sqrt c\le\frac35$$  However, as $a,b,c&lt;1$, $$\sqrt a +\sqrt b + \sqrt c&gt; a+b+c=1&gt;\frac35.$$ So my upper bound is always larger than the given one. Putting char into a java string for each N characters I have a java string, which has a variable length.   I need to put the piece "&lt;br&gt;" into the string, say each 10 characters.   For example this is my string:  `this is my string which I need to modify...I love stackoverlow:)`   How can I obtain this string?:  `this is my&lt;br&gt; string wh&lt;br&gt;ich I nee&lt;br&gt;d to modif&lt;br&gt;y...I love&lt;br&gt; stackover&lt;br&gt;flow:)`   Thanks How to compare two TeX codes and mark differences with color I would like to find easy tool, which compares two TeX codes and generates a PDF file of the first code, in which the differences from the second code are marked by a given color. I use winedt 7.0 under windows 7.  I just noticed that latexdiff provides what I need. As far as I understand it is included in Miktex. Is there an interface (menu commands) in winedt 7.0, which allow to work with latexdiff ? Word for "the entire back part of the body"? When we lie down, the "back part of the body" is in contact with the bed. It includes the heels, the calves, the backside, the back, and the back of the neck, and the back of the head etc.  How do we refer to the entire "back part" of the body? Removing Ubuntu from UEFI Bios Menu Where should I put my bash scripts I noticed that my American friends tend to use the past perfect form when they use the verb mention in its past form, almost despite of the context of the sentence. I hear them say  "you had mentioned" a lot more often even in situations where the use of simple past would have been perfectly fine. Have you noticed it too and is it one of those unwritten rules, or is there a more formal explanation to it?  It seems like there was more verbs like that, but I am having a hard time remembering it now. If I do, I will edit the post and likely change the title to accommodate other verbs. Avoid large spaces between text and equations I use the options  \renewcommand{\baselinestretch}{1.25} \setlength{\parskip}{0pt} \setlength{\parindent}{0pt}    in the preamble of my document and most of the time the document looks like intended. Once in a while though, especially when I use multiline-equations, I get huge spaces right before and after the equation and the surrounding text, for example:    Is there any way I can avoid that without removing the \parskip option? If I call finalize() on an object from my program code, will the JVM still run the method again when the garbage collector processes this object?  This would be an approximate example:  MyObject m = new MyObject();  m.finalize();  m = null;  System.gc()   Would the explicit call to finalize() make the JVM's garbage collector not to run the finalize() method on object m? Bounded measurable function and integral with charcteristic function I have an odd error that I have been unable to find anything on this. I wanted to change the user comment with the following command.  $ sudo usermod -c "New Comment" user   This will work while logged onto a server but I want to automate it across 20+ servers. Usually I am able to use a list and loop through the servers and run a command but in this case I get a error.  $ for i in `cat servlist` ; do echo $i ; ssh $i sudo usermod -c "New Comment" user ; done  serv1 Usage: usermod [options] LOGIN  Options: lists usermod options  serv2 Usage: usermod [options] LOGIN  Options: lists usermod options . . .   When I run this loop it throws back an error like I am using the command incorrectly but it will run just fine on a single server.  Looking through the ssh man pages I did try -t and -t -t flags but those did not work.  I have successfully used perl -p -i -e within a similar loop to edit files.  Does anyone know a reason I am unable to loop this? Can someone tell me how to get a closed form for  $$\sum_{k=1}^n k^p$$  For $p = 1$, it's just the classic $\frac{n(n+1)}2$.   What is it for $p &gt; 1$? How should we handle a question which was deleted and reasked? A user has asked  which did not receive much attention, and thus the user deleted the post. After some time, the user asked the  (with just slight changes to the title and a tag change), so that it could receive a bit more attention. The strange thing is that the question was not downvoted or poorly written, and yet the user deleted the original post. Now, since the original question was deleted, I could not mark the new one as a duplicate (it threw an error). My question is, how do we handle such questions? Just let them be as such or let the user know about it or is there another way to handle such situations?