I spent an hour today trying to figure out why  return abs(val-desired) &lt;= 0.1   was occasionally returning False, despite val and desired having an absolute difference of &lt;=0.1. After some debugging, I found out that -13.2 + 13.3 = 0.10000000000000142. Now I understand that CPUs cannot easily represent most real numbers, but this is an exception, because you can subtract 0.00000000000000142 and get 0.1, so it can be represented in Python.  I am running Python 2.7 on Intel Core architecture CPUs (this is all I have been able to test it on). I'm curious to know how I can store a value of 0.1 despite not being able to apply arithmetic to particular floating point values. val and desired are float values.
My code:  a = '2.3'   I wanted to display a as a floating point value.  Since a is a string, I tried:  float(a)   The result I got was :  2.2999999999999998   I want a solution for this problem. Please, kindly help me.  I was following .
So basically I want to show:  $\aleph_{\alpha}^{\aleph_{1}} = \aleph_{\alpha}^{\aleph_{0}}\cdot2^{\aleph_1}$ , Where $\omega\leq\alpha&lt;\omega_1$  There is a proof that I found;    But I don't understand his proof for the limit case of $\alpha$.  To be more specific, I dont understand why $ \left( \sup_{\omega \le \beta &lt; \alpha} \aleph_{\beta}\right)^{\aleph_1} \le \left( \prod_{\omega \le \beta &lt; \alpha} \aleph_{\beta}\right)^{\aleph_1}$  Any insights or help is deeply appreciated.  Cheers A result of Erdős on increasing multiplicative functions Erdős proved that if $f(n)$ is a monotone increasing function from the natural numbers to the positive reals, and $f(n)$ is completely multiplicative, then there exists some constant $C$ such that $f(n)=n^C$ for all $n$.  I have not been able to find a nice proof of this online and was hoping someone could provide a proof. Let $A$ be a commutative ring and $S$ a multiplicative closed subset of $A$. If $A$ is a PID, show that $S^{-1}A$ is a PID.   I've taken an ideal $I$ of $S^{-1}A$ and I've tried to see that is generated by one element; the ideal $I$ has the form $S^{-1}J$ with $J$ an ideal of $A$. $J$ is generated by one element but I can't see why $I$ has to be generated by one element, maybe I'm wrong. Java Command line arguments I need a regular expression to select all the text between two outer brackets.  Example: some text(text here(possible text)text(possible text(more text)))end text  Result: (text here(possible text)text(possible text(more text))) My computer no longer boots Windows or the installed operating system. Instead, I may get this error:  PXE-E61: Media test failure, check cable -or- Check cable connection!  PXE-M0F: Exiting PXE ROM.   and/or one of the following messages or similar:  Operating System not found  No boot device available- No bootable devices--strike F1 to retry boot, F2 for setup utility  No bootable device -- insert boot disk and press any key  No Boot Device Found. Press any key to reboot the machine  Default Boot Device Missing or Boot Failed  Reboot and Select proper Boot device or Insert Boot Media in selected Boot device   What does this mean and what can I do?     This question comes up often and the answers are usually the same. This post is meant to provide a definitive, canonical answer for this problem. Feel free to edit the answer to add additional details. I have this on the command line:    ln -sf $PWD/wine-   and then I hit Tab to complete the filename.  In earlier versions of Ubuntu, this worked just fine to complete the wine- filename (and as a side-effect $PWD would be expanded at that time).  But now it turns it in to  ln -sf \$PWD/wine-   which isn't what I meant at all and doesn't complete anything as the file does not literally start with $.  How do I get completion back to the less broken behaviour?  set tells me these are my current settings:  BASHOPTS=checkwinsize:cmdhist:expand_aliases:extquote:force_fignore:hostcomplete:interactive_comments:progcomp:promptvars:sourcepath SHELLOPTS=braceexpand:emacs:hashall:histexpand:history:interactive-comments:monitor Can Sasuke use Tsukuyomi? How come I never see cosmic rays in steam like they appear in a cloud chamber? How can the pixel values of a raster image be extracted under a polygon fishnet? I have a single band raster image of 30m by 30m resolution. I have already created a polygon fishnet (grid) of 300m by 300m with point labels over that. How can I extract the mean pixel value of the raster image overlaying each feature in the fishnet grid? Is it possible with Arcgis?  Please inform me. Honey changing into unusable, hardened clump I buy raw, unfiltered honey from the grocery store in jars sold/packed directly by the farmer. When I had used the last jar to about half, I noticed the honey beginning to dry(crystalize?) to the point where I couldn't use the honey around these spots.  Not too long after this, the entire jar had crystallized into a block of unusable hard stuff.   I didn't do anything differently with this jar than the last jar, but only now am I having the issue. My question(s):   Why is the honey crystallizing, and why so rapidly?   1) Is the honey unusable at this point?  2) Should I store the honey differently after purchasing it(move from jar to other container)?  3) I've never seen this happen to the filtered, strained(fake) honey from the store, so what causes this to happen in the raw and unfiltered form? If you have a line passing through the middle of a circle, does it create a right angle at the intersection of the line and curve? More generally, is it valid to define an angle created between a line and a curve? Is the tangent to the curve at the point of intersection a valid interpretation (I.e a semi circle has 2 right angles) I saw it in a debate thread and it got me curious now. I have white blank on the posts.    App Version: 1.0.89 Device Manufacturer: Meizu Device Model: m2   OS Version: 5.1 (1464689330)    I can't see the questions and the answers and the comments.  I saw that it's a common issue..  Does it have a fix?   EDIT -  I saw  answer. This answer is ~2 years old. It says that it will fix in the next update.  His version is 1.0.59 - mine is 1.0.89. Huge different.   The problem is still exists! How can I do development on my Android device? I have a pretty long commute to work and own an android phone. I figure it would be nice to do some simple programming on the way. I'm not picky on which language to code on. I usually have an internet connection on the train.  I've been looking through the android market but haven't found any apps that offer a "development environment" or an editor with a compiler. Is any development ON the Android possible? Does an app for this exist? Need to schedule a job every hour in jenkins Will airlines compensate me if my entertainment system is not working? In long haul flights, if I get a seat and after take off I found out that entertainment system is not working, I asked a flight attendant to change my seat but she apologized because there are no empty seats to move to.   Is it common to ask for a compensation for such an inconvenience? do major airlines compensate you in such cases? How can I remap a keyboard key? One of my laptop's keys has fallen off. Is there any way I can remap another key to serve as that key?  I'll 'sacrifice' the other key because I never use it. "A/An" preceding a parenthetical statement When a/an precedes a parenthetical aside (sometimes seen in informal/conversational writing), should the vowel rule depend on the first word in parentheses, or the next word in the "regular" flow of the sentence?     I need a (memorable) idiom (preceding an m word; use a)   or     I need an (memorable) idiom (preceding an i word; use an) I switch back and forth between two computers constantly:   OSX Snow Leopard  Ubuntu 10.10    I'd like to be able to make Ubuntu use the same keyboard shortcuts as OSX System Wide, for the following keyboard sequences only (ie I don't want to make Ctrl act like Super)   Super+C -> Copy Super+V -> Paste Super+T -> Open a new tab in whatever browser I'm in.  Super+W -> Close a tab in whatever browser I'm in.    So in short, is there anyway for me to map just these keyboard sequences to the following, system wide ?   Super+C -> Ctrl+C Super+V -> Ctrl+V Super+T -> Ctrl+T  Super+W -> Ctrl+W   I know there are ways for me to do this for vim, and Firefox, and I'm sure specifically for most applications... but I would prefer to have to do this just once and have it work that way system wide!  I'm using a standard PC keyboard, that is "Generic 105 key (intl) PC" on Ubuntu. I'm also using the same keyboard on my Mac mini. Is it possible to follow a user automatically?