For continuous distribution $P(X_3<X_2<\max(X_1,X_4))$ equals?
Probability of $p(x_1<x_2<\max(x_3,x_4))$
Why can't the Polynomial Ring be a Field? I'm currently studying Polynomial Rings, but I can't figure out why they are Rings, not Fields. In the definition of a Field, a Set builds a Commutative Group with Addition and Multiplication. This implies an inverse multiple for every Element in the Set.   The book doesn't elaborate on this, however. I don't understand why a Polynomial Ring couldn't have an inverse multiplicative for every element (at least in the Whole numbers, and it's already given that it has a neutral element). Could somebody please explain why this can't be so? Possible Duplicate:          On Windows I am able to switch between keyboard layouts by pressing Alt+Shift. Is there a similar keyboard shortcut in Ubuntu? How to understand the Ubuntu file system layout? Run cmd.exe in Administrator mode without explorer.exe I've recently had trouble with explorer.exe not working.  I found a possible solution , using .  The problem is that I cannot "right-click Command Prompt, and then click Run as administrator", since explorer.exe does not work for even a second without crashing.  I tried to use the  to open cmd as administrator, but I get an error 1327 because I have a blank password.    My question is, is there any other way to run cmd.exe with admin privileges?  If not, is there any way to run sfc.exe without admin privileges?  If not, does anyone have solution to my original problem of explorer.exe stopping and restarting ad nauseam? How does the "this" keyword work? So basically as it stands I have a laptop which has no cd/dvd drive, and I don't have a usb drive.  The laptop has windows 7 installed with ubuntu 11.04 installed through wubi.  What I want to do is remove windows completely, and make ubuntu the only OS installed on the system.  Is there a way to do this without re-installing ubuntu? (i.e. can I take my wubi install away from windows?)  or is there a way to from inside ubuntu have it run the ubuntu iso somehow so I can just wipe the system and install it fresh? (even if it means I need to have an e.g. 2gb partition just for the image to reside in). Add leading zeroes to number in Java? Powers of infinite cardinals in the generic extension Prevent Windows 7 from sleep + power button hook I'm used to not shutdown Windows but to sleeping it. I set up power button (PB) action to do it. When I want to shutdown I must go to start -> Shutdown. That's OK.  Now I think of a mechanism that will be hooked up to a PB. Should be started after I press PB but before OS will go to sleep. Something that will check few conditions (i.e. running backup, running AV scan, ...) and if true (something is running) prevent go to sleep.  Optionally: It would be nice to start the same "mechanism" before restart and shutdown (invoked not only from Start menu, but also by other software (i.e. installers) but with option to allow some sources (i.e. UPS software)  Generally: How to run something after PowerButton but before Sleeping. How to code (C#.NET, vbs, batch (preferred)) sleep prevention (cancellation). Series as an integral (sophomore's dream) I need help with this exercise.  I need to prove $$\int_{0}^{1}x^{-x}\ dx=\sum_{n=1}^{\infty}n^{-n}$$  I think I should use some convergence theorem, but I'm stuck.  Thanks a lot! I am trying to integrate one Salesforce org to other org by using Oauth setup, I wanted to use  use consumer key and consumer secret key in my REST class to connect with the org, after connection part completion, I want to access Get(), Put(), Post(), etc. Including the ability to set Oauth and Authorization headers needed for Salesforce Rest API calls.  Actually I'm new in REST implementation so can you please explain me by using code samples. Why does the following code sometimes causes an Exception with the contents "CLIPBRD_E_CANT_OPEN":  Clipboard.SetText(str);   This usually occurs the first time the Clipboard is used in the application and not after that. A closed ball in a metric space is a closed set Why $¬¬\bot \not\in PROP$? I'm reading Dalen's Logic and Structure.  He gives the definition of the set $PROP$:     Definition $\bf2.1.2$ The set $PROP$ of propositions is the smallest set $X$ with the properties       $\begin{array}{rl} \rm(i)&amp;p_i\in X(i\in N),\bot\in X,\\ \rm(ii)&amp;\varphi,\psi\in X\Rightarrow(\varphi\wedge\psi),(\varphi\vee\psi),(\varphi\to\psi),(\varphi\leftrightarrow\psi)\in X,\\ \rm(iii)&amp;\varphi\in X\Rightarrow(\neg\varphi)\in X.\\ \end{array}$   Then there are some examples:        And he says that $¬¬\bot \not\in PROP$, but I don't understand it. Isn't $¬¬  \bot=\bot$ due to the property of double negation? Considering this is true, $\bot\in PROP$. Of course, in this question, I'm pressuposing some kind of evaluation, that $¬¬ \bot$ becomes $\bot$ due to the law of the double negation, but perhaps it should be hold in an unevaluated form.  Ex:. $1+1=2$ because we presupose the $1$ merges with $1$ and then becomes two. If the merge (evaluation) does not happen, then I guess:  $$1+1=1+1$$ $$2=2$$ $$2\neq 1+1$$ $$1+1\neq 2$$  Perhaps it's something like that, I took the idea from Mathematica. Sometimes it does treats things as different in the absence of full evaluation. I am a beginner to python coding in GIS. I want to calculate the total number of counts in raster attribute table. In order to do that:   I would like to build a attribute table of raster data use a loop through attribute table using ARCPY.SearchCursor()   Therefore, I wrote a code to build an attribute table. However, I am getting an error while running the code and not able to figure out the error in the code.  Code:  import arcpy # Create the geoprocessing object  import arcgisscripting gp = arcgisscripting.create()  #To overwrite output arcpy.env.overwriteOutput = True  #Set environment settings gp.workspace = "C:/Subhasis/Test/raster-read"  #Build Raster Attribute Table gp.BuildRasterAttributeTable_management("sti-9", "Overwrite")  Error Message: Traceback (most recent call last):   File "C:/Subhasis/Test/raster-read/test.py", line 15, in &lt;module&gt;     gp.BuildRasterAttributeTable_management("sti-9", "Overwrite") ExecuteError: ERROR 000049: Failed to build attribute table Failed to execute (BuildRasterAttributeTable). I have this value    How to read that in English? translating from my native language, I would say     Ten base of nine.   but is that really correct? Trying to rig a Map I'm trying to make a "simple" accordion map in Blender 2.79, for animated and still render purposes.  I will map graphics onto each face, and I don't want the faces to get stretched/distorted.  I do however, want to be able to create a hinge-type rig, to be able to fold open and close the map like an accordion without having to manually position each face edge (which would distort the faces anyways).  I looked into using an Armature, but the faces got distorted. I tried to use a Hinge constraint, but I if understand correctly, it would require each flap of the map to be a distinct element - I don't want that. I found solutions involving Weight painting, but I don't think I want any of the map's flaps to be anchored - also there is only one face per element and I don't know if Weight Painting is appropriate.    How can I rig this map properly to open it and close it without any distortion? Group theoretic meaning of natural isomorphisms between certain functors So imagine you have a group $G$ and we consider the set of group homomorphisms from $\mathbb{Z}$ to  $G$ specified by  $\forall g$ $\in G$ $\exists$   $\phi(1)=g$. Each of these homomorphisms is in 1-1 relation with the elements of $G$.  Consider groups for a moment in the context of category theory, viewing the groups as one object categories and thereof group homomorphism as functors. What would a natural isomorphism mean in group theory terms for G?  My thoughts are that the natural transformations equate to maps between homomorphisms and since the homomorphisms are in 1-1 relation with the elements of G, then a natural transformation is a map between group elements, i.e another element of the group. I'm not entirely convinced by this.   Anyway continuing my reasoning a natural isomorphism is a map between the homomorphisms that has an inverse, the thing is in relation to the elements of G this is every element? Furthermore I'm looking to find an equivalence class defined by this natural isomorphism, is this just a collection of the elements that are each others inverses?  Thanks in advance for any assistance. if command in find -exec I was just trying to list all directories and files under current directory and also write if they are file or directory with the following command:  find -exec echo `echo {} : ;if [ -f {} ]; then echo file; else echo directory;fi` \;   I know it is a silly command, I can use other things like -type f or -type d, but I want to learn why that piece of code did not work as I expected. It just prints directory to all of them. For example while output of find is:  . ./dir ./dir/file   output of my code is :  . : directory ./dir : directory ./dir/file : directory   And output of   echo `echo dir/file : ;if [ -f dir/file ]; then echo file; else echo directory;fi`   is  dir/file : file   I am working on Ubuntu 14.10 and using find (GNU findutils) 4.4.2 Having trouble with Windows XP Read Only Settings on a folder I am having trouble with a folder that needs to be read-write for iTunes to open. For a while it was read-write, but it seemingly inexplicably changed to read-only now. When I try to change it back from that, it says it does it, but as soon as I try to open iTunes or the properties for the folder it will be listed as read-only again.  If anyone knows how I can change the folder from read-only so that it will be permanently read-write it would be incredibly helpful.  How can one change the properties of a file/folder from read-only to read-write in Windows XP?