Shortcut for determining equivalence relations?
Number of equivalence relations on a set
Why does mathematical convention deal so ineptly with multisets? I want to run a script to simply change the current working directory:  #!/bin/bash cd web/www/project   But, after I run it, the current pwd remains unchanged! How can I do that? Calculate the sum of inverse values of ${n\choose 0}, {n\choose 1}, ... {n\choose n}$ Calculate $$A={1\over {n\choose 0}}+ {1\over {n\choose 1}}+ ...+{1\over  {n\choose n}}$$  and  $$B={1\over {n\choose 0}}- {1\over {n\choose 1}}+ ...+{(-1)^n\over  {n\choose n}}$$     My idea for $A$ is some probabilistic reasoning. Color the sets $$\{\}, \{1\}, \{1,2\}, \{1,2,3\},...\{1,2,...,n\}$$ and ask our self what is the probability that I choose colored set among all sets. Clearly this is exactly ${n+1\over 2^n}$ and on the other side it is $A$:  probability that I take empty set is ${1\over {n\choose 0}}$,   probability that I take colored set with 1 element is ${1\over {n\choose 1}}$  probability that I take colored set with 2 elements is ${1\over {n\choose 2}}$  and so on ...   So $A ={n+1\over 2^n}$. But I have no idea how to attack $B$. CSS technique for a horizontal line with words in the middle Python rounding error with float numbers Using [Authorize] without SimpleMembershipProvider In Ubuntu, applications can be opened from a terminal. But sometimes it isn't clear what the appropriate command is to do this.  So, having an application open, how can I get the command used to launch it, without having to search anywhere (just by looking at it)? Difference between ' and " on command line (bash)? I used to use '' and "" (single and double-quotes) interchangeably on the command line, but I recently noticed that '$HOME/some/dir' is not expanded, while "$HOME/some/dir" is. I searched around a little bit and found that "" allows some protection of special characters, while '' allows full protection. So what other characters are protected by '' and not ""?  EDIT: What are practical situations in which these differences might be significant? How to recover a removed file under Linux? By accident, I used rm on a file I didn't want to delete. Is there a way that I can get it back under Linux? Starcraft Installation asks for a mythical Disk 2 I just purchased the Starcraft Battle Chest containing Starcraft and BroodWar.  When I try to install Starcraft I get halfway through and I'm prompted to "Insert Disk 2".  The box did not contain a second disk.  My computer is Windows 7 (x64). What do I need to do to continue?  Box Contents:   Starcraft Disk Broodwar Disk WoW Trial Disk Unable to install rJava in R 3.0 in Ubuntu 13.04 every planar graph can be expressed as a union of five edge-disjoint forests How can I prove that every planar graph can be expressed as a union of (maximum) five edge-disjoint forests?  Only thing I can think about is going somehow like the $5$ color theorem but I get stuck in the middle. Or with induction, but still something doesn't fit. Can you help? What exactly is the cause of RAM incompatibility? I'm looking at rather short QVL lists from manufacturers, and I'm wondering what is the underlying cause of RAM incompatibility aside from the obvious: Obvious Reasons for Incompatibility  RAM Generation (DDR, DDR2, DDR3, DDR4) Form Factor / pin count RAM Type (ECC vs Non-ECC, Registered vs not, Buffered vs not) Minimum speeds on a board that cannot adjust the memory frequency Non-standard voltage range on a board that cannot adjust the memory voltage Channel count (single vs dual vs quad) Bad or inoperable module Mismatched set  Not Obvious Reasons  Brand SKU Max Capacity Speed too high  As in, why can't motherboard manufacturers just list the specifications of the RAM they will accommodate, and support every memory chip of that category instead of listing specific SKUs from specific brands? What happens electrically/physically that causes boards to fail to POST / operate with RAM that is otherwise 'compatible' with all of the specifications of RAM that is on the QVL? I have some files/directories on an external hard drive connected using USB to my Windows XP laptop. I am trying to delete those files but every time I try, I get an error "Cannot delete ....: Access Denied. Make sure disk is not full or write protected and that the file is not currently in use".  I checked that the directory is not is use. However, the permissions are set to read-only. Even if I remove the "read-only" checkbox, in Properties->Attributes, it automatically comes back again. How do I fix this? Is it a virus that is automatically changing it back to read-only?  regards,  JP How to analyse 'Element not Found' exceptions when working with Selenium Is it mandatory to have a link to the theme designer? I just wanted to know if it's ok to modify/remove links pointing to the designer of the theme.  In my case I have "theme by" and the site's logotype, would it be ok to remove the logotype and write the site's name? Or remove it altoghether?  Does it have to do with the particular designer of the theme?  Thanks Object Positions Reset On Blender Load So I am attempting to make a modular environment in Blender, so I'm modeling many pieces in one scene to make sure they all match up properly before separating them out.  However, whenever I restart Blender after saving and closing it, many of my grouped objects (and their subobjects) have positions reset NOT to where I placed them.  For example, take a look at this:   Here you can see that the door pieces are in the "open" state, when I left them closed AND the "column" for the wall on the left has been moved from being flush with the wall (on the side) to being inside it.  It appears to be trying to move all of the objects to 0,0,0 which is what is messing this up. I'm not sure if it's an object hierarchy problem, but here is my hierarchy if anyone has ideas there:  Wall_Normal (parent)   Wall_Normal_Column (child)   Empty Axis Object (parent)   Door_Left (child a) Door_Right (child b)   Is there a reason why object positions (and their relative subobjects) aren't being saved? Let's say you tell me to produce randomly a number from 1-100, and I choose the number 47. Can it be said that there is a specific reason I chose the number 47, and that it is not completely random? By random I mean that there is absolutely no reason this number in particular was chosen.    It seems odd to me, since it seems like since I have applied conscious effort to produce or choose a number within that range, or even without range, that it can't be truly random, but there might be a reason why I chose that number amongst the many others I could have chosen.  I guess the general question, which I'm interested to know if any philosophers in the past have discussed, is whether our thoughts are necessarily based on prior thoughts, or if thoughts can be truly spontaneous and random? I can’t get used to the new Unity system. I’d like to move the left Unity panel to the bottom of screen (like Windows 7 – more similar is better).  But I can't find a way. Is it possible? I'm using a flow to set a field to a certain value (01, 02, 03) depending on the value of another field on the same record. I initially wanted to do it with process builder but because of the mapping it seems I would need three 'criteria nodes' or a formula field. Furthermore, it seems Salesforce is recommending using flows instead of process builder for before update actions as it is faster.  The problem with Flows is that I found a way to trigger it when the record is new or updated but not when the specific field is changed so it triggers every time the whole record is updated even when the field stay the same.  On Process Builder, you can use isChanged and then call the flow with specific record but that kinds of defeat the point of using flows for before Update.  So is there a possibility to do the same thing directly in flow ?  Thank you for the help !