Subsets of $\Bbb N$ are well ordered. So two subsets of $\Bbb N$,  A and B could be compared by comparing the least elements in A\B and B\A; whichever has the lesser is the lower.  This relation appears also transitive.   It looks to me that this "ordering" will find a "least" in any set of subsets of $\Bbb N$.  But this would produce an effective well ordering of the continuum, which is impossible.  So the proposed "order" is either non-transitive or it will fail to find the "least" in some set of subsets of $\Bbb N$.   Is there immediately obvious where the mistake (if any)?  PS The proposed relation is not even an ordering, as detailed below. Although the counter example from the other post will work here as well.
So, to explain the title, I'm referring to the necessity of the axiom of choice in the existence of a well ordering on reals, or any uncountable set.  Now, while tweaking some sets, I came across this :  We start with the natural numbers, $N$. We take the power set of the naturals, $P(N)$.  Then we remove all the finite subsets of $N$ from $P(N)$. Let us call this new set $S$. This set is the set of all infinite subsets of $N$.  It is easy to show that $S$ has uncountable cardinality, same as that of real numbers. This is because the removal of finite subsets only removes a countable number of elements. (Haven't posted this deduction, for it is very easy, but I may post it if it is not so evident)  Now, we seek to find an ordering on the set $S$. Every set in this set is an infinite subset of natural numbers, so each of these sets are well ordered by the natural ordering of $N$.  Taking any two sets in $S$, say $A$, and $B$, we seek to order them by checking their elements lexicographically. We compare the first two elements in $A$, and $B$. Let them be $a_1$, and $b_1$ respectively. If $a_1 = b_1$, then we move on to the second elements in the sets, $a_2$, and $b_2$, and so on. If, at any point, $a_n &lt; b_n$, then $A &lt; B$, or if $b_n &lt; a_n$, then $B &lt; A$.  This order seems to be a well ordering of the uncountable infinity of reals. I don't seem to have invoked the axiom of choice anywhere in the construction of this set $S$.  So, why isn't this a well ordering on the uncountable of reals?
What are Zombies and what causes them? Are there Zombie processes and Zombie objects? When trying to mount an exfat filesystem, I get the following error:  Error mounting /dev/sda6 at /media/gkp/Backup: Command-line  `mount -t "exfat" -o "uhelper=udisks2,nodev,nosuid" "/dev/sda6" "/media/gkp/Backup"'  exited with non-zero exit status 32: mount: unknown filesystem type 'exfat'   Exfat is used on some USB sticks and camera sd cards. What can I do to mount this type of filesystem? How to find patches with data in Raster and then how to extract those patches? I have a single band raster file as drawn in the labeled image attached.  The size of raster is around 4k pixel in each x and y axis. Large part of this raster is empty. Only in small portions of the raster contains data as labeled. Is there any efficient way I can extract rectangular patches around the data portions of the large tif raster file? Any pythonic way using gdal or rasterio or some other package. What I have done so far: I have followed from sklearn.feature_extraction.imageway to extract 2D patches where there is data as follows. from sklearn.feature_extraction.image import extract_patches_2d im = imageio.imread(largeFilePath) # reading the large image x, y = np.nonzero(im) # taking xy locations with non zero values  # determining xleft, xright, yleft and yright of the non zero area in  raster  xl,xr = x.min(),x.max()  yl,yr = y.min(),y.max()   #Extraing the non zero area from my original raster only_desired_area = im[xl:xr+1, yl:yr+1]  # my desired window to extract  window_shape = (480, 480)  # 2D Ptaches extraction B = extract_patches_2d(only_desired_area, window_shape, max_patches=100)  Issue: This doesn't have georeference information because I haven't used gdal or rasterio Is there a pattern to which Star Trek ships get the definite article? Some ships in Star Trek are referred to with definite articles. "The Enterprise", "The Defiant". Other ships are referred to without them. "Voyager", "Enterprise". Is there a pattern to or explanation for this behavior? Can't learn the third Word of Power from Wulfgar How can Cooper communicate with his daughter before the time he went to space? I wanted to know how I could configure multi-touch gestures in Ubuntu. In windows I can do this using the synaptics driver software.  I have already used synclient to configure the taps, palmdetect, scroll, etc. But I'd also want gesture support. Is is even possible?  System-Info: Ubuntu 12.10, Synaptics clickpad Proving identities (mod $pq$) using Fermat's little theorem? Floating point precision while using Python's max() Splitting all lines in layer at vertices using QGIS I want to automatically split all lines in a QGIS layer at their vertices (). I've done a Google search and found , which is quite close but the workflow is complicated. Because I'll have to train my co-workers (who are unfamiliar with GIS) to use this tool, I want something as simple as a plugin or something that doesn't require GRASS. Since it's been a long time from 2010 - the time of , I wonder if there is any better way to achieve the same result? What are some examples of induction where the base case is difficult but the inductive step is trivial? According to :     ...proofs by mathematical induction   have two parts: the "base case" that   shows that the theorem is true for a   particular initial value such as n = 0   or n = 1 and then an inductive step   that shows that if the theorem is true   for a certain value of n, it is also   true for the value n + 1. The base   case is often trivial and is   identified as such, although there are   cases where the base case is difficult   but the inductive step is trivial.   What are some examples of proofs by induction where the base case is difficult but the inductive step is trivial? I have a problem when I try to start a Workflow 2013 in SharePoint Server 2013. I believe the error is related with permissions, but I cannot be sure.  Here is the error message in the log:  RequestorId: ef9edb7c-cc3d-5e10-3681-eada907596a4.  Details: System.ApplicationException: HTTP 401 {"Transfer-Encoding":["chunked"],"X-SharePointHealthScore":["0"],"SPRequestGuid":["ef9edb7c-cc3d-5e10-3681-eada907596a4"],"request-id":["ef9edb7c-cc3d-5e10-3681-eada907596a4"],"X-FRAME-OPTIONS":["SAMEORIGIN"],"MicrosoftSharePointTeamServices":["15.0.0.4420"],"X-Content-Type-Options":["nosniff"],"X-MS-InvokeApp":["1; RequireReadOnly"],"Cache-Control":["max-age=0, private"],"Date":["Thu, 31 Jan 2013 16:36:44 GMT"],"Server":["Microsoft-IIS\/8.0"],"WWW-Authenticate":["NTLM"],"X-AspNet-Version":["4.0.30319"],"X-Powered-By":["ASP.NET"]}  The HTTP response content could not be read.  'Error while copying content to a stream.'. at Microsoft.Activities.Hosting.Runtime.Subroutine.SubroutineChild.Execute(CodeActivityContext context) at System.Activities.CodeActivity.InternalExecute(ActivityInstance instance, ActivityExecutor executor, BookmarkManager bookmarkManager) at System.Activities.Runtime.ActivityExecutor.ExecuteActivityWorkItem   The question is: What permissions do I need to configure in SharePoint for the WF publisher and the WF manager service account?  I’ve set a WF Manager service account named “wfservice” (this account is a local admin and has the sysadmin permissions in SQL Server), and I published the workflow and tested it using the account “wfuser”. Both accounts have full control permissions in the web app and are site owners, for testing WF 2013 purposes.  I’ve already done the DNS flush, as mentioned in Andrew Connell’s article, and I’m still getting an Unauthorized exception in the Item Workflow Status.  Anyone knows what’s going on? Which permissions do I need to configure? How do I upgrade to a newer version of Ubuntu? SQL-Server: The backup set holds a backup of a database other than the existing Can the coefficient of static friction be less than that of kinetic friction? Why did the snake wink at Harry at the zoo? This is mostly a memory question - I'm having a hard time remembering this and I can't read the book right now.  On the first book, a snake at the zoo winks at Harry. For the sake of the question, we'll assume that snakes can in fact wink.  I have a fuzzy memory here - I think that it winked before Harry had any kind of interaction with the snake (was this before or after Harry broke the glass?)  So, why did the snake wink at Harry? Given that they had not met ever before.  I suppose that the only reason it would wink at Harry would be because it knows Harry can communicate with it. But this would imply that snakes are capable of sensing such ability on wizards - is there (other) evidence that this is true? Cross-site inbookmarks:mine search inbookmarks:mine was fixed for searching within a particular Stack Exchange site, but often I find myself wanting to search for a question I favorited/bookmarked, but not remembering which site it was on when it could conceivably have been on a number of different sites. On the cross-site search at  it does not work, presumably because we have different user ids on each site. Is there a way it could be made to work? Note that this request is for searching, not just viewing, so it's not a duplicate of . Just viewing is not very helpful when you have a huge volume of bookmarks across Stack Exchange sites. How do I alter a language item link? I am looking to modify the default output of Drupal 8 of links in a certain situation, the language switcher. Ideally I want to be able to do that in a twig template and not have to produce a  that overwwrites that whole link generation system and add a BIG if for the cases I need to overwrite.  I think the output layout should be controllable in the twig template similar to  (this answer outputs the same url for every languages)  I am using bootstrap as a base theme so i'd like to use the bootstrap markup for my links (btn btn-primary, dropdown)  Here is my code I am trying to make links--language-block.html.twig  {%- if links|length == 2 -%}     {# show only alternate language button #}     {%- for key, item in links -%}         {%- if not item.attributes['#options']['set_active_class'] -%} {# &lt;--- this is always true!? #}             &lt;a href="{{ item.link['#url'] }}" class="btn btn-primary"&gt;{{ item.link['#title'] }}&lt;/a&gt; {# #url is always the same what ever the language it is pointing to! #}         {%- endif -%}     {%- endfor -%} {%- elseif links|length &gt; 2  -%}     {# show selected language in button and other languages in drop down #}     &lt;button class="btn btn-primary dropdown-toggle" type="button" data-toggle="dropdown"&gt;{{ selectedLanguage }}&lt;span class="caret"&gt;&lt;/span&gt;&lt;/button&gt;     &lt;ul class="dropdown-menu"&gt;         {% for key, item in links %}             {%- if not item.attributes['#options']['set_active_class'] -%} {# &lt;--- this is always true!? #}             &lt;li&gt;&lt;a href="{{ item.link['#url'] }}"&gt;{{ item.link['#title'] }}&lt;/a&gt;&lt;/li&gt;             {% endif %}         {% endfor %}     &lt;/ul&gt; {%- endif -%}   Anyone has an idea on how to do this? "The ones" or "those"? I recently corrected  &quot;ghettos, such as the ones found...&quot; to &quot;ghettos, such as those found...&quot;  Was I correct, or are both versions right? I'm well aware of the combinatorial variant of the proof, i.e. noting that each formula is a different representation for the number of subsets of a set of $n$ elements. I'm curious if there's a series of algebraic manipulations that can lead from $\sum\limits_{i=0}^n \binom{n}{i}$ to $2^n$.