Suppose $\mathcal{A} = \{a,b\}$ or $\mathcal{A} = \{a \}$. Is it ok to write $\mathcal{A} \setminus b$ to indicate  \begin{cases}    \mathcal{A} \setminus b &amp; \text{if } b \in \mathcal{A} \\   \mathcal{A} &amp; \text{otherwise}  \end{cases} If not, what would be an appropriate notation for that?
The "correct" way to write a set without a specific element is as follows: $S \setminus \{s\}$  But in some contexts this is cumbersome to write/type or read, and it detracts from the flow of the writing. Is it acceptable to just use $S \setminus s$?  Edit: By "cumbersome" i mean they look bad when you're trying to inline formulas in LaTeX.
I just want Telegram to be run and I have added it to startup apps. The point is that I need it to be minimized. Any commands? This equation is directly given in my book and I am don't know anything about its proof.I tried L'Hospital rule by differentiating the both numerator as well as denominator(division rule), but the result is still coming in indeterminate forms.I am a beginner , and haven't practiced limits that much. This formula is really confusing me. "To your left" versus "on your left" Value too great for base (error token is "09") Argument list too long error for rm, cp, mv commands How can I sound proof bathroom walls? I'm trying to figure out the best, least intrusive way of sound proofing the walls of a bathroom. The bathroom shares a wall with my bedroom, and my 3 yea old's bedroom. The main problem is the sound of water running (plus every bump on the counter and everything) echos loud and clear through the wall into my sons room.  I found  and it seems like a good choice. Another option is adding another layer fo drywall with something like  between them. But all the walls and ceilings in the house are textured. So replacing just one or two walls in a room is just not possible.   This is the layout of the two rooms. I've added red box around the wall with the most noise.   Is there anything else I'm missing here that I could do to dampen the noise short of tearing the bathroom apart? I found a feature request at  but it doesn't seem easy to get a column view with Nautilus while with Mac OS X it's a default feature.  Have I missed something or is this not currently possible? I've been told that when "the" is proceeded by a vowel sound, like "apple" or "hour", it's pronounced as "thee" and not as "thu".  But after listening to a couple of songs, I noticed that sometimes this "rule" is not followed. Take for example the two Katy Perry's songs, "Roar" and "The one that got away". In the first she sings "I got thee eye of thu tiger", but in the second she sings "Thu one that got away".  I don't know if it was sang this way to better suit the song melody (I understand nothing about those techniques), but I got confused. What's the correct pronunciation?  Thanks in advance. How do you change your hostname in Windows 7? Not the computer name, but the hostname. Angle between 2 points Given the following image:   $\hskip{1.5 in}$   Supposing $A(100, 300)$ and $B(300, 100)$, how can I find the angle $\alpha$ between A and B?  On a side note, what's the main difference between a point and a vector? translating a point to a vector is as simple as Point = Vector? Sometimes I find articles where the terms are interchangable How i recover my icloud username and password One of the topics that seems to come up regularly on mailing lists and online discussions is the merits (or lack thereof) of doing a Computer Science Degree. An argument that seems to come up time and again for the negative party is that they have been coding for some number of years and they have never used recursion.  So the question is:   What is recursion? When would I use recursion? Why don't people use recursion? Recently a few friends and I came up with an idea for an app. To facilitate the creation of it, we set up LAMP on an Ubuntu Server 12.04. This box is running from my home. We've set up 3 user accounts. I'm still pretty new to Linux, but I have a bit of experience from using Ubuntu on my own box.  Today I was playing around with SSH and looking at the logs (I need to learn how to read that information to know how the server is performing, right?) and I saw the strangest thing.  In /var/log/auth.log and /var/log/auth.log.1 I saw a bunch of failed login attempts for 'root' and a few usernames I'm not familiar with. I looked over them and for as far as I can see no user has been authenticated except for the actual users on the system. A lot of the IP-addresses listed seem to be from Russia.  As of now this server contains nothing but a vanilla Ubuntu Server with LAMP, but even so, with the following command:  sudo grep -i fail /var/log/auth.log | wc -l   I get 3412 as a result. This seems very excessive for a server that has been up since April 8th. It gets worse, because running the above command on auth.log.1 returns 23075 (!!!!) results.  It seems obvious that people are trying to break into the server. Not that it contains anything of value, but once we start making progress on the app we wouldn't want our intellectual property stolen.  Should I be worried? And what can I do about it?  EDIT:  I found some very useful information  and this allowed me to run a script that splits and sorts all the invalid passwords and invalid users that tried to log in. May come in handy to someone who ended up here through Google! My flight got canceled yesterday and I am currently waiting for the delayed next flight.   Is there any website that keeps records of airlines being delayed/canceled? I would like to know my chances. I did find some sites through google (flightaware, flightstats), but they focus on us flights only and I am currently in the azores. Lebesgue measurable set that is not a Borel measurable set Random integer in VB.NET I need to generate a random integer between 1 and n (where n is a positive whole number) to use for a unit test. I don't need something overly complicated to ensure true randomness - just an old-fashioned random number.  How would I do that? Google spreadsheet sorting messes up cell comments I'm running into this weird problem with Google spreadsheets: if the cells have comments on them and I sort the spreadsheet, the rows sort but the comments stay in the same position, and don't move with the cells they're attached to.  In other words, the cells look like this:  A C  &lt;-- comment on this cell B   and then I sort by this column:  A B  &lt;-- comment remains on this cell (stays in position) C  &lt;-- comment should have remained attached to this cell   This means that sorting is completely broken and I can't use it at all, because I clearly need the cell comments to stay with the cell they're attached to.  Is this a bad bug in Google Spreadsheets, or am I missing something here? How to change an application Icon How to debug EntityMalformedException? I've got fatal error EntityMalformedException: Missing bundle property on entity of type node. in entity_extract_ids() (line 7700 of .\includes\common.inc) when trying to access user/xyz.  I tried to retrieve info about the malformed node at line 7700, where the error message is built, thinks like :  if (!isset($entity-&gt;{$info['entity keys']['bundle']}) || $entity-&gt;{$info['entity keys']['bundle']} === '') {  dpm($info);// or dpm($entity);  throw new EntityMalformedException(t('Missing bundle property on entity of type @entity_type.', array('@entity_type' =&gt; $entity_type))); }   dpm($entity) returns an unexpected user object, and $info a huge qty of things.   Could somebody put me on the right way ?  I already read whatever I could find about Missing bundle property errors, but none helped solving.  dpm($entity) returns  uid (String, 2 characters ) 70 name (String, 9 characters ) John pass (String, 55 characters ) $S$DUwPuOuDPiDL4nRTYXqc7a5uOfMKey7pyhOFUEKka1XM... mail (String, 30 characters ) john@example.com theme (String, 0 characters ) signature (String, 0 characters ) signature_format (String, 13 characters ) filtered_html created (String, 10 characters ) 1396286331 access (String, 10 characters ) 1397146661 login (String, 10 characters ) 1396513460 status (String, 1 characters ) 1 timezone (NULL) language (String, 2 characters ) fr picture (NULL) init (String, 30 characters ) john@example.com data (Array, 5 elements) roles (Array, 1 element) og_user_node (Array, 0 elements) message_subscribe_email (Array, 1 element) field_bio (Array, 0 elements) field_name_first (Array, 1 element) field_name_last (Array, 1 element) field_facebook_url (Array, 0 elements) field_linkedin_url (Array, 0 elements) field_twitter_url (Array, 0 elements) user_trusted_contacts (Array, 1 element) group_group (Array, 1 element) group_access (Array, 1 element) metatags (Array, 0 elements) rdf_mapping (Array, 3 elements) realname (String, 13 characters ) John Doe content (Array, 13 elements) entity_view_prepared (Boolean) TRUE privatemsg_disabled (Boolean) FALSE Proving that cardinality of the reals = cardinality of $[0,1]$ Homework problem, intro to topology. Here's what I've done so far. Am I on the right track? And, how would you advise me to proceed from here?  I have already established that $\left |[0,1] \right | = \left |[0,1) \right|$. Now I wish to show that $\left |[0,1) \right| = \left |\mathbb{R} \right |$. I will try to do this by constructing a bijection $f: [0,1) \rightarrow \mathbb{R}$.  Given $x \in [0,1)$, consider the following countably infinite subset of $\mathbb{R}$: $x^c = \{x+1, x-1, x+2,x-2,x+3,x-3,\ldots   \}$.  Then we have that $$ \bigcup_{x \in [0,1)} x^c = \mathbb{R}, $$ and if $x_1, x_2 \in [0,1)$ with $x_1 \neq x_2$, then $x_1^c \cap x_2^c = \varnothing$.