Interpretation of a statement that I think I can prove by mathematical induction
Proof of an inequality by induction: $(1 + x_1)(1 + x_2)...(1 + x_n) \ge 1 + x_1 + x_2 + ... + x_n$
What's the best option to display Unicode text (hebrew, etc.) in VB6 I have some customers who want to use our speech therapy software in Hebrew.  The programs are in VB6. The best option I'm aware of are:   use the Forms 2.0 controls from MS Office, but you can't distribute them.    $899   $499   Any other options? The setuid permission bit tells Linux to run a program with the effective user id of the owner instead of the executor:  &gt; cat setuid-test.c  #include &lt;stdio.h&gt; #include &lt;unistd.h&gt;  int main(int argc, char** argv) {     printf("%d", geteuid());     return 0; }  &gt; gcc -o setuid-test setuid-test.c &gt; ./setuid-test  1000  &gt; sudo chown nobody ./setuid-test; sudo chmod +s ./setuid-test &gt; ./setuid-test  65534   However, this only applies to executables; shell scripts ignore the setuid bit:  &gt; cat setuid-test2  #!/bin/bash id -u  &gt; ./setuid-test2  1000  &gt; sudo chown nobody ./setuid-test2; sudo chmod +s ./setuid-test2 &gt; ./setuid-test2  1000     Wikipedia :     Due to the increased likelihood of security flaws, many operating systems ignore the setuid attribute when applied to executable shell scripts.   Assuming I'm willing to accept those risks, is there any way to tell Linux to treat the setuid bit the same on shell scripts as it does on executables?  If not, is there a common workaround for this problem? My current solution is to add a sudoers entry to allow ALL to run a given script as the user I want it run as, with NOPASSWD to avoid the password prompt. The main downsides to that is the need for a sudoers entry every time I want to do this, and the need for the caller to sudo some-script instead of just some-script I have some simple python code that searches files for a string e.g. path=c:\path, where the c:\path part may vary. The current code is:  def find_path(i_file):     lines = open(i_file).readlines()     for line in lines:         if line.startswith("Path="):             return # what to do here in order to get line content after "Path=" ?   What is a simple way to get the text after Path=? Is there an efficient way to enumerate the unique subgroups of the symmetric group? Naïvely, for the symmetric group $S_n$ of order $\left | S_n \right | = n!$, there are $2^{n!}$ subsets of the group members that could potentially form a subgroup. In addition, many of these subgroups are going to be isomorphic to each other. I feel that the question has an easy answer in terms of the conjugacy classes, but I don't see how. If the answer generalizes to all finite groups, please elaborate! I want to change the key bindings on some of the keys on my keyboard.  I want some to run commands and others to activate different keys.  What applications can I use to do this?      Index:       (from within System Settings)             I'm still looking for answers using dconf and any other method. Suppose I have a field that contain the following data:   ========================== |  Email Address         | ========================== | Jack@wonderland.com    | | Peter@nobodyland.com   | | Jill@wonderland.com    | ==========================   Is there a calculated formula in SharePoint that will give me the following result? (It will help me to retrieve the sub-string from the Email Address column and give me the answer as shown in the UserName and Domain column):   =========================================================== |  Email Address         |  UserName  |      Domain       | =========================================================== | Jack@wonderland.com    |   Jack     |   wonderland.com  | | Peter@nobodyland.com   |   Peter    |   nobodyland.com  | | Jill@wonderland.com    |   Jill     |   wonderland.com  | =========================================================== If $f(x + y) \leq yf(x) + f(f(x))$ for all real numbers $x$ and $y$, then prove that $f(x) = 0$ for all $x ≤ 0$. What is the typographic reasoning here? Does it make the text look less crowded? I want to create a simple figure where images are connected with arrows. Here is what I did:  \begin{tikzpicture} \node[](A) {\includegraphics[width=0.2\textwidth]{a}}; \node[right=1mm of A](B) {\includegraphics[width=0.2\textwidth]{b}}; \draw[-&gt;] (A) to (B); \end{tikzpicture}     But I want the arrow to start and end right at the images with no space between. How can I do that? I try to understand why for a connected Lie group $G$ the first fundamental group $\pi_1(G)$ is abelian, and mainly why the second fundamental group is trivial $\pi_2(G)=0$?  Thanks for anyone who give me references for a 'simple proof' of these results Can anyone help me with this limit problem without L'Hopital rule and Taylor series? $$\lim_{x\rightarrow\ -\infty}\left(-2\frac{\arctan(x)}{\pi}\right)^x$$ How do I remove the OneDrive folder from my File Explorer folder tree in Windows 10? I don't use or want to use OneDrive, but after upgrading to Windows 10 it's been installed automatically and added to the sidebar of every explorer window:    I can't seem to figure out how to get rid of it. I can't uninstall it like a normal app, and I can't seem to unpin it in Explorer's options.  I tried following  to getting rid of it, but that seems to only remove stored OneDrive files.  I've also tried following another  and , but I can't seem to edit group policies on my computer (maybe because I upgraded from Win7 Home Premium?).  All I would really like is to be able to remove the OneDrive shortcut from my explorer sidebar, though being able to uninstall OneDrive would be a bonus.  I'm not sure what I should try now. Is there a way to remove OneDrive from Windows 10? How can I prevent someone from resetting my password with a Live CD? Recently one of my friends came over to my place, within 15 minutes he hacked my account using a Live CD and reset the password in front of me. I was baffled to see such a thing. Please guide me to prevent such a future attempt using a Live CD. Graph vertex chromatic number in a union of 2 sub-graphs $G_1$ is graph on the set of vertices $\{1,2,3,4,5,6,7,8\}$, $G_1$ vertex chromatic number is 5. $G_2$ is graph on the set of vertices $\{7,8,9,10,11,12,13,14,15,17,18,19,20\}$, $G_2$ vertex chromatic number is 7. We know $G_1$ and $G_2$ have an edge between vertex 7 and vertex 8. (We already used 2 different colors on them both). $G$ is graph on the set of vertices $\{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20\}$, and its set of edges is the union of the edges set of $G_1$ with the edges set of $G_2$. The vertex chromatic number of $G$ is: 5 / 7 / 12 / we can't know without further information Prove the answer. I think I got it, can someone approve? After the union to $G$, we copy the colors of $G_2$ to 7,8,9,10,11,12,13,14,15,16,17,18,19,20, obviously, $G$ vertex chromatic number is 7 and can't be less. We go through the vertices 1,2,3,4,5,6,7,8. We look for a vertex that doesn't connect to a different vertex. (There must be one, because if only one edge was missing in $G_1$, our chromatic number of $G_1$ was 7, but it's 5). Once we find a missing edge, we color both its vertices in the same color. We go through vertices 1-6, and color each vertex that doesn't have a color, with the colors of $G_2$ that we didn't use in $G_1$ (there should be 4-5 of them). I have a DB Server running CentOS 6.4 and MySQL 5.5 from RPMs (not source).  I have dozens of databases but one of them is being hit quite hard with large selects which locks out other updates which in turn locks out other selects (at least I think this is what's happening!)  To alleviate this I would like to replicate one of the databases onto the same server so that the writes can write to the "master" and reads can be done on the "slave". I don't have the luxury of additional hardware.  I have found a lot of guides on the internet describing how to replicate to a different server, and one () describing how to replicate to the same server but it doesn't seem to be geared towards retrofitting this functionality to an existing database with 10s of GB of data in it already. It also talks about compiling MySQL from source.  Does anyone know how I can retrospectively convert my MySQL 5.5 config to replicate one of my databases on the same server?  My existing DB runs on port 3306 so I feel it should be as easy as firing up another instance of MySQL on port 3307 and making some changes to my.cnf but not sure what changes.  Thanks in anticipation. Local BLAST Copy Number per Hit I generated a series of local BLAST databases using makeblastdb of metagenomic data and am searching for the presence of a particular gene. While I can do the normal BLAST analysis looking at e-values, % identity, etc. I haven't been able to figure out how to determine how many times a given sequence exists in the database.  So: given a BLAST database of metagenomic data where a particular gene may exist multiple times, how do I determine the copy number of a given BLAST hit?  Thanks in advance. I've been using the beta iCloud Photo Library for a week and a bunch of photos got duplicated and I'd like to wipe all the photos out and start over.  I have backups of all the photos and have turned off iPhoto Cloud Library on all iOS devices. When I log into the web app - it still shows dozens of albums and I can delete all the photos, then go to deleted items and then purge them, but the ghost albums are still there messing things up.  I've turned off the library entirely and you can see there is a 30 day waiting period.     If I click on albums, there are pages of them and no delete button anywhere. If I turn on the library on an iOS device, data starts flooding back as if I wanted to recover the photos.  I don't want to recover anything, I want a clean wipe and clean slate.  Currently, there are 7807 photos in the deleted album and no way to mass delete them. I have 31 albums that show up in iCloud and no way to delete them.  Is there some way to accelerate this or must people wait a month for a corrupt library to eventually be purged to start over?  (I have tickets open with AppleCare after  and it's escalated to engineering, but I was informed that it might be a week or two before it gets seen :-( Perhaps someone has a better idea to clear things out or noticed something I've missed.) How do I prevent and/or handle a StackOverflowException? I would like to either prevent or handle a StackOverflowException that I am getting from a call to the XslCompiledTransform.Transform method within an Xsl Editor I am writing. The problem seems to be that the user can write an Xsl script that is infinitely recursive, and it just blows up on the call to the Transform method.  (That is, the problem is not just the typical programmatic error, which is usually the cause of such an exception.)  Is there a way to detect and/or limit how many recursions are allowed?  Or any other ideas to keep this code from just blowing up on me? How to update Ubuntu terminal? How to update Ubuntu terminal? Background Nowadays, I see &quot;them&quot; used to mean &quot;those&quot; a lot. I don't know if it was as common in the past. For example, take &quot;one of &quot;. On researching about it, I found some people say it comes from a dialect of British English. Some others say it is a &quot;non-standard&quot; usage. I see this usage in Canadian English also, and it seems some people use it in a sarcastic way. Moreover, I have seen a song titled &quot;one of them days&quot;. I also read, in the book called &quot;A Broken Promise&quot;, &quot;&quot; Finally, Wikipedia says that it is a usage in  (a common name for the Southern Midland dialect of American English):  Pronouns and demonstratives &quot;Them&quot; is sometimes used in place of &quot;those&quot; as a demonstrative in both nominative and oblique constructions. Examples are &quot;Them are the pants I want&quot; and &quot;Give me some of them crackers.&quot;    Question(s): What would you say about the usage of this word? Is it correct? Could we use it in daily speech? Could this usage go beyond a specific dialect and be used in other dialects, regions, etc.? Does it really originate from Appalachian English? Why did this usage become popular among other English speakers? Note: I have already seen a similar question:  However, it only says, &quot;ungrammatical,&quot; there. This question is specific to this situation only, and there is more to it.