Which is Better to Use?
Using "utilize" instead of "use"?
As we know a first order theory $T$ is finitely axiomatizable if there is a finite set $F\subseteq T$ of axioms such that $F\vdash \sigma$ for every $\sigma \in T$.   How we can prove if $\mathsf{ZF}$ is consistent, then $\mathsf{ZF}$ is not finitely axiomatizable? By using the Reflection Theorem or any other if we could use? Change date format [YYYYMMDD] to [MM/DD/YYYY] I generated a report that formats date as 20160509 and my Google Sheets locale is already set to United States. I've played around with various options within Format > Number > Date Format but I can't change the dates to MM/DD/YYYY format without doing a simple find and replace. How do I accomplish this? We have a fairly big MS SQL 2008R2 database that resides on a SSD drive. The drive itself only has ~110Gb of space, and the database files are the only files on the drive.  The database is in "Simple" recovery mode, and only has two files, .MDF and .LDF.   The disk is now nearly full: the MDF is currently 109Gb in size. However, SSMS tells me there's nearly 18Gb of "Space Available" (in the 'General' properties page), and if I go through the motions of Shrinking the file it also tells me there's 18Gb of space free. SSMS also tells me the database size is around 132Gb, which surprises me - that wouldn't fit on the drive!  From what I've read, shrink is a really bad idea. However, I'm starting to see replication errors (could not allocate space for object). We've previously tried shrinking the database, but within a few hours the file was back to it's original size.  How should we proceed - given there's apparently 18Gb of free space, should SQL automatically use that free space? Or is it as simple as: we really need more disk space? How can we connect a PHP script to MS Access (.mdb) file?  I tried by including following PHP code:  $db_path = $_SERVER['DOCUMENT_ROOT'] . '\WebUpdate\\' . $file_name . '.mdb'; $cfg_dsn = "Provider=Microsoft.Jet.OLEDB.4.0;Data Source=" . $db_path; $odbcconnect = odbc_connect($cfg_dsn, '', '');   But it failed and I received following error message:   Warning: odbc_connect() [function.odbc-connect]: SQL error: [Microsoft][ODBC Driver Manager] Data source name not found and no default driver specified, SQL state IM002 in SQLConnect in C:\web\WebUpdate\index.php on line 41 How can I assign custom icons to folders? How to make unit selection circles merge? Suppose $f$ is an isometric (i.e., distance preserving) function on $\mathbb{E}^2$ such that $f(0,0) = (0,0)$.  Then I want to show that $f$ is necessarily linear.  Now $f$ is linear iff $f$ is both additive and homogenous.  The following is an attempted proof for the homogeneity of f (missing the last step); still more, I have no idea how to argue for the additivity of $f$.  Any ideas?  Let $x \in \mathbb{E}^2$ and $\alpha \in \mathbb{R}$   We know that $\forall x \in \mathbb{E}^2$, $\Vert x - 0 \Vert = \Vert f(x) - f(0)\Vert = \Vert f(x) - 0 \Vert$ so that $\Vert x\Vert = \Vert f(x)\Vert$.  From this we immediately have the following facts:  $\Vert x \Vert = \Vert f(x) \Vert$  $\Vert \alpha x \Vert = \Vert f(\alpha x) \Vert$  We can then argue that since $\Vert \alpha x\Vert = |\alpha| \Vert x \Vert = |\alpha| \Vert f(x) \Vert = \Vert \alpha f(x) \Vert$, we also have that $\Vert f(\alpha x) \Vert = \Vert \alpha f(x)\Vert$.  Finally, we have that  $\Vert \alpha x - x \Vert = \Vert \alpha f(x) - f(x) \Vert$   iff $ \Vert (\alpha - 1)x \Vert = \Vert (\alpha - 1) f(x) \Vert$   iff $|\alpha - 1| \Vert x \Vert = |\alpha - 1| \Vert f(x) \Vert$  Since the last of these statements is in fact true, we now have $\Vert \alpha x - x \Vert = \Vert \alpha f(x) - f(x) \Vert$ as desired.  Now at this point it seems like I have all of the facts required to assert that $f(\alpha x) = \alpha f(x)$, but I can't figure out how to formally state why without illegally appealing to visual intuition.  Any ideas? How do I check if an array includes a value in JavaScript? An .mov video that is upside down in Windows appears right side up in OSX How can I add "page # of ##" on my document? I want to add a footer to my document displaying the current number out of total number of pages. How do I do that? The  tag doesn't appear to be very useful.  It's used in a variety of ways (for reading, writing, showing, transforming, compiling, translating, obfuscating, obtaining, ... source code) on 1747 questions right now, and doesn't appear to be adding any classification value to the site.  Can we get rid of it? I have a matrix and need to highlight some elements in the matrix. I have found how to highlight a single element (I want to put the cell in the square):  $$ A = \begin{bmatrix} \fbox{0} &amp; \fbox{0} &amp; 0 \\  \fbox{0} &amp; \fbox{0} &amp; 0 \\ 1 &amp; 1 &amp; 1 \\  \end{bmatrix}$$   But how can I outline elements of the submatrix like in the picture below? I need just a frame where some elements are located. Is there a term for the moment when a lot of users visit/log onto your website at the same time? Is there a term for the moment when a lot of users visit/log onto your website at the same time? How to make a traditional division How to make the traditional division? Like that:  a |b_ r  c Emacs: How to use a major mode for non-standard file extension Suppose I have a dataframe consisting of six time series. In this dataframe, some observations are missing, meaning at some timepoints all time series contain a NA-value. In R, one possible imputation package that can be used to impute time series data is Amelia. However, this package does not work for observations that are completely missing. Are there other ways to impute my data? For what it's worth, the amount of missing observations is less than 20% of all observations. Reputation has been changed but not reflected on tooltip. I have a large file and I would like print from each sequential 50 lines , the 15th and 25th lines.  sed -n '15,25p' inputfile   How to modify this command to print only lines 15 and 25 and to loop over each 50 lines in the file. Will an iOS reinstall make a jailbroken iOS device "unjailbroken" and “supported by Apple” again? Will an    Work on any jailbroken-iPhone and Make a jailbroken-iPhone "unjailbroken"? Make a jailbroken-iPhone "supported by Apple"?   Similarly, does such an iOS reinstall reset the iPhone (jailbroken or not) back to a "clean, factory default" state?  My near-term purpose: I have an iPhone 4S running iOS 5.1 I'd like to jailbreak to at least install better Google Voice integration like . Kill Command in linux