How many days in a week? Seven both to hear and speak. How many weeks in a month? Four, as the swift moon runneth.  What is the meaning of 'as the swift moon runneth'?
What is the meaning of “runneth” in ?
How do I upgrade to the unreleased version of Ubuntu for testing? How can I get Firefox to open torrent files with Transmission? Every time I download a torrent file (.torrent), Firefox thinks I should open it with a text editor. How can I get it to open with Transmission? In Edit -> Preferences -> Applications, there's no setting for torrent files, and no apparent way to add a new filetype. Here is a question from my number theory class.  Prove  $$(p-k)!(k-1)!\equiv (-1)^k \text{ mod p} $$ Help please! Cyclic vectors in a real vector space Let $V$ be an n-dimensional vector space over $\mathbb{R}$ and $T:V \rightarrow V$ be linear. Call a vector $v \in V$ cyclic if $V$ is spanned by $\{v, \ Tv, \ T^2v,..\}$.  Question:  Show that $v$ is cyclic for $T$ then there is some $k \geq 1$ such that   $$B=\{v, \ Tv,..T^{k-1}v \}$$ is linearly independent in $V$ and that $T^kv$ lies in  the span of $B$.  Thoughts:  If we suppose that no such $k$ exists, then every subset of the form $\{v, \ Tv,..T^{l-1}v \}$ is linearly dependent, or it is linearly dependent with $T^lv$ not lying in it span.  There are in effect then two cases to consider.  Suppose every subset of the form $\{v, \ Tv,..T^{l-1}v \}$ is linearly dependent. Then $T^{l-1}$ can be expressed as a linear combination of $v,...,T^{l-2}v$. Now, $\{v, \ Tv,..T^{l-2}v \}$ is also linearly dependent by assumption and so we can express $T^{l-2}$ as a linear combination of  $v,...,T^{l-3}v$ etc... Continuing in this way, we show that $T^{l-1}v= \lambda v$ for some $\lambda \in \mathbb{R}$. Thus $$B=\{ \mu v \ | \ \mu \ \text{is an eigenvalue of} \ T^mv \ \text{for some} \ m \}$$ This is 'at best' countably infinite, and therefore could not span $V$ even if it were 1-dimensional, wince our base field is $\mathbb{R}$, which is uncountable.  Suppose then that $B$ is linearly independent for some $k$ but that $T^kv$ does not lie in its span. I can't see how to progress this argument.  Note: This question is for second year Undergraduates, and I think there must be some more simple approach; even the first part surprises me if we need to argue using the uncountability of $\mathbb{R}$, so any alternative approaches are also appreciated. I am visiting Vietnam in November 2015, I will entering the country on the 10th and my flight home is 14 days later, I will be leaving Vietnam and travelling to Cambodia in between the 2 weeks then travel back into Vietnam to get my flight home on the 24th November, do I need a visa? Can't get hold of anyone at Embassy and not clear about entering twice on the website. When is using the past perfect tense not necessary? Ackermann Function primitive recursive I am reading the wikipedia page on ackermann's function,   And I am having trouble understanding WHY ackermann's function is an example of a function which is not primitive recursive.  I understand that the ackermann function terminates, and thus is a total function. So why is it not primitive recursive? The only information that i can find on the wikipedia page is      [Ackermann's function] grows faster than any primitive recursive function and is therefore   not primitive recursive   Which isn't a good example of why it is not primitive recursive.  Could anyone explain to me how exactly ackermann's function is NOT primitive recursive please? I am using the algorithmic package to typeset an algorithm. I would like to have connecting lines between the beginning and end of a loop or conditional like in the algorithm2e package. Is there an easy way to accomplish this, or am I better off switching to algorithm2e? Is this a valid proof for the reverse triangle inequality: Given $x,\,y\in\mathbb{R}^n$, $\|x-y\|\ge |\|x\| - \|y\||$. $\def\a{{\bf a}} \def\b{{\bf b}}$ $\def\x{{\bf x}}$ $\def\y{{\bf y}}$  I've seen various methods of proving the reverse triangle inequality but I was wondering if this one is fine as well.   Prove the reverse triangle inequality:  Given $\x,\,\y\in\mathbb{R}^n$, $\|\x-\y\|\ge |\|\x\| - \|\y\||$.   $\textbf{Solution}$ Let $\x,\y \in \mathbb{R}^n$. Now, $\x=\x-\y+\y$ and so $||\x|| = ||\x-\y+\y|| \le ||\x-\y|| + ||\y||$ by triangle inequality. Thus, $||\x|| - ||\y|| \le ||\x-\y||$ [*].   Now for $\y$. Again, $\y = \y-\x+\x$ so $||\y|| = ||\y-\x+\x||$ implies $||\y|| \le ||\y-\x|| + ||\x||$ by triangle inequality. So, $||\y|| - ||\x||\le ||\x-\y||$. Hence, $-||\x-\y|| \le ||\x|| - ||\y||$ [**].   By [*] and [**], $-||\x-\y|| \le ||\x|| - ||\y|| &lt; ||\x-\y||$ implying $\bigl ||\x|| - ||\y|| \bigr\rvert \le ||\x-\y||$ for all $\x,\y \in \mathbb{R}^n$. How can I find my hardware details? Is there any built-in software or terminal method allowing me to view the hardware profiles on my system? Windows equivalent of such a feature would be Device Manager. How to draw a return arrow from node-3 to node-1 SUID-bit not working for executables within /tmp directory Printing the value of getuid() and geteuid() from an executable with SUID-bit (chmod +s) turned-on, seems to result with the original caller ID instead of the owner id if the executable is located within the /tmp directory.  When compiling the exact same code to home directory (and executing chmod +s), this seems to work as expected.  I've searched a lot and could not find any reference to such behavior.  Does anybody know why is this happening?  this source is simple as that:  #include &lt;stdio.h&gt; #include &lt;stdlib.h&gt; #include &lt;sys/types.h&gt; #include &lt;unistd.h&gt;  int main(){     printf("%d\n%d\n", getuid(), geteuid());     return 0; } I'm looking at buying a second-hand Mac, probably one that does not include an OS installation disk.  How can I scan it to make sure that it has not had security threats installed on it?  Is there a CD or DVD image I can boot it up with to perform this scan offline?  Edit: prospective machine would be a 2011- or 2012-vintage MacBook Pro.  Also note that I don't have reliable access to high-speed internet, so solutions that involve downloading 5GB over the Internet are not ideal.  For others, though,  may be helpful. Get the generated SQL statement from a SqlCommand object? I have the following code:  Using cmd As SqlCommand = Connection.CreateCommand     cmd.CommandText = "UPDATE someTable SET Value = @Value"     cmd.CommandText &amp;= " WHERE Id = @Id"     cmd.Parameters.AddWithValue("@Id", 1234)     cmd.Parameters.AddWithValue("@Value", "myValue")     cmd.ExecuteNonQuery End Using   I wonder if there is any way to get the final SQL statment as a String, which should look like this:  UPDATE someTable SET Value = "myValue" WHERE Id = 1234   If anyone wonders why I would do this:   for logging (failed) statements for having the possibility to copy &amp; paste it to the Enterprise Manager for testing purposes Give an example of three positive integers m, n, and r Screen resolution stuck at 1024x768 Is there a subtle difference between "somebody" and "someone", "anybody" and "anyone"? Are there any subtle differences between "somebody" and "someone", or can they be used completely interchangeably? Similarly, can you imagine a situation in which you would prefer "anybody" to "anyone" or vice versa? Automatically convert quotations in the form of "abc" to become ``abc" I'm having trouble understanding the ROC curve.  Is there any advantage / improvement in area under the ROC curve if I build different models from each unique subset of the training set and use it to produce a probability? For example, if $y$ has values of $\{a, a, a, a, b, b, b, b\}$, and I build model $A$ by using $a$ from 1st-4th values of $y$ and 8th-9th values of $y$ and build model $B$ by using remained train data. Finally, generate probability. Any thoughts / comments will be much appreciated.   Here is r code for better explanation for my question:  Y    = factor(0,0,0,0,1,1,1,1) X    = matirx(rnorm(16,8,2)) ind  = c(1,4,8,9) ind2 = -ind  mod_A    = rpart(Y[ind]~X[ind,]) mod_B    = rpart(Y[-ind]~X[-ind,]) mod_full = rpart(Y~X)  pred = numeric(8) pred_combine[ind]  = predict(mod_A,type='prob') pred_combine[-ind] = predict(mod_B,type='prob') pred_full          = predict(mod_full, type='prob')   So my question is, area under ROC curve of pred_combine vs pred_full. jQuery: Selecting and manipulating html elements outside the DOM