A follow up to this question:    For this 3-tuple: (a, b, c)...  Would it be {{a}, {a, b}, {a, b, c}}?
It seems to me that tuples are just as elementary as sets. Can tuples be reduced to sets?
Windows wildcards with files having more than 3 characters extensions On Windows 7, I have a directory containing the following four files:   xxx.txt xxx.txt2 xxx2.txt xxx2.txt2   With the file have more than 3 character as a file extension, the behavior of the wildcard * seems odd:  dir *.txt  10/13/2014  04:14 PM                 6 xxx.txt 10/13/2014  04:17 PM                 6 xxx2.txt 10/13/2014  04:17 PM                 6 xxx2.txt2 10/13/2014  04:14 PM                 6 xxx.txt2            4 File(s)             24 bytes            0 Dir(s)   6,660,980,736 bytes free   I would expect to see only the two files with txt extension and not the ones with txt2 (like it would on a Linux machine). Does MS-DOS ignore the truncate the file extension to 3 characters or does it add automatically another wildcard at the end? If I want to delete only the files with txt extension and not the one with txt2, which command should I use? Thanks Let $f:[0;1]\to\mathbb R$ be continiously differentiable Let $A$ be an $n \times n$ matrix with real enteries. Define $\langle x,y\rangle_A = \langle Ax,Ay\rangle, \quad x,y \in \mathbb R^n$ , where $\langle,\rangle$ is a standard inner product on $\mathbb R^n$. Then  $\langle x,y\rangle_A$ is an inner product iff  1)  $\ker A = \{0\}$.  2) $\operatorname{rank} A= n$.  3) all eigenvalues of $A$ are positive.  4) all eigen value of $A$ are non negative.  Clearly if $\ker A \neq \{0\}$, then there exist $x \neq 0$ such that $Ax =0$, then $\langle Ax, Ax\rangle_A = 0$, then $\langle ,\rangle_A$ is not inner product, so $\ker A = \{0\}$, thus rank of $A$ is $n$.  I am unable to check the 3) and 4) option. Please help to check the other option. Thank you Evaluate the integral $\int \frac{\sec x}{\sqrt{3+\tan x}}dx$ Evaluate the following integral.$$\int \frac{\sec x}{\sqrt{3+\tan x}}dx$$  On putting $t=\tan x$ I am getting $$\int\frac{1}{\sqrt{(t^2+1)(t+3)}}dt$$.  How should i proceed from here. How do I detect unsigned integer multiply overflow? I was writing a program in C++ to find all solutions of ab = c, where a, b and c together use all the digits 0-9 exactly once. The program looped over values of a and b, and it ran a digit-counting routine each time on a, b and ab to check if the digits condition was satisfied.  However, spurious solutions can be generated when ab overflows the integer limit. I ended up checking for this using code like:  unsigned long b, c, c_test; ... c_test=c*b;         // Possible overflow if (c_test/b != c) {/* There has been an overflow*/} else c=c_test;      // No overflow   Is there a better way of testing for overflow? I know that some chips have an internal flag that is set when overflow occurs, but I've never seen it accessed through C or C++.    Beware that signed int overflow is undefined behaviour in C and C++, and thus you have to detect it without actually causing it. For signed int overflow before addition, see . I have a map of a city and a .csv-file containing 700 geographic coordinates pointing to locations within that city.  How can I plot these 700 locations on the map? "I have never said" versus "I never said" I have never said this.   I never said this.    Is the usage of have in the first sentence justified or grammatically correct?   What is the difference in meaning?   When should I use one form over the other? It seems that there are many ways to prove the Sylow theorems. I'd like to see a collection of them. Please write down or share links to any you know. Use grep --exclude/--include syntax to not grep through certain files I'm looking for the string foo= in text files in a directory tree. It's on a common Linux machine, I have bash shell: grep -ircl &quot;foo=&quot; *  In the directories are also many binary files which match &quot;foo=&quot;. As these results are not relevant and slow down the search, I want grep to skip searching these files (mostly JPEG and PNG images). How would I do that? I know there are the --exclude=PATTERN and --include=PATTERN options, but what is the pattern format? The man page of grep says: --include=PATTERN     Recurse in directories only searching file matching PATTERN. --exclude=PATTERN     Recurse in directories skip file matching PATTERN.  Searching on grep include, grep include exclude, grep exclude and variants did not find anything relevant If there's a better way of grepping only in certain files, I'm all for it; moving the offending files is not an option. I can't search only certain directories (the directory structure is a big mess, with everything everywhere). Also, I can't install anything, so I have to do with common tools (like grep or the suggested find). What is the need for Autobiographer badge? What is the reason that Autobiographer badge is kept in Stack Exchange?  This does not show any participation and people can just fill garbage to achieve this badge.   Is there a reason behind it? For each of the following, give an example of a sequence of functions $f_n$ that converges to f  A. uniformly but not in the mean square sense.  B. in the mean square sense but pointwise nowhere.  I know that for part A the domain of the function cannot be bounded but other then that I'm not sure how to go about the problem I have a hard time finding a how-to.  I would like to set up a simple ESD mat and wrist wrap, but I am not sure about is the the 1 MOhm resistor should be, if at all.  Several options:   1 MOhm from ground outlet to the mat, wire from the common earthing on the mat to the wrist wrap. 1 MOhm from ground outlet to the mat, wire from another contact on the mat to the wrist wrap. 1 MOhm from ground outlet to the mat, 1 MOhm from the same mat contact to the wrist wrap. wire from ground outlet to the mat, 1 MOhm from the same mat contact to the wrist wrap. wire from ground outlet to the mat, wire from another mat contact to the wrist wrap.   I am not sure why the 1 MOhm wire is needed since the mat itself already has that kind of resistance (as long as the wrist wrap does not connect to ground directly, but through the mat).  Which solutions above are ok? Which is best? Should I do something else instead? Eigenspace of the companion matrix of a monic polynomial How do I prove that the eigenspace of an $n\times n$ companion matrix  $$ C_p=\begin{bmatrix} 0 &amp; 1 &amp; 0 &amp;\cdots &amp; 0\\ 0 &amp; 0 &amp; 1 &amp;\cdots &amp; 0 \\ \vdots&amp;\vdots &amp;\vdots&amp;\ddots&amp;\vdots\\ 0 &amp; 0 &amp; 0 &amp;\cdots &amp;1 \\ -\alpha_0 &amp;-\alpha_1 &amp;-\alpha_2 &amp;\cdots&amp;-\alpha_{n-1} \end{bmatrix} $$ equals $\operatorname{Span}\{v_{\lambda} \} $ where $v_{\lambda}$ is an eigenvector of the companion matrix w.r.t. the eigenvalue $\lambda$: $$ v_{\lambda} =  \begin{bmatrix} 1 \\ \lambda\\ \lambda^{2} \\ \vdots\\ \lambda^{n-1} \end{bmatrix}. $$ I'm trying to install Anbox in my new Ubuntu 16.04 using instructions from  . It seemed to work, but I got no icon in my dash, so I suspect that the installation is not complete. With Synaptic  Package Manager I can see that anbox-common &amp; anbox-modules-dkms are installed, but I have no icon in my dash, so I tried running   sudo snap install --edge --devmode anbox   and got this error:  error: cannot install "anbox": Get    https://search.apps.ubuntu.com/api/v1/snaps/details/core?channel=stable&amp;fields=anon_download_url%2Carchitecture%2Cchannel%2Cdownload_sha3_384%2Csummary%2Cdescription%2Cdeltas%2Cbinary_filesize%2Cdownload_url%2Cepoch%2Cicon_url%2Clast_updated%2Cpackage_name%2Cprices%2Cpublisher%2Cratings_average%2Crevision%2Cscreenshot_urls%2Csnap_id%2Csupport_url%2Ccontact%2Ctitle%2Ccontent%2Cversion%2Corigin%2Cdeveloper_id%2Cprivate%2Cconfinement%2Cchannel_maps_list:    dial tcp: lookup search.apps.ubuntu.com on [::1]:53: read udp    [::1]:54255-&gt;[::1]:53: read: connection refused   What am I doing wrong? Why was the connection refused? According to the instructions, it seems this is the correct command to install it.  ps: I'm not that familiar with Linux, I'm more of a Windows guy, trying to learn Linux. Please require more reviewers on First Posts On the one hand, I see very few posts in the review queue when I visit.  On the other hand, I see a lot of pretty awful first posts sitting on the front page.  This leads me to suspect that robo-reviewers are blowing through the queue.  Given how empty the queue is, could you please increase the number of people who have to check in before a post leaves the queue?  Of course, some honey-pot solution to detect and disable the auto-clickers would be even better. What is a StackOverflowError? Multiplication of matrices &mdash; taking the dot product of the $i$th row of the first matrix and the $j$th column of the second to yield the $ij$th entry of the product &mdash; is not a very intuitive operation: if you were to ask someone how to mutliply two matrices, he probably would not think of that method. Of course, it turns out to be very useful: matrix multiplication is precisely the operation that represents composition of transformations. But it's not intuitive. So my question is where it came from. Who thought of multiplying matrices in that way, and why? (Was it perhaps multiplication of a matrix and a vector first? If so, who thought of multiplying them in that way, and why?) My question is intact no matter whether matrix multiplication was done this way only after it was used as representation of composition of transformations, or whether, on the contrary, matrix multiplication came first. (Again, I'm not asking about the utility of multiplying matrices as we do: this is clear to me. I'm asking a question about history.) $E[e_te_s\Delta B_t\Delta B_s]$ for $\Delta B_t$ Brownian motion increments and $e_t(\omega)$ a measurable function. Failed review audit - for me quite clearly off-topic, can it be removed from the audit set? Number of onto functions