Ideals in direct product of rings
Structure of ideals in the product of two rings
Where can I ask a question about finding general software that meets certain requirements? I have a list of requirements for a program, but I don't know what program meets these criteria. That's about general-purpose software, for example, not a programming IDE or statistical workbench, questions about which would certainly go to respective sites.  Is this question appropriate on Stack Overflow? Where should I ask about it? On Super User or elsewhere? All I remember is the guy was sent to a planet to test something or he did something illegal, and time moved really fast on the planet but slow to the outside world. He had to fix something to leave the planet I think. His dad was also dying and he checked how many days he had left every day, but in the end his dad didn't actually die as time was fast. It took place on a sandy planet. (no) Properties in Java? Is there a simple, constructive, 1-1 mapping between the reals and the irrationals? Is there a simple, constructive, 1-1 mapping between the reals and the irrationals?  I know that the Cantor–Bernstein–Schroeder theorem implies the existence of a 1-1 mapping between the reals and the irrationals, but the proofs of this theorem are nonconstructive.  I wondered if a simple (not involving an infinite set of mappings) constructive (so the mapping is straightforwardly specified) mapping existed.  I have considered things like mapping the rationals to the rationals plus a fixed irrational, but then I could not figure out how to prevent an infinite (possible uncountably infinite) regression. Is the empty set a group? I know that a set G with a binary operation $*$ is a group, if:   $a*b\in G$, for all $a, b \in G$. $*$ is associative:   $$(a*b)*c=a*(b*c) \\ \text{for all }a, b, c\in G.$$   An identity element $e \in G$ exists, such that   $$a*e = e*a = a\\ \text{for all }a\in G.$$   For all elements $a \in G$, there exists an $a^{-1} \in G$, such that:   $$a*a^{-1} = a^{-1}*a=e.$$  Can I use that to show that the empty set is a group? Not including stdlib.h does not produce any compiler error! Is there a way of moving unwanted villagers out faster? A problem regarding to Schur's lemma Let $\rho: G \to GL_n(\mathbb{C})$ be an irreducible representation, and $g\in Z(G)$. Show $\rho(g)$ is a scalar multiple of the identity matrix $I$.   I think I have it, here is my solution:  Since $\rho(g) \in Hom_G(\mathbb{C}, \mathbb{C})$ and $\rho$ is irreducible, consider a nonzero eigenvalue of $\rho(g)$, say $\lambda$, we have $\rho(g) -\lambda $ is a zero map by Schur's lemma, as the map contains a non-trivial kernel (i.e. the eigenvectors associated to $\lambda$ are in the kernel).  But I didn't use the condition that  $g\in Z(G)$, so are there something wrong with my solution? Why does parameter expansion with spaces without quotes work inside double brackets "[[" but not inside single brackets "["? I'm confused with using single or double brackets. Look at this code:  dir="/home/mazimi/VirtualBox VMs"  if [[ -d ${dir} ]]; then     echo "yep" fi   It works perfectly although the string contains a space. But when I change it to single bracket:  dir="/home/mazimi/VirtualBox VMs"  if [ -d ${dir} ]; then     echo "yep" fi   It says:  ./script.sh: line 5: [: /home/mazimi/VirtualBox: binary operator expected   When I change it to:  dir="/home/mazimi/VirtualBox VMs"  if [ -d "${dir}" ]; then     echo "yep" fi   It works fine. Can someone explain what is happening? When should I assign double quotes around variables like "${var}" to prevent problems caused by spaces? NSDate Format outputting wrong date double perpendicular symbol (for independence) I found from  that I could use the independence symbol:     \newcommand\independent{\protect\mathpalette{\protect\independenT}{\perp}} \def\independenT#1#2{\mathrel{\rlap{$#1#2$}\mkern2mu{#1#2}}}    I was wondering how this works. Can anybody explain? I don't know the commands mathpalette, rlap, and mkern2mu. I'm having a difficult time understanding this statement. Can someone please explain with a concrete example? What do you call someone who is supported? Synonym for a supportee (Which doesn't seem to be a word)?  I created products that retail and we sell them and give the proceeds to charities. Trying to figure out a single word to use as a page title for those that we support were we can list the charities (With their permission of course).  Thanks Anchor Text code string is automatically modified by WordPress I have created an ad for a merchant wanting to rent ad space on my website home page. After creating the ad, (anchor text and pic/graphics with embedded hyperlink) the merchant has requested I remove my url from the ad code. The anchor text along with the embedded hyperlinks links to the merchant's home page.  Problem is I don't know how my url was added to the code as I never inputted it in the original code in the first place. Somehow it was added by I think, WordPress or my server (PHP).  When I view the page source I do see my url was added to the ad code.  Can anyone help explain this and tell me how I can remove the url? Also, if I am able later to remove my url, how will it affect the hyperlink and anchor text?  Thank you, -Dan  Hi s_ha_dum,  I have read your answer and have now made sure the code reads as abosolute url.  Here it is with absolute url:  &lt;strong&gt;If you are interested in helping others treat and prevent hypertension, consider a healthcare degree from &lt;a href="http://elearning.loyno.edu/"&gt;Loyola Online Courses today!&lt;/a&gt;&lt;/strong&gt;   It still shows in page source however with my url addended to the code string.  What am I not understanding? Thank you! When I add LIMIT 1 to a MySQL query, does it stop the search after it finds 1 result (thus making it faster) or does it still fetch all of the results and truncate at the end? Converting expressions to polynomial form How to change specific values in a List Does it give higher quality to shoot in low-res mode in-camera, or to downsize high-res photos later? Suppose you want to store your photos at some lower resolution, let's say about ~1 MB large.  You own a camera able to make photos at 5 MPix and more.  And, you want to have the maximum quality at the smaller size.  Would it be better to make a photo at highest resolution and then resize it with PC software (with a good filter of course), or to directly set the camera to make photos at 2 MPix only? How to modify the space between the numbers and text of sectioning titles in the table of contents? Show that the following series of function defines a continuous differentiable function function in $\mathbb R$. $$\sum_{n=1}^{\infty}\frac{\sin (nx^2)}{1+n^3}.$$  We have , $|f_n(x)|=\left|\frac{\sin (nx^2)}{1+n^3}\right|\le \frac{1}{1+n^3}\le \frac{1}{n^3}=M_n \text{ (say) }$  As, $\sum M_n$ is convergent so, the given series is uniformly convergent. Also , each $f_n(x)$ is a continuous function in $\mathbb R$. So, the given series converges to a continuous function , say $f(x)$.  But how we can show that $f(x)$ is differentiable function ?  Please help...