Iterating a command in Maple
How to define a recurrence relation in Maple without the command proc?
Which tools and technologies are used to build the Stack Exchange Network? What tools and technologies are used to build the Stack Exchange Network?  See also: So I had an exam today and one of the questions were: Give an example of a function $f$ which is nowhere continuous but $|f|$ should be continuous at all points. At first I had no idea how to do it then I came up with this, even though I know it's wrong:  $$f(x)= \begin {cases} \ \sqrt{x}&amp;\text{if }x &lt;0\\ \sqrt{-x}\ &amp;\text{if }x &gt; 0\\ \end {cases}$$  Like I said I know it's wrong..but can someone give me an example of this? Thanks. How do I skip specific tests when building an rpm? I am building an RPM of git version 2.13.0. The build has gone ok but one of the tests are failing:  Config variable ${LIB_HTTPD_SVN} is not defined Config variable ${LIB_HTTPD_SVN_PATH} is not defined   I cannot find any info about these variables so I was going to just skip the tests. How can I do that? This is exercise 1.6.1 of   Suppose that 501 distinct integers are selected from 1 . . . 1000. Show that there are distinct selected integers $a$ and $b$ such that $a | b$. Show that this is not always true if 500 integers are selected.  This seems like it should be simple but it's has been stumping me for a few days.  Here's my idea for a proof:  Let $S$ be a set of 500 distinct integers between 1 and 1000 that don't divide each other. Let $S_{1-500}$ and $S_{501-1000}$ partition $S$ into sets containing the elements ≤ and > than 500, respectively. Then consider $2 S_{1-500}$ and $\frac{1}{2}S_{501-1000}$, the result of multiplying the elements of these sets by 2 and 1/2, respectively. Because elements of S are coprime, $S_{1-500}$, $S_{501-1000}$, $2 S_{1-500}$, and $\frac{1}{2}S_{501-1000}$, are disjoint. Also note that each of these sets is a subset of the integers from 1 to 1000. One can deduce that the cardinality of the union of these sets is 1000, and therefore they form a partition of the integers from 1 to 1000.  Now, I know this demonstrates that you can't add another number to $S$ that is coprime with all the elements in $S$, which means that a coprime subset of the integers from 1 to 1000 can have at most 500 elements. Can someone articulate why this is true for me? Also, this was in a section on the Pigeonhole principle, can someone rework the proof to utilize that, and possibly make it simpler? Thanks. Determining if an arbitrary point lies inside a triangle defined by three points? Is there an algorithm available to determine if a point P lies inside a triangle ABC defined as three points A, B, and C? (The three line segments of the triangle can be determined as well as the centroid if they are needed.)  Grid space is defined as Screen Space, that is, 2D Cartesian with the Y-Axis flipped so "up" is negative y and the origin is the upper left corner. What is a word for "cannot-be-wrong" attitude? When speaking with someone recently I was continuously taken aback by how he could not concede even the slightest detail in my argument (which was not unreasonable), and it happened another time previously. Both times had to do with me pointing out 'error' in his action.  He very much exhibits that 'I cannot be wrong' attitude.  I first thought to call this arrogance or pride but he is not overbearing like arrogance demands and he does not show excessive self esteem that pride demands.  What is a word that can accurately describe this attitude? How to get product recommendations Possible Duplicate:          I have a question of the form "what companies provide service X?"  I checked meta, and apparently such questions are highly discouraged on all Stack Exchange sites. Which is fine, but it obviously raises the meta-question: Where can I ask my question?  (In particular, I know that there are people hanging out on Stack Overflow who have probably needed the same service, so if an answer exists, they possess it...)  Edit: I should perhaps point out that the service I'm looking for is rather specific and slightly obscure. Otherwise, yeah, this would be a 10-second exercise with Google. I am new to Linux and Ubuntu. When I don't know how to do something with this OS I search on the web and Ask Ubuntu and always find the answer.  But sometimes it's not a great answer nor complete tutorial. I follow the instructions anyway, but I don't know what all the commands mean.  So my question is:   When I follow a tutorial, am I 100% safe? If not, then how can I tell I am in danger? remove locked by android device manager message I have played with Android device manager and I have blocked my phone. I have deblocked but everytime my phone enters into standyby it apears me the message "locked by android device manager" and I have to enter the password again.  Do you know how to remove this message? Underscores in custom fields While trying to perform a WP_Query using meta_query(), I had some trouble because the custom fields created by a plugin had _ in the beginning of its name.   Although I noticed it was stored this way in the database, I had no idea why it was there and thought I had to reference it without the underscore (for the record, that is wrong).  Why do some custom fields start with underscores and others don't? What are the underscores used for? Are they mandatory in some circumstances? apt-get cannot connect to Ubuntu archives How can I bake the cloth simulation into keyframed vertices or shape keyed vertices? I'm simulating a cloth. How can I bake the cloth simulation into keyframed vertices or shape keyed vertices? A subring of the field of fractions of a PID is a PID as well. Let $A$ be a PID and $R$ a ring such that $A\subset R \subset \operatorname{Frac}(A)$, where $\operatorname{Frac}(A)$ denotes the field of fractions of $A$. How to show $R$ is also a PID?   Any hints? Convergence of $\int\limits_1^{\infty}x^\alpha\sin(x^\beta)dx$ I need to show that $$ \int\limits_1^{\infty}x^\alpha\sin(x^\beta)dx $$ converges if and only if $\alpha + 1 &lt; \beta$. I used substitution and integration to get $$ \lim\limits_{t\to\infty}\int\limits_1^tx^\alpha\sin(x^\beta)dx \overset{u = x^\beta}{\underset{du = \beta x^{\beta-1}}{=} }\lim\limits_{t\to\infty}\left(\frac{1}{\beta}\int\limits_1^{t^\beta}u^{\frac{\alpha + 1 - \beta}{\beta}}\sin{u}du\right) $$ If $\alpha + 1 -\beta &lt; 0$, then we have a product if a function with bounded anti-derivative and a differentiable decreasing function which tend to 0, and from Dirichlet's criterion, the integral converges.   For the converse, I used integration by parts $$  = \frac{1}{\beta}\lim\limits_{t\to\infty}\left(\left.-u^{\frac{\alpha + 1-\beta}{\beta}}\cos{u}\right|_1^{t^\beta} + \frac{\alpha+1-\beta}{\beta}\int\limits_1^{t^\beta}u^{\frac{\alpha + 1-2\beta}{\beta}}\cos{u}du\right) $$ For $\alpha + 1 -\beta\geq 0$, I get that the first term indeed diverges, but this is not enough to show total divergence. How can one show it? mysterious error: \pdfendlink ended up in different nesting level than \pdfstartlink I ran into the "mysterious"  \pdfendlink ended up in different nesting level than \pdfstartlink   error.  According to , "this happens when hyperref is used under pdftex and a citation splits across a page boundary".  The given solution is to manual fix the citation to not split across the page boundary.  However, this workaround isn't feasible for me, as the documents are automatically generated on a server with no user interaction.  Is there any solution to the problem known, perhaps an experimental hyperref action or a patch to pdftex?  (Probably, one could use luatex to solve the problem, but for other reasons, luatex is not an option in this project.)  MWE:  \documentclass[%draft               ]{article} \usepackage{hyperref} \setlength{\textwidth}{3cm} \setlength{\textheight}{3cm}  \begin{document} Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna \href{http://www.tug.org/errors}{aliquyam erat, sed diam voluptua.} \end{document} How many physical degrees of freedom does the $\mathrm{SU(N)}$ Yang-Mills theory have? The $\mathrm{U(1)}$ QED case has two physical degrees of freedom, which is easy to understand because the free electromagnetic field must be transverse to the direction of propagation. But what are the physical degrees of freedom the $\mathrm{SU(N)}$ Yang-Mills theory?   I believe that the $\mathrm{SU(N)}$ Y.M. theory has four degrees of freedom, and it is easy to see that by gauge fixing (such as the Lorentz condition or the Coulomb condition) that we can always remove one redundant degree of freedom. But then we still haven't completely fixed the redundant degrees of freedom. Thus my question is:     How many physical degrees and how many are redundant degrees of freedom does the Y.M. theory have?    I would be interested to understand how we can determine this mathematically, and also to understand what the physical intuition behind this is? So I was thinking... If heat I feel is just lots of particles going wild and transferring their energy to other bodies, why am I not burned by the wind?  When I thought about it more I figured out that wind usually carries some humidity, and since particles of liquid are moving same speed as the wind, they are basically static relative to each other, so no energy is transferred between them (wind and water particles). And if that water sticks to my skin and wind blows, it'll evaporate thus taking energy from my skin and make me feel cold.  Thing is, I don't think that's really the case but even if it is, if I somehow dry out the wind, will it burn me if it's strong enough? And winds can reach some pretty high velocities (though I must admit I'm not sure if they are comparable to movement of atoms in warm bodies etc...).  So. Bottom line. Can I be burned by wind in some perfect scenario? How do i fix this Eevee rendering Problem? I can notfix this issue when selecting Eevee for my renders. It gets really annoying. I can get rid of them temporary when I scroll out or into the viewport. Does anyone have an Idea how I can fix that?  thanks c: How do I completely remove an image from my .blend file? Do ideal gases at zero Kelvin have potential energy?