If ex is followed by two words or adjectives, then does ex imply to the first adjective only or it will be applied to second adjective aswell e.g, ex-muslim pakistani.
Does it mean neither a muslim nor a pakistani anymore? Or it means muslim and ex pakistani. I will be very thankfull if you people kindly elaborate this for me.
When would I use a voltage regulator vs voltage divider? When would you use a voltage regulator vs a resistor voltage divider?  Are there any uses for which a resistor divider is particularly bad? Without appealing to the axiom of choice, it can be shown that (Proposition:) if $X$ is well-orderable, then $2^X$ is totally-orderable.  Question: can we show the stronger result that if $X$ is well-orderable, then so too is $2^X$?  Proof of Proposition. Pick any well-ordering of $X$. Then the lexicographic order totally orders $2^X$.  More explicitly: for any two $f,g \in 2^X$, define $f &lt; g$ iff   there exists $x \in X$ such that $f(x) \neq g(x)$, and if $x \in X$ is minimal such that $f(x) \neq g(x)$, then $f(x)=0$ and $g(x)=1$.   It can be shown that $&lt;$ totally-orders $2^X$. Proving $9^n - 8n - 1$ is divisible by $8^2$ for $n\ge 0$? Shell Script for logging into a ssh server I tried writing a shell script which can do automatic login into a ssh server using password which is mentioned in the script. I have written the following code:  set timeout 30 /usr/bin/ssh -p 8484 root@172.31.72.103 expect  {    "root@172.31.72.103's password"     {       send "password\r"     } }   This code is not running properly, still it is asking for the password. Can somebody please help me in solving this Positive integer multiples of an irrational mod 1 are dense I'm not sure how to solve this one. Thank you!  $2.$ For any $\alpha\in \mathbb R$ we define $$\lfloor \alpha \rfloor = \max_{n\in\mathbb Z}\{\,n\mid n\leq \alpha\,\}$$ and $$\alpha\bmod 1 = \alpha - \lfloor \alpha \rfloor$$ Let $\alpha$ be irrational. (a) Given $n\in\mathbb N$ show that $\{\,k\alpha\bmod1\mid k\in\mathbb N\,\}\cap\left[0,\frac{1}{n}\right]\neq\emptyset$ (b) Prove that $\{\,n\alpha\bmod 1\mid n\in\mathbb N\,\}$ is dense in $[0,1]$. What is the purpose of -e in sed command? I can't find any documentation about the sed -e switch, for simple replace, do I need it?  e.g.  sed 's/foo/bar/'   VS  sed -e 's/foo/bar/' I understand Big-O notation, but I don't know how to calculate it for many functions. In particular, I've been trying to figure out the computational complexity of the naive version of the Fibonacci sequence:  int Fibonacci(int n) {     if (n &lt;= 1)         return n;     else         return Fibonacci(n - 1) + Fibonacci(n - 2); }   What is the computational complexity of the Fibonacci sequence and how is it calculated? Differences in meaning when the verb tense changes (headlines) !! Do not use the future tense after unless   [✓]  I won't go unless you go   [✘] [I won't go] unless you will go. [✘]   Why not? Even if the above is prescriptive, what may be some reasons? In my separate question , I quote: unless = if not. If not can precede future tense; so why can't unless?  Footnote:  motivated this. How do i find nichrome temperature Prove that the functions $f(z)$ and $\overline{f(\overline{z})}$ are simultaneously holomorphic.   I take this to mean that $f(z)$ is holomorphic if and only if $\overline{f(\overline{z})}$ is holomorphic.  Let $g(z)=\overline{f(\overline{z})}$. Note that $\overline{g(\overline{z})}=f(z)$. So it suffices to prove that if $f(z)$ is holomorphic, then $g(z)$ is holomorphic.  Write $f(z)=u(z)+iv(z)$. Since $f(z)$ is holomorphic, the real and imaginary parts satisfy the Cauchy-Riemann equations:  $$\frac{\partial{u(z)}}{\partial{x}} = \frac{\partial{v(z)}}{\partial{y}}, \frac{\partial{u(z)}}{\partial{y}} = -\frac{\partial{v(z)}}{\partial{x}}.$$  We have $g(z) = u(\overline{z})+i(-v(\overline{z}))$. To prove that $g(z)$ is holomorphic, we must prove that its real and imaginary parts satisfy the Cauchy-Riemann equations:  $$\frac{\partial{u(\overline{z})}}{\partial{x}} = \frac{\partial{(-v(\overline{z}))}}{\partial{y}}, \frac{\partial{u(\overline{z})}}{\partial{y}} = -\frac{\partial{(-v(\overline{z}))}}{\partial{x}}.$$  How can we obtain this from the above relations? Transcendental Extensions. $F(\alpha)$ isomorphic to $F(x)$ Let $E$ be an extension field of $F$ and $\alpha \in E$. Then $\alpha$ is transcendental over $F$ if and only if $F(\alpha)$ is isomorphic to $F(x)$, the field of fractions of $F[x]$.   This was a theorem in an abstract algebra textbook with a very brief proof. Can someone please explain why this theorem holds? I'm having difficulty grasping the concepts at hand.  Thanks! An awful lot of people seem to use the phrase "substitute X for Y" to mean "replace X with Y", while I've always used and understood it as "replace Y with X". This makes sense to me, given that a substitute is the replacement, not the thing which has been replaced.  I thought I might be able to figure things out from a dictionary, but now after seeing two sorts of definitions, I'm even more confused:   to put or use in the place of another to take the place of; replace   The first one suggests that the object will be the substitute (replacement), the thing put into place, while the second suggests that the object will be the thing which has been replaced.  Is one of these usages more correct in any sense? (I know this is probably a pointless question, since people will continue to speak the way they speak.) Is there perhaps a difference between American and British English?   And most importantly, is there any reliable way to tell what someone means when they ask how to substitute honey for sugar, or is the verb simply guaranteed to cause confusion? So I found this on the Wolfram website today:     So I was wondering about how one might be able to (if possible) solve those four problems by hand. Here are the problems, $\LaTeX$ed:    $ \lim_{x \to +\infty} \dfrac {\sqrt{x^3-x^2+3x}}{\sqrt{x^3}-\sqrt{x^2}+\sqrt{3x}} $ $ \displaystyle\sum_{k=1}^{\infty} \dfrac {(-1)^{k+1} k^2}{k^3+1} $  $ \dfrac {\mathrm{d}}{\mathrm{d}u} \left[ \dfrac {u^{n+1}}{(n+1)^2} \cdot \left[ (n+1) \ln u - 1 \right] \right] $  $ \displaystyle\int_0^{2\pi}\displaystyle\int_0^{\frac{\pi}{4}}\displaystyle\int_0^4 \left( \rho \cos \phi \right) \rho^2 \sin \phi \, \mathrm{d}\rho \mathrm{d}\phi \mathrm{d}\theta$     Ideas   The degree of the numerator is $\frac{3}{2}$. The degree of the denominator is $\frac{3}{2}$. The expression is of an indeterminate form, namely $\frac{\infty}{\infty}$, so we use l'Hoptial's Rule.  No ideas, really.  Derivatives are always pretty easy, although this one is a bit bashy. Basically bash Product and Chain Rules, etc.  Integration by Parts bash? The $\mathrm{d}\theta$ part is very trivial. I mean for the $\rho$ and $\phi$. How to create Motion Trail in Cycles I want to create a motion trail effect for a sword like known in games look at that example if you have an solution that looks not as fancy as in the picture don't mind to post it. I'll accept anything useful. How do I install VMware player on a Mac os X? I went to their site, and downloaded a .bundle which automagically turned into a .txt file after downloading.   Long story short, I can't run the txt file because I guess Mountain Lion Mac os X isn't a strict Linux box and is missing some core components to do that type of installation.  Does anyone know how to install VMware? tags of mundanity that are gratuitously applied to posts It's an additional unnecessary burden to the honest stacker during suggested edit duty. A question presents some code then the minor editor adds a tag like 'for-loop' or 'forms'.  These tags are so general that they only have a handful of followers. They serve no useful purpose and are the cause of many too minor edits. Why not permit culling of generic tags? How to Translate Content type name using i18n module? I am developing a multilingual site that supports English and Norsk bokmal. I have set English as my default language. I wanted to translate the contents and the other things in the site.  My real problem started when I found that I was unable to see the translation of the content type's name. I went to admin/config/regional/translate/translate and translated everything, but still my content type's name is not translated.  I have attached a screenshot of the translation page. Still I don't find a way to translate the content type's name. How to use "who" vs. "that" I often get confused when trying to use who vs that.  Some examples that often confuse me:  That     The person that went to the store.      The people that went shopping.      The persons that went shopping.      The group that went shopping.   Who     The person who went to the store.      The people who go shopping.   Please explain when to use either for plural subjects and singular subjects.  Animate and inanimate objects as well. How to make /sbin/shutdown, /sbin/reboot etc. require sudo again in 16.04? For whatever reason, we do no longer need to be root (or using sudo) to run /sbin/shutdown, /sbin/reboot etc.  This seems to be because those executables are now symlinks to /bin/systemctl which handles everything as normal user.  However, what if I want shutdown and reboot to require root authentication again? How can I achieve this?