Is statement like "If x>7, then x^2>49" a conditional proposition?
Sentence vs proposition
Pass an extra argument to a callback function I've tried everything I can think of. Resetting the router, changing the channel number and band.   The internet connection is fine, and then just hangs for a minute or 2, then returns to normal.   The wifi icon remains connected, and I have the latest 10.10.4 update installed. At first I thought it was a DNS bug with Yosemite, and have played with the settings such as changing DNS provider, changing the IPV6 to IPV4 only etc.  Driving me nuts. Has anyone had a similar problem? I've checked the surroundings with wifi scanners and have chosen the best channel available.     One thing I have noticed, it seems a lot more reliable on 5GHz as opposed to 2.4Ghz It seems to affect my Macbook Pro Retina 13in Early 2015 a lot more than the other devices on the network. I'm using a Virginmedia  1. I am thinking about a wizard who has a rat familiar (from the  spell), and has the  spell prepared. Can he use his familiar's senses to teleport into another room (where the familiar is hiding) by looking through the eyes of the rat and casting misty step?  The wizard could use his action to switch to the familiar's senses and then use his bonus action to cast the spell. This would greatly reduce the "blind and deaf" time he experiences from doing this. Consider this equation :   $$\sqrt{\left( \frac{dy\cdot u\,dt}{L}\right)^2+(dy)^2}=v\,dt,$$  where $t$ varies from $0$ to $T$ , and $y$ varies from $0$ to $L$.  Now how to proceed ?   This equation arises out of following problem :   A cat sitting in a field suddenly sees a standing dog. To save its life, the cat runs away in a straight line with speed $u$. Without any delay, the dog starts with running with constant speed $v&gt;u$ to catch the cat. Initially, $v$ is perpendicular to $u$ and $L$ is the initial separation between the two. If the dog always changes its direction so that it is always heading directly at the cat, find the time the dog takes to catch the cat in terms of $v, u$ and $L$.  See my solution below :   Let initially dog be at $D$ and cat at $C$ and after time $dt$ they are at $D'$ and $C'$ respectively. Dog velocity is always pointing towards cat.  Let $DA = dy, \;AD' = dx$  Let $CC'=udt,\;DD' = vdt$ as interval is very small so $DD'$ can be taken straight line.  Also we have $\frac{DA}{DC}= \frac{AD'}{ CC'}$ using triangle property.  $\frac{dy}{L}= \frac{dx}{udt}\\ dx = \frac{dy.udt}{L}$  $\sqrt{(dx)^2 + (dy)^2} = DD' = vdt \\ \sqrt{(\frac{dy.udt}{L})^2 + (dy)^2} = vdt $  Here $t$ varies from $0-T$, and $y$ varies from $0-L$. Now how to proceed? Proving the limit of a function of a sequence is equal to the function of the limit of that sequence Suppose $f$ is a continuous function at $x = c$ in $[a,b]$.  Prove that for any sequence ${x_n}$ in $[a,b]$ converting to $c$, the sequence $\{f(x_n)\}$ converges to $f(c)$.  That is, $$ \lim_{n\to\infty}f(x_n)= f\left(\lim_{n\to\infty}x_n\right)$$    This proof seems simple but there are a few things that I need to know first. If $\{x_n\}$ converges to $c$, is it sufficient to substitute $c$ in for $\lim_{n\to\infty}x_n$?  Also needing some guidance on the structure of this proof.  Thanks! Review of a proof for De Moivre's theorem using mathematical induction The following is a rigorous proof of De Moivre's theorem by means of mathematical induction. The theorem put simply is that:  Any complex number, $z = a+bi$, on a cartesian plane can be expressed in polar form, where $a=r\cos\theta$ and $b=r\sin\theta$ and $r$ is the absolute distance from the origin to the point $z$. In light of this, the expression for the complex number $z$ in polar form is $z=r(\cos\theta+i\sin\theta)$ In order to find the $n^{th}$ power of $z$, the following rule applies: $$\displaystyle z^n=(r(\cos\theta+i\sin\theta))^n=r^n(\cos n\theta+i\sin n\theta)$$ where $n\in\mathbb N$ (I have confined $n$ to the natural numbers given that I intend on using mathematical induction to prove the theorem.  Base step: We must prove that what is stated is true for $n=1$, hence $$z^1=r^1(\cos 1\cdot\theta+i\sin1\cdot \theta)$$ $$=r(\cos\theta+i\sin\theta)$$ which is true. Next we assume it is true for $n=k$, and therefore proceed to the inductive step. Inductive step: When calculating $z^{n+1}$, it's the same as calculating $z^nz$, hence $$z^{n+1}=(r^n(\cos n\theta + i\sin n\theta))(r(\cos \theta+i\sin \theta))$$ $$=r^nr(\cos n\theta+i\sin n\theta)(\cos\theta +i\sin \theta)$$ $$=r^{n+1}(\cos n\theta\cdot\cos\theta+\cos n\theta \cdot i\sin\theta+i\sin n\theta\cdot\cos\theta+i^2\sin n\theta\cdot\sin\theta)$$ from here, $i^2=-1$, and therefore $+i^2\sin n\theta\cdot\sin\theta$ becomes $-\sin n\theta\cdot\sin\theta$. In addition to this, the following trigonometric identities will be used: $$\sin(n\theta + \theta) = \sin n\theta\cdot\cos\theta+\cos n\theta\cdot\sin\theta$$ $$or$$ $$k\sin(n \theta+\theta)=k\sin n \theta\cdot\cos \theta + \cos n\theta\cdot k\sin\theta$$ $$and$$ $$\cos(n \theta + \theta)=\cos n\theta\cdot\cos\theta-\sin n\theta\cdot\sin\theta$$ by using these, the original equation has now become $$=r^{n+1}(\cos(n \theta + \theta) + i\sin(n \theta + \theta))$$ then, after factoring out $\theta$, the theorem becomes $$=r^{n+1}(\cos((n+1)\theta)+i\sin((n+1)\theta))$$ which completes the proof. Question: is this proof correct all the way through? Or have I missed any conditions? If all is well in the case of this proof, could somebody aid me in proving it for $\{n|n\in\mathbb R,n\geq1\}$ Account not acting as an administrator correctly My account, david, is in the Administrators group on a Windows 7 machine.  I am still having problems with programs that I should be able to use, such as SQL Server. Specifically, my account seems to not have correct permissions when I am working.  I know with an Administrator account I should have full access. How can I force my account (david) to act like an admin account and have full access to everything? Terminal only shows up as a black window Using Drupal 7.14 with the PHP filter on I have the following in a Basic Page content type:  &lt;?php if ($is_mobile == TRUE):?&gt; &lt;div class="fb-like-box" data-href="http://www.facebook.com/a page" data-width="710" data-height="600" data-show-faces="false" data-border-color="#73AA4B" data-stream="true" data-header="false"&gt;&lt;/div&gt; &lt;?php else: ?&gt; &lt;div class="fb-like-box" data-href="http://www.facebook.com/a page" data-width="900" data-height="600" data-show-faces="false" data-border-color="#73AA4B" data-stream="true" data-header="false"&gt;&lt;/div&gt; &lt;?php endif; ?&gt;   I get the error message:  Notice: Undefined variable: is_mobile in eval() (line 1 of D:\websites\modules\php\php.module(80) : eval()'d code).  I sort of understand - I'm trying to grab a variable from the Drupal system but is there any way to do this? Maybe using Tokens? How can't install a 338KB app when I have 474MB free? I have a Motorola phone, with 8GB of internal memory.  To my surprise, in a few days, I had 474MB of free space, but couldn't install a 338KB app!! So, clearly the limit of ~25MB referred to in some comments ( and ) are not always the case. A user just told me the following:     Actually it's "25MB or 10% of the storage", whichever is hit first. So   with e.g. 10 GB internal storage, it would hit you as soon as you drop   below 1 GB free. Crazy, but that's what it is.   Actually, that's not correct, because I didn't have to free up 1GB of internal memory. But anyway, half a gigabyte is enough to run a full operational system. I've seen similar complaints of hundreds of MB not enough to install apps ~ 1MB or similar small operations ( and ).  What's wrong here? Make hyperref take pdfinfo from \title and \author I once read about an option for hyperref that automatically takes the info provided via the standard \author and \title, and puts it into the pdfinfo. Now I want to implement it in my template and can't find it anywhere in the hyperref manual nor anywhere else.  Did I dream about this or can someone help me out here?  (A similar, but more general question: ) What is the difference between range and xrange functions in Python 2.X? How to make text aligned left/center/right in the same line? I am trying to align some text to left/center/right in the same line. For example, I want to put my phone number on the left, my name in the center, and my email on the right, how do I do that? How to reduce VM size? How does the Flash breathe while utilizing his super speed? How do the Flashes breathe utilizing their super speed? The air pressure would be extreme. Do they run in a pressurized bubble? How can I do a full shutdown of windows 10 without logging in? Find the limit $\lim_{n\to\infty} \frac{x_1 y_n + x_2 y_{n-1} + \cdots + x_n y_1}{n}$ When $\lim_{n\to\infty} x_n = a$, and $\lim_{n\to\infty} y_n = b$, find the limit, $$\lim_{n\to\infty} \frac{x_1 y_n + x_2 y_{n-1} + \cdots + x_n y_1}{n}.$$ Thank you for your help in advance. Why are all the textures in my file pink? How much willpower do gravely wounded soldiers lose? The text says they suffer a permanent reduction? Proving that if $|f''(x)| \le A$ then $|f'(x)| \le A/2$ Suppose that $f(x)$ is differentiable on $[0,1]$ and $f(0) = f(1) = 0$. It is also   known that $|f''(x)| \le A$ for every $x \in (0,1)$. Prove that   $|f'(x)| \le A/2$ for every $x \in [0,1]$.   I'll explain what I did so far. First using Rolle's theorem, there is some point $c \in [0,1]$ so $f'(c) = 0$.  EDIT: My first preliminary solution was wrong so I tried something else. EDIT2: Another revision :\  I define a Taylor series of a second order around the point $1$: $$ f(x) = f(1) + f'(1)(x-1) + \frac12 f''(d_1)(x-1)^2 $$ $$ f(0) = f(1) + f'(1)(-1) + \frac12 f''(d_1)(-1)^2 $$ $$ |f'(1)| = \frac12 |f''(d_1)| &lt;= \frac12 A $$  Now I develop a Taylor series of a first order for $f'(x)$ around $1$: $$ f'(x) = f'(1) + f''(d_2)(x-1) $$ $$ |f'(x)| = |f'(1)| + x*|f''(d_2)|-|f''(d_2)| \leq \frac{A}{2} + A - A = \frac{A}{2} $$  It looks correct to me, what do you guys think?  Note: I cannot use integrals, because we have not covered them yet.