I Googled how to do share my wifi connection from my Mac (new Macbook Pro)  to my iPhone (5S) and I tried their way. System Preferences > Sharing > Internet Sharing but then i don't have the same options they showed me.   I have share your connection from: Thunderbolt bridge, wi-fi, bluetooth PAN, and bluetooth DUN.    When I choose wifi, which is what I'm supposed to chose from what i've read, I only get two options in the to computers using: Thunderbolt bridge and bluetooth pan but no wifi and neither is working   All the other share you connection from options allow me to do so with computers using wifi thunderbolt bridge and bluetooth pan.   What should I do? Thanks
I'm using OSX 10.9. I'm trying to set up Internet Sharing to connect my Android to my Mac directly over Wi-Fi. Every tutorial I've come across (including ) mentions checking a box for "AirPort" in a "To computers using" list. However, the option is simply not available on my machine:    I have a few related questions:   Why isn't the AirPort option available? Is there anything I can do to make it available? If there isn't, how can I work around it to finish setting up Internet Sharing so I can connect my Android and my Mac directly over Wi-Fi?
How do I break out of a loop in Perl? I'm trying to use a break statement in a for loop, but since I'm also using strict subs in my Perl code, I'm getting an error saying:     Bareword "break" not allowed while   "strict subs" in use at ./final.pl   line 154.   Is there a workaround for this (besides disabling strict subs)?  My code is formatted as follows:  for my $entry (@array){     if ($string eq "text"){          break;     } } What's the best way to deal with hot/stuck pixels in long exposure night photographs? I discovered red/blue/white pixels on my night photographs tonight. Trying to confirm this, I took a black image with the lens on and indeed I saw a whole lot of them (I didn't count them but at least a good fifty on the whole picture).   I'm not exactly sure if they are hot pixels, stuck pixels or anything else.  I quickly gave a check to my last exported JPEG files (I get RAW out of the camera) and couldn't find anything. After a quick search, I've seen that Lightroom is caring about those pixels after RAW conversion.  I've read that, with Canon DSLRs, there is a software process that could take care of that directly on my camera. I don't know if I can use it without getting things even more messy.   My question is: Considering my crazy pixels are not visible on my pictures, should I get too emotional about them? My camera is under warranty but is it really worth it to return it to Canon? If it's only to receive it back 1 month later after Canon just used the very same menu to map out the pixels, it's a bit ridiculous. Could this be a sign that my camera has a bigger problem?  It seems related to shutter speed. When shooting a black image at 1/250s I get nothing. When shooting the same setup but 1s, I get a few of them. The more I increase the shutter speed, the more crazy pixels I get. Limit of $\left(1-\frac{1}{n^2}\right)^n$ (Fitzpatrick Advanced Calculus 2e, Sec. 2.4 #12)  For $c \gt 0$, consider the quadratic equation $x^2 - x - c = 0, x &gt; 0$.  Define the sequence $\{x_n\}$ recursively by fixing $|x_1| \lt c$ and then, if $n$ is an index for which $x_n$ has been defined, defining  $$x_{n+1} = \sqrt{c+x_n}$$  Prove that the sequence $\{x_n\}$ converges monotonically to the solution of the above equation.  Note: The answers below might assume $x_1 \gt 0$, but they still work, as we have $x_3 \gt 0$.    This is being repurposed in an effort to cut down on duplicates, see here: .  and here: . How to unit test an object with database queries I've heard that unit testing is "totally awesome", "really cool" and "all manner of good things" but 70% or more of my files involve database access (some read and some write) and I'm not sure how to write a unit test for these files.  I'm using PHP and Python but I think it's a question that applies to most/all languages that use database access. If $n\times n$ matrix $A$ has eigenvalues $1,-1$ and $n\times n$ matrix $B$ also has eigenvalues $1,-1$, can I then say something about eigenvalues of $AB$ and $BA$? Spaces in files names in \input or \includegraphics I'm going crazy...  I have a file I want to include which path is C:\Users\Matthieu\Documents\Folder withOneSpace\myFile.tex. (As you can see with the \, I'm on windows actually)  I tried the following but none works:  \input{C:/Users/Matthieu/Documents/Folder withOneSpace/myFile} \input{C:/Users/Matthieu/Documents/Folder\ withOneSpace/myFile} \input{C:/Users/Matthieu/Documents/Folder withOneSpace/myFile.tex} \input{C:/Users/Matthieu/Documents/Folder\ withOneSpace/myFile.tex}   I also tried to put the file out of the folder with a space and it works (no surprise):  \input{C:/Users/Matthieu/Documents/myFile} --&gt; Works   All I found is to put a \ before the space but it doesn't work at all. --> Please help ! :) Below is an example from I.N. Herstein:       Let  $R=\Bigg\{\left( \begin{array}{ccc} a &amp; b \\ -b &amp; a \end{array} \right)\Bigg|a,b\in \mathbb R\Bigg\}$ and let $\mathbb C$ be the field of complex numbers. Define $\psi :R\to \mathbb C$ by $\psi\left( \begin{array}{ccc} a &amp; b \\ -b &amp; a \end{array} \right)=a+bi.$       It is asked to prove that $\psi$ is a ring isomorphism of $R$ onto $\mathbb C$ .    can anyone help me with some hint how to prove the ring isomorphism. Photo Map tip in QGIS 3 on windows What does limit actually mean? I have been in a deep confusion for about a month over the topic of limits! According to our book, the limit at $a$ is the value being approached by a function $f(x)$ as $x$ approaches $a$.  I have a doubt that in real number line we can never ever reach the closest value to $a$ because always a more closer value will exist.  Now when talking about our methods for calculating limit, what method comes in our mind when we have to calculate where the value approaches? Let's say we have to find what value $f(x)$ approaches when $x$ moves from $[0,a)$.  So we calculate the value of $f(x)$ at $x=0$, say $4$, and then at $x\to a$.   But the problem is that we don't know the value $x\to a$, so we say the value is $a-h$ where $h\to 0$ and calculate the value of $f(a-h)$, say $5-h$.  Now here is where my doubt starts! In the final step we put the value of $h=0$ say in that it is an infinitesimal quantity.  My doubt is that $h$ was tending to $0$ means that it was never equal to zero  maybe it is infinitesimally small, not a stationary value, not an imaginable value, but we know for sure that it is not  equal to $0$. Maybe it is the point closest to zero, but it is not equal to zero and when we use the result $5-h=5$ we are actually making an error which is tending to zero. Maybe the error is very small, but still, there is some error in that we cannot calculate it but we can see that there is this infinitesimal error present.  That means we don't get the exact limiting value or last value of $f(x)$.  $x$ belongs to $[0,a)$ but a value approximate to infinitesimal? Isn't it right! We get an approximated value? In the King James version of the Bible there is a verse like this:     The Lord is my strength, and my fortress, and my song. And He is become my salvation.   Is it still feasible to use "is become" instead of "has become" and what is the semantic difference? Changing user preferences via console? The machine that I'm currently using is an extremely slow netbook. Whenever I go to change user preferences in Blender, it stalls out. What I need to do is activate the "emulate 3 button mouse" checkbox. Is there a way to do this via console/script? Find all polynomials $P:\mathbb{C}\rightarrow\mathbb{C}$ such that $$P(x^2)=P(x)^2 .$$   Here is what I tried:  First, it is easy to see the constant solutions, namely $P\equiv 0,P\equiv 1$.  Let $r$ be a root of $P$ (i.e. $P(r)=0$). It follows that all terms in the infinite sequence $r,r^2,r^4,\dots,r^{2n},\dots$ are roots of $P$. To avoid a polynomial with infinite roots, we have to have the sequence be periodic. So it turns out that either $r=0$, or the roots of $P$ are roots of unity of degree $2n$ for some $n\in\mathbb{N}$.  In the first case, we get $P(x)=xQ(x)$. Plugging in, we get $$x^2Q(x^2)=x^2Q(x)^2\implies Q(x^2)=Q(x)^2 ,$$ i.e. that $Q$ satisfies the same condition as $P$.  In the second case, we have $P(x)=(x^{2n}-1)Q(x)$. Plugging in, we get $(x^{2n}-1)Q(x^2)=(x^{2n}-2x^n+1)Q(x)^2$. I was not sure how to proceed from here. How to print all printable ASCII chars in CLI? How do I remove diacritics (accents) from a string in .NET? I'm trying to convert some strings that are in French Canadian and basically, I'd like to be able to take out the French accent marks in the letters while keeping the letter. (E.g. convert é to e, so crème brûlée would become creme brulee)  What is the best method for achieving this? "Coming soon" pages & SEO I am setting up my personal website, and I have designed a simple "Coming Soon / Under Construction" page which basically has nothing but a small notice for the users.   What kind of SEO can I make on this page such that it won't harm the full website's ranking later on? In , one learns two definitions of free groups associating with sets.        Let $A$ be a set, the free group of $A$, $F(A)$ is the initial object in the category $\mathcal{C}$, where \begin{equation} \operatorname{Obj}(\mathcal{C})=\{A\xrightarrow{g}G\}, \end{equation}where the codomain $G$ are groups, and \begin{equation} \operatorname{Hom}(\mathcal{C})=\{\text{Commutative Diagrams } A\xrightarrow{g_1}G_1\xrightarrow{\phi}G_2\xleftarrow{g_2}A\}  \end{equation} where $\phi$ are group homomorphisms.   Also $F(A)$ has the concrete construction with elements being non-redundant words with alphabet $A$, and the group multiplication being juxtaposition and reduction.      But what good are free groups? Why are they useful?  says they are useful in topology, but does not explain why explicity.   Can someone give some examples that an undergraduate can understand? I am asking about examples that can show the usefulness of this abstract construction. So I guess the identification of $\mathbb{Z}=F({a})$ does not really count. If $p$ and $q = 2p + 1$ are both odd primes, show that $-4$ and $2(-1)^{(1/2)(p-1)}$ are both primitive roots modulo $q$. If $p$ and $q = 2p + 1$ are both odd primes, show that $-4$ and $2(-1)^{(1/2)(p-1)}$ are both primitive roots modulo $q$.   I cannot get heads nor tails of how to even start this let alone finish it Deep confusion with conventions and signs in geometric optics This is an equation given in my book.     The question is why have they used a negative sign on the LHS?   Now, if you try to derive the mirror equation with simple geometry, you get  1/v +1/u =1/f . I got that equation without applying any signs there!  So what is the need to apply the signs ‘here'?   If i try to derive this equation ( the one in the photo ) i get the exact answer, but with the positive sign in the LHS. WHY we use the negative sign in the derivation, and then  again we use conventions while solving the questions? Can you explain closures (as they relate to Python)? I've been reading a lot about closures and I think I understand them, but without clouding the picture for myself and others, I am hoping someone can explain closures as succinctly and clearly as possible.  I'm looking for a simple explanation that might help me understand where and why I would want to use them.