$f$ holomorphic at $B(0,1)$ and $|f(z)|<1$ for every $z\in B(0,1)$ has 2 solutions and $f(z)=z$ Prove for every $z\in B(0,1)$ $f(z)=z$
Schwarz's Lemma, fixed points question
What is the difference between == and === in php. I am unsure when to use both.  Updated note: So that it shows up in StackOverflow search, the difference between == and === is the same as the difference between != and !==. How do get my sitelinks to appear on Google search results? Let $l \in\mathbb{R} $ and $ f:(0,\infty) \to \Bbb R $ be a function such that $ \lim_{x\to \infty} xf(x)=l $ .  Prove that  $ \lim_{x\to \infty} f(x)=0 $.  Any help would be appreciated - I found this difficult to prove Electromagnetic black hole? So I was thinking about something for the past while  Consider a large spherical foam-ball with homogeneous density. Where a foam ball is defined as an object that can absorb matter with 0 friction (example: a gravitational well without an object inside). This is a purely theoretical construct.  If the foam-ball has a radius R and a charge Q. What charge must the foam-ball have, such that there is well defined sphere or horizon such that any object with a negative charge (even if it is the slightest bit) must travel faster than C in order to escape the field of the ball.  Aka what charge would turn this into a black-hole for all objects with opposite sign on their charge?  Once again I assume the foam-ball is a single particle, that doesn't repel itself... its just a very large homogenous 'thing' with charge. My question was closed for being a "shopping list question", even though it was very much related to the topic of the site. Why? I viewed in this post  a solution to my question, but...    Are there any easier way (or alternative) to do this using colors?  Thank you. ------------------ edited after showed than it´s duplicate ------------- I think that there are many sols, but for example this is easy using a normal table without pgf...     I´m trying to adapt to similar colors to apply to the table probabilitiess Java Serialization with non serializable parts I have:  class MyClass extends MyClass2 implements Serializable {   //... }   In MyClass2 is a property that is not serializable. How can I serialize (and de-serialize) this object?  Correction: MyClass2 is, of course, not an interface but a class. Irreducible polynomial is always separable in char 0 field "Meet my boss" or "meet with my boss"? What is the difference between "meet" and "meet with"?  For example, which of these should I say?        I met my boss yesterday    I met with my boss yesterday   I'm meeting my friends tonight    I'm meeting with my friends tonight I am often interested in the installation triggers (postinst, postrm) or certain parts of packages (like /usr/share and /etc). Currently, I am running the next command to retrieve the source code:  apt-get source [package-name]   The downside is, this file is often much bigger than the binary package and does not reflect the installation tree.  Right now, I am downloading the packages through :      Download the actual file   This takes too long for me and as someone who really likes the shell, I would like to do something like the next (imaginary) command:  apt-get get-deb-file [package-name]   I could not find something like this in the . The most close I found was the --download-only switch, but this puts the package in /var/cache/apt/archives (which requires root permissions) and not in the current directory. If a set is $F_\sigma$ and is of first category then it is a countable union of closed nowhere dense sets We say a set is $F_\sigma$ if it is a countable union of closed sets. We say a set is of first category if it is a countable union of nowhere dense sets.  The question is, if a set of $F_\sigma$ and of first category, is it true that this set is a countable union of closed nowhere dense sets. How can I calculate this limit: $\lim\limits_{x\to 0} x\left\lfloor\frac{1}{x}\right\rfloor$? Calculate the following limit. $$ \lim_{x\to 0} x\left\lfloor\frac{1}{x}\right\rfloor $$ Where $\left\lfloor x \right\rfloor$ represents greatest integer function or floor function, i.e greatest integer less than or equal to $x$.  Thanks. The text for  says:     {1}{G}, {T} : Target creature you control fights another target creature. (Each deals damage equal to its power to the other.)   Does this have anything to do with combat? Or is it just direct damage between two creatures? For example, can one of the creatures have defender? Or what if one of them is tapped?   I've been assuming it is more like the damage dealt by a .  Also: are the two creatures then “tapped” until their next untap step? ie: could you use Ulenvald Tracker to make two creatures fight in your pre-combat step, then enter the combat phase with a creature who just “fought” untapped? Could you make two creatures fight who are both tapped? JMustache attribution is incorrectly listed as Butterknife 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? How do I remove repeated elements from ArrayList? I have a MacBook Pro with Mini DisplayPort and I want to use target display mode to use a Thunderbolt iMac as an external display. If this works, would I need a Mini DisplayPort cable or a Thunderbolt cable? Is there an open source alternative to "Adobe Digital Editions"? For the moment I run Adobe Digital Editions under Wine to download ebooks burdened with ditigal restriction management. I only use it to open .acsm files supplied by ebook-shops, which contain authentication information required to download the actual DRM'ed ebook files, which I then transfer to my reader-device with calibre. My question is, if there exist open source alternatives to Adobe Digital Editions. They don't need much functionality. I just want to put the .acsm-file in and get the .epub out (no, I don't want to remove the drm, that'd be illegal afaik). Prove that $Ax=0$ has infinite solutions if and only if $ \text{rank}(A)&lt;n$   Here is one way of my if proof, but I don't know how to proof the other part.  Let $r$ be the rank of $A$. Then $ r\leq  n$. If $ r&lt;n$, then there are $n-r$ linearly independent solutions. Furthermore any linear combination of these solutions will also be a solution of $Ax=0$. Hence, in this case, the equation $Ax=0$ has infinite number of solutions How to make the simple three square box and connect them? I want to make the three square box and simply connect them.