Prove that $\lim\limits_{z \to \infty} |f(z)| = \infty$ where $f(z)$ is entire and has entire inverse $g(z)$.  I can show that the limit cannot be finite since if it were, then we can use Liouville's theorem to conclude that $f$ is constant. But how do I show that the limit is actually infinity?   Every answer in the other question uses some of Picard's theorem, the Open mapping theorem, Riemann's theorem. The only theorems I've covered which are relevant to the question are Casorati-Weierstrass and Liouville.
Can we prove that every entire one-to-one function is linear?
jQuery get the rendered height of an element? How do you get the rendered height of an element?  Let's say you have a &lt;div&gt; element with some content inside. This content inside is going to stretch the height of the &lt;div&gt;. How do you get the "rendered" height when you haven't explicitly set the height. Obviously, I tried:    var h = document.getElementById('someDiv').style.height;   Is there a trick for doing this? I am using jQuery if that helps. Show that $n$ lines separate the plane into $\frac{n^2+n+2}{2}$ regions "'key' is not valid for passed 'access_token', token not found" when trying to login using Google on Android SE app Which is the best way to put function plots into a LaTeX document? I am faced with the following problem: Servers get saturated since current load balancing strategy is based on client IP. Some corporate clients access our servers from behind large proxies so all clients appear with same IP to our load balancer. I think we are using some hardware load balancing device (can investigate further if necessary). We need to maintain session affinity (site is constructed in ASP), so all requests with same IP get routed to the same node.  Since all the communication goes over the HTTPS, no request data (like session Id) is available to balancer as a client discriminator. Is there a way to use some other data besides the IP to distinguish between clients and route the clients even when coming from same IP to different nodes?  Note: I need to maintain the traffic between the balancer and nodes safe (encrypted). Block IPs if they access a resource Computing second partial derivative with polar coordinates Consider the polar coordinates with $x=r\cos\theta$ and $y=r\sin\theta$.  I can show using the chain rule that $$\frac{\partial}{\partial x} = \frac{x}{r} \frac{\partial}{\partial r} -\frac{y}{r^2} \frac{\partial}{\partial \theta}$$   What is the method to compute $\dfrac{\partial^2}{\partial x^2}$? I don't know how to do it. Is there a public API for Stack Overflow? How can I connect a texture node to a material with Python? I know that the compiler will sometimes initialize memory with certain patterns such as 0xCD and 0xDD.  What I want to know is when and why this happens.  When  Is this specific to the compiler used?  Do malloc/new and free/delete work in the same way with regard to this?  Is it platform specific?  Will it occur on other operating systems, such as Linux or VxWorks?  Why  My understanding is this only occurs in Win32 debug configuration, and it is used to detect memory overruns and to help the compiler catch exceptions.  Can you give any practical examples as to how this initialization is useful?  I remember reading something (maybe in Code Complete 2) saying that it is good to initialize memory to a known pattern when allocating it, and certain patterns will trigger interrupts in Win32 which will result in exceptions showing in the debugger.  How portable is this? In Java, for a string x, what is the runtime cost of s.length()? Is it O(1) or O(n)? I've been told that code such as:  for (int i = 0; i &lt; x.length(); i++) {     // blah }   is actually O(n^2) because of the repeated calls to x.length(). Instead I should use:  int l = x.length(); for (int i = 0; i &lt; l; i++) {     // blah }   Is this true? Is string length stored as a private integer attribute of the String class? Or does String.length() really walk the whole string just to determine its length? By "hand cipher", I mean a symmetric cipher for which encryption and decryption can can both be performed with a pencil on graph paper, consuming about 10-20 seconds per character by a proficient user. Additional simple tools, e.g. a deck of cards or a multiplication table, may be used to expedite the process. No mathematical proficiency is required other than mental addition, subtraction, and maybe multiplication.  Basically, it should be a cipher that someone of average mathematical abilities can master, and it should require no digital technology or cryptographic tools that cannot be constructed out of paper.  For example, four-square in CBC mode seems secure to me because CBC is a well established mode of operation and four-square seems to be a good block cipher as it accommodates large keys and seems to produce a random-looking output. However, the fact that four-square in CBC was never widely adopted before digital encryption became a consumer technology leads me to believe that someone broke the cipher and thus discouraged people from using it.  So is there any hand cipher that the best supercomputers would take years to cryptanalyze? If not, then for which hand cipher is the best known attack the most complex? Prove for any $a&gt;1$ there exist a natural number, $N$, such that $a^n&gt;n$ for all $n \ge N$  My attempt:  By definition, for $N$ to be a natural number $1\le N \le ∞$ for any integer $N$.  By induction, the base case $n=1$ is true because $a^1&gt;1$ which is true.  Now assume that $a^k&gt;k$ is true, then it is also true for $n= k+1$.  Hypothesis  $a^{k+1}&gt;k+1$  Now I am not sure if I am on the right track $S^2 \times S^2$ is diffeomophic to $G_2(\mathbb{R}^4)$ $G_2(\mathbb{R}^4)$ is the Grassmannian manifold of two-dimensional subspaces of $\mathbb{R}^4$. I would like a detailed proof. Can it be done explicitly? I mean, showing the map and checking its differentiability using charts? Expectation and variance of the geometric distribution How can one use memorylessness and the  and the  to find the expectation and variance of the geometric distribution?  I will post my own answer, but as always, that shouldn't stop anyone else from posting theirs. Is there a way to enable/disable a wireless network interface via the command line (so I can put it in a bat file)?  When I'm in the office I use a wired connection, but Windows still occasionally bugs me about my wireless connection not being connected (even though I turned off the option for notifying me when there's no connectivity).  I'm guessing the only way to stop it from bugging me is to disable the interface, but I'd rather not have to go into the network settings every time I need to do so.  I'd like to set up a bat file or a shortcut that I can use to enable/disable the wireless (preferably a single one that toggles the current state), and then just set up a keyboard shortcut for that.  I just have no idea how to do so from the command line. I'm trying to make a command block that spawns an item in front of you if you are holding an item with a specific name. I've got these two working scripts;  /testfor @p[r=10] {Inventory:[{tag:{display:{Name:"Item Name"}}}]}  /testfor @p[r=10] {SelectedItemSlot:0,Inventory:[{Slot:0b,­id:"minecraft:diamond_sword"}]­}   but I can't get them together. The block should only look for an item in the active slot. QGIS locked into fullscreen mode on Ubuntu 12.04 String manipulation with & or + in VB.NET In iOS 6 and below I could double tap the home button, tap and hold an app, and  click the red - to close an application(s).  In iOS 7 this does not work. How can I restart an app that's exploding without resetting the entire OS?