PHP equality seems obviously wrong in foreach loop
Why does PHP consider 0 to be equal to a string?
I am trying to prove that:  Let $f$ be analytic in the closed unit disc with $f(z)\leq 1$ for $|z|\leq1$.  For a given $0&lt;r&lt;1$ and $|z_1|,|z_2|\leq r$, $z_1\neq z_2$ then,   $$\left|\frac{f(z_2)-f(z_1)}{z_2-z_1}\right|\leq \frac{1}{(1-r)^2}.$$  My attempt is: part a  of the question asks to prove $$\left|\sum_k^\infty a_nz^n\right|\leq \frac{ |z^k|}{1-|z|}.$$   So, \begin{eqnarray*}  \left|\frac{f(z_2)-f(z_1)}{z_2-z_1}\right|&amp;=&amp; \frac{|\sum_1^\infty a_nz_2^n-\sum_1^\infty a_nz_1^n|}{|z_2-z_1|}\\  &amp;\leq&amp; \frac{\frac{ |z_1 |}{1-|z_1|}+\frac{ |z _2|}{1-|z_2|}}{|z_2-z_1|}\\  &amp;\leq&amp;\frac{1}{(1-r)^2} \frac{   |z_2| ({1-|z_1|})+  |z _1| (1-|z_2|) }{|z_2-z_1|}\\ \end{eqnarray*} But could not prove that the last term is controlled by 1. can't read from SQlite database Suppose I have a question in my mind that I think is answerable but because I don't already know the answer, I'm not sure how to express in a way that makes it clear and definitively answerable. I suspect that someone more knowledgable than me would understand what I'm trying to get at though and could help me word the question properly.  Is there a good place to find this sort of help? As I was trying to validate our pcb design, I measured the impedance matching on the digital transmission lines, and got stuck with the oscilloscope not showing what I expected. We are using the PicoScope 4227, but I suspect that the strange measurement is not directly related to the specific oscilloscope but more to general on how to measure digital signals.  My setup is as follow: I measure the output-pin of an FPGA with both oscilloscope input A and B.  Input A (blue) is measured using the oscilloscope probe set to x10.  Input B (red) is measured using a 50-ohm coxial cable terminated at the scope input with 50-ohm.  As you can see, Input B seems correct, no reflection ect.  But Input A (the probe) has some overshoot, and ringing.  The probe should be calibrated and valid to 250MHz, so I don't get was is wrong. ?  I suspect that the small probe-clip adds some inductance, and therefore we see the ringing. But I really don't know.    EDIT After reading your answers, I walked got into our lab storage and started looking, and found a probe GND clip like the one showed in the answer below.   When I use that clip, I get the output below. Which is really a huge improvement. Disable output buffering Is output buffering enabled by default in Python's interpreter for sys.stdout?  If the answer is positive, what are all the ways to disable it?  Suggestions so far:   Use the -u command line switch Wrap sys.stdout in an object that flushes after every write Set PYTHONUNBUFFERED env var sys.stdout = os.fdopen(sys.stdout.fileno(), 'w', 0)   Is there any other way to set some global flag in sys/sys.stdout programmatically during execution? Set the maximum character length of a UITextField How can I set the maximum amount of characters in a UITextField on the iPhone SDK when I load up a UIView? What does 'apt-get install update' do? I saw this snippet in some installation instructions:  $ apt-get install update   I know what apt-get install XXXX does and I know what apt-get update does, but I can't find any info on what this combined statement does. What does it do? Typesetting linguistic rewrite rule I'm trying to (more or less) replicate this phonological rewrite rule:    I'm using the package , and what I manage to accomplish is this:  \documentclass{article} \usepackage{phonrule} \begin{document}  \phonc     {\phonfeat{$-$cnt\\ +hi}}     {[$\alpha$grv]}     {\oneof{%         \phonfeat{$-$cnt\\ $\alpha$grv}\phold\\         \phold\phonfeat{$-$cnt\\ $\alpha$vce}%     }}  \end{document}     My main problem here is what appears after the "when" slash:  (1) The package only provides a left curly bracket - how can I add a right one as well?  (2) The two options within the curly brackets are not well aligned. I think comparing the two pictures themselves says it better than what I could do with words. Looping through array and removing items, without breaking for loop Introduction to string theory How to identify a downvoting stalker Possible Duplicate:          Yeah I got a deranged stalker that keeps downvoting me.  Anyone know how going about identifying such individuals?  (I just got 4 all at the same time just after making a new post).      that was the question I originally asked. Please tell me, what is so wrong with it ? If $P(A \cup B \cup C) = 1$, $P(B) = 2P(A) $, $P(C) = 3P(A) $, $P(A \cap B) = P(A \cap C) = P(B \cap C) $, then $P(A) \le \frac14$ We have ($P$ is probability): $P(A \cup B \cup C) = 1$ ; $P(B) = 2P(A) $ ; $P(C) = 3P(A) $ and $P(A \cap B) = P(A \cap C) = P(B \cap C) $. Prove that $P(A) \le \frac{1}{4} $. Well, I tried with the fact that $ 1 = P(A \cup B \cup C) = 6P(A) - 3P(A \cap B) + P(A \cap B \cap C) $ but I got stuck... Could anyone help me, please? Difference between administrative and user mode of MiKTeX I am a new user of Ubuntu 12.04.   I installed Ubuntu and Windows XP, and I want to use both operating systems. When I restart or boot my PC the GRUB menu does not appear.  How can I solve this problem? Is it possible to make the -init method private in Objective-C? I need to hide (make private) the -init method of my class in Objective-C.  How can I do that? Why can't we see the selected reasons when there are pending close votes for a question? When users vote to close a question, the original poster can't see the selected reason why until after the question is already closed.  If they could see this information, they might be able to edit the question to make it more acceptable and averting the need to close it.  For example, the owner of this  cannot see the reason why his question is being voted to close: Why there are real numbers with infinite digits, but no such natural numbers (or another reason why real numbers are uncountable) This question is me trying to understand (again) why there can be no one-to-one correspondence between the sets of natural and real numbers.  The source of confusion is this: if we abstract completely from the properties and operations on numbers and just think of them as strings of digits, it appears to be possible to list all the real numbers between $0$ and $1$ and all positive integers having the same digits in the same (or reverse) order, for example:  $$0.1 \to 1$$  $$0.01 \to 10$$  $$0.0101 \to 1010$$  $$0.110101 \to 101011$$  I use binary expansion for simplicity.  Since irrational numbers have infinite expansions, we would have to consider some kind of 'infinite natural numbers', like:  $$101110001\dots$$  or  $$\dots101110001$$  I think the main (and only) reason why such numbers don't exist is this requirement:   We need the sets of real and natural numbers to be ordered. We need to be able to do arithmetics on real and natural numbers.   Obviously, if we consider any of two types of 'infinite natural numbers' and the usual absolute value, we find that it's impossible to order them, or do arithmetics with them.  The only way is to change the norm (to $p-$adic norm for example).  While with the real numbers it's still possible to order them, and do arithmetics with them when they have infinite amount of digits in their expansion (or at least in principle).     Is my reasoning correct? Are the two requirements (ordering and arithmetics) enough to explain why natural numbers with infinite amount of digits do not exist, while real numbers do?   This confusion is not restricted to me alone, see  for example What is difference between: "I have been married with (was married with, married) her for three years." What is the difference between the three sentences below?   I have been married with her for three years. I was married with her for three years. I married her for three years. I have a bash script that makes a cURL request and writes the output to a file called resp.txt.  I need to create an exclusive lock so that I can write to that file and not worry about multiple users running the script and editing the text file at the same time. Here is the code that I expect to lock the file, perform the request, and write to the text file: ( flock -e 200 curl 'someurl' -H 'someHeader' &gt; resp.txt ) 200&gt;/home/user/ITS/resp.txt  Is this the correct way to go about this?  My actual script is a bit longer than this, but it seems to break when I add the flock syntax to the bash script. If someone could explain how these file descriptors work and let me know if I am locking the file correctly that would be awesome! How to capture the scale of a scene? My framing in the following photo completely failed to capture the sheer height of the waterfall.  If you don't know I was standing at the top of the waterfall, and the "splinters" at the bottom are full-size tree trunks 2 feet in diameter, you wouldn't have a clue how tall it is.  It just looks like a smaller, shorter waterfall shot with a slower shutter speed.    My question isn't about this picture or waterfalls in particular, but about framing to capture the scale of your subject in general.  What are techniques to show just how big something really is?  Or conversely, something really small?  Especially things like rocks or water that look roughly the same at any size.