I'm using Ubuntu 11.10.  The python 2.7.2 provided has a bug that has been corrected in the latest 2.7.2 sources from the python repository.  What is the recommended way to replace the ubuntu provided python with the python from source? Or put another way, how do I "update" the ubuntu-provided one?  Ideally, I would just be able to create new .deb(s) that "update" the python2.7/python2.7-dev provided by Ubuntu.
I want to install the latest Python tarball on Ubuntu, downloaded from .  Is this is a correct way to install?  ./configure make make install   If not, how do I do that?
Limit $\frac{x^2y}{x^4+y^2}$ is found using polar coordinates but it is not supposed to exist. Consider the following 2-variable function:     $$f(x,y) = \frac{x^2y}{x^4+y^2}$$   I would like to find the limit of this function as $(x,y) \rightarrow (0,0)$.   I used polar coordinates instead of solving explicitly in $\mathbb R^2 $, and it went as the following:  $$ x = r \cos \theta, \qquad y = r\sin\theta $$   Hence,  $$\lim_{(x,y) \to (0,0)} \frac{x^2y}{x^4 + y^2} = \lim_{r \to 0}\frac{r^2\cos^2\theta(r\sin\theta)}{r^4\cos^4\theta + r^2\sin^2\theta}$$  This simplifies to,  $$ \lim_{r \to 0} \frac{r^3 \cos^2\theta\sin\theta}{r^2(r^2\cos^4\theta + \sin^2\theta)}$$  Simplifying $r^3/r^2$, we finally get;  $$\lim_{r \to 0} \frac{r (\cos^2\theta\sin\theta)}{r^2\cos^4\theta + \sin^2\theta}$$  Now from the above, we find that as $r \to 0$ the limit is $0$.   I wanted to verify this answer so I checked on Wolfram Alpha. Explicitly without changing to polar coordinates, it said that the limit does not exist at $(0,0)$ and rightly so. Then how is it that with polar coordinates, the limit exists and is $0$? Am I doing something wrong in this method?  Also, what should I do in this situation, and when should I NOT use polar coordinates to find limits of multi-variable functions? Why does an integral change signs when flipping the boundaries? Let us define a very simple integral:   $f(x) = \int_{a}^{b}{x}$    for $a,b\ge 0$.  Why do we have the identity $\int_{a}^{b}{x} = -\int_{b}^{a}{x}$?  I drew the graphs and thought about it but to me integration, at least in two-dimensions, is just taking the area underneath a curve so why does it matter which direction you take the sum? Does anyone have a Terminal command-line recipe for making a new bootable USB flash drive for one of the new MacBook Air's?  Is there a way to dd copy the USB boot device that comes in the box and make the new copy bootable?  I'd like to make a new backup copy of the USB rescue device for my MBA, preferably on a much larger flash drive with room for a backup of some of my working directories.  Added:  And is it possible to make, not just a rescue drive, but a bootable USB drive that will boot a fully updated version of the OS (say 10.6.8 or later)?  If so how on a MacBook Air 11, and how big a USB stick will this require? Why use static_cast(x) instead of (int)x? I've heard that the static_cast function should be preferred to C-style or simple function-style casting.  Is this true?  Why? mysqli_fetch_assoc() expects parameter / Call to a member function bind_param() errors. How to get the actual mysql error and fix it? How many RSA keys before a collision? I was wondering how many possible private/public keys exist? If a million people – for whatever reason – would try to generate 5 keys each in the same minute (on the same date and time) is there a high chance of collision? I believe GUID would suffer from that problem as many bits are reversed for date/time (and GUID version) and isn't meant to be used in that way.  Would RSA suffer from collisions if many keys were to be generated in the same moment? Is the amount of possible keys known? I know RSA is based on prime numbers and small numbers are to be rejected. I’m sure values above a certain amount of digits/bits are rejected because software may not be able to support those large values?  So: How many RSA keys before a collision? And if you would try to make many at the same time, would that give you a high chance of collision? Detecting an undefined object property What's the best way of checking if an object property in JavaScript is undefined? Is there any way to find out what happened to a post card sent from other country? Does "Root A" follow the fact about Takatsuki and the One-Eyed Owl? In Root A, Takatsuki does seem to be fascinated by Kaneki's name, but,      I didn't at all expect her to be the One-Eyed Owl.   I just looked her up on the  and it says that       she is the One Eyed-Owl as well as the horror novelist.   Is this true only in the manga or is it also true in Root A? How can I find $\gcd(a^m+1,a^n+1)$ with $a,m,n$ positive integers? How can I find $\gcd(a^m+1,a^n+1)$ with $a,m,n$ positive integers?    I have this idea:  Let $d=\gcd(m,n)$. Then there exist positive integers $x,y$ such that $mx-ny=d$ (WLOG). We shall find $G=\gcd(a^m+1,a^n+1)$.  If $m,n$ are odd, then $d$ is odd, therefore one and only one of $x,y$ is even. We have:  $$a^{ny}(a^d+1)=a^{mx}+a^{ny}=(a^{mx}-1)+(a^{ny}+1)=(a^{mx}+1)+(a^{ny}-1).$$  If $x$ is even and $y$ is odd, then $a^{m}+1\mid a^{mx}-1$ and $a^{n}+1\mid a^{ny}+1$, therefore $G\mid a^{ny}(a^d+1)$. If $x$ is odd and $y$ is even, then $a^{m}+1\mid a^{mx}+1$ and $a^{n}+1\mid a^{ny}-1$, thus $G\mid a^{ny}(a^d+1)$. However, since $\gcd(a^m+1,a^{ny})=\gcd(a^n+1,a^{ny})=1$, so $\gcd(G,a^{ny})=1$, hence $G\mid a^d+1$. We also have $a^d+1\mid a^{m}+1$ and $a^d+1\mid a^{n}+1$, so $a^d+1\mid G$. Thus $G=a^d+1$.  If $v_2(m)=v_2(n)=v_2(d)=k&gt;1$, then there exist some odd numbers $m_1,n_1,d_1$ such that $m=2^km_1,n=2^kn_1,d=2^kd_1$. We shall have $m_1x-n_1y=d_1$, so one and only one of $x,y$ is even, and we can use the same argument when $m,n$ are odd, so $G=a^d+1$.  However, if $v_2(m) \neq v_2(n)$, I cannot find any solutions for this. I think that $G \in \{1,2\}$, but I cannot prove or disprove it. How can I find $G=\gcd(a^m+1,a^n+1)$ if $v_2(m) \neq v_2(n)$ ? Moreover, is there anything from my arguments that can be improved ? Does the following limit exist? $$\lim_{x \to 0} x\sin\left(\frac{1}{x}\right)$$  If yes, then I have to find it; if no, then I need to give reason why. I couldn’t figure out how to prove this formally, can someone please help me out. Language Options -> Spell Checking in Windows 10 version 1803 Convert Month Number to Month Name Function in SQL For which Natural $n\ge2: \phi(n)=n/2$ Short story set in the near future where all wars are settled on the moon using automated machines? Plot Details/Summary  Another one where I have only sketchy memories of the tale, I fear.   The setting for this one is the near future (from the writer's perspective, which I think was the 1970s).  Man's reached a point where bloodshed and loss of life are no longer necessary to settle conflicts.  Instead, all disputes are settled through an annual combat held on the surface of the moon, using the best combat machines each nation can come up with.  The protagonist, as I recall, is an engineer for the Americans.  He recollects past conflicts, and the circumstances for this years fracas.  Much of the combat is told from his observers' perspective.  The actual conflict is a rather clever affair, with a description of each team's designs and all the tricks and gee-whiz things they built into them.  The protagonist's team manages to prevail, when they managed to use an attack as a feint, with the real attack being a swarm of microscopic machines (they did not use the term nanites) that destroyed the opposing machine from the inside.  Timeframe/Other Details  I think this one dates from the 1970s.  I don't think it more recent, given my recollections of when I read it, and also the technology descriptions they used in it.  There is an outside chance that the combat is not between rival nations, but rival corporations.  That would change the premise of "man evolving beyond bloodshed", of course.  I think it's nations fighting, though.  I am almost 100% certain this was in a sci-fi magazine, not an anthology. Is there a way to step between 0 and 1 by 0.1?   I thought I could do it like the following, but it failed:  for i in range(0, 1, 0.1):     print i   Instead, it says that the step argument cannot be zero, which I did not expect. Site specific magic comment links How to obtain a confidence interval for a percentile? RSA, DES, AES, etc., all use (relatively) complicated mathematics to encrypt some message with some key. For each of these methods, there have been several documented vulnerabilities found over the years. Some even believe that there is a vulnerability in AES known only to the NSA.  On the other hand, the one-time pad is not only ridiculously simple, but also has been shown to be impossible to crack (if used appropriately).  Say you have some message to be encrypted with length n. Simply generate a random string with length m where m is at least as large as n, and perform modular addition of the random string onto the message.  As long as the random string is generated with a high-enough-quality random number generator, and as long as the same one-time pad isn't reused, it should be impossible to crack.  If this is true, all we would need to perfect are fast, cryptographically secure deterministic random number generators. Use the key as a starting seed for the RNG and you have a powerful uncrackable encryption scheme which is simple to understand and implement.  Blum-Blum-Shub is a fast, cryptographically secure PRNG, and there are others too.  I have written a C++ program which uses two 2048-bit primes (which match the necessary criteria) for Blum-Blum-Shub and uses a password which the user enters - converted into a starting seed - to run byte-wise modular addition. The process is fast, deterministic, and if the literature I have read is correct then it should be very secure.  So why is so much time and effort invested in coming up with convoluted encryption cyphers when mathematics shows that the simplest is often the best? Prove the inequality $|xy|\leq\frac{1}{2}(x^2+y^2)$