Rotating a circle about a larger circle
Plotting an epicycloid
Quoting backslashes in Python string literals I have a string that contains both double-quotes and backslashes that I want to set to a variable in Python. However, whenever I try to set it, the quotes or slashes are either removed or escaped. Here's an example:  &gt;&gt;&gt; foo = 'baz "\"' &gt;&gt;&gt; foo 'baz ""'   So instead of baz "\" like I want I'm getting baz "". If I then try to escape the backslash, it doesn't help either:  &gt;&gt;&gt; foo = 'baz "\\"' &gt;&gt;&gt; foo 'baz "\\"'   Which now matches what I put in but wasn't what I originally wanted. How do you get around this problem? A net $\varphi : [0, \omega_1) \to M$ on a metric space $M$ converges $\iff \varphi$ is eventually constant I want to prove that      If $M$ is a metric space, then a net $\varphi : [0, \omega_1) \to M$ converges if and only if $\varphi$ is eventually constant. ($[0, \omega_1)$ is the set of ordinals less than $\omega_1$, where $\omega_1$ is the first uncountable ordinal, with the order topology).   $(\Leftarrow)$ is clear.  My trouble is with $(\Rightarrow)$. Suppose that $\varphi \rightarrow x$.  Let $U = \{ \alpha \in [0, \omega_1) \, \mid \varphi(\alpha) \neq x \}.$  If $U = \emptyset $ we are done, so assume $U \neq \emptyset$. Since $[0, \omega_1)$ is well ordered, there is a $\alpha_1 \in U$ such that $ \alpha_1 \leq \alpha \, \, \forall \alpha \in U.$  If $ U \setminus \alpha_1 = \emptyset$ we are done. If not, we repeat the procedure.  It is clear that if $card(U) = n$ for some $n \in \omega$ then we only have a finite set of ordinals $\{\alpha_1, \ldots, \alpha_n\}=U$ so $\varphi$ is constant for $\alpha &gt; \alpha_n.$  If $U$ is countably infinite, then $U = \{\alpha_n\}_{n \in \omega}$ and since $[0, \omega_1)$ is sequentially compact and the $\alpha_n$'s are countable ordinals  we obtain a convergent subsequence $\{\alpha_{n_k}\}$ of $U$ to some countable ordinal $\beta \in [0, \omega_1)$ $[\beta = \cup_{n_k \in \omega}\alpha_{n_k}???],$ hence $\varphi$ is constant for all $ \alpha &gt; \beta.$     But what if $U$ is uncountable?    Idea: If $U = [0, \omega_1),$ then since $\varphi \rightarrow x$, for every $n \in \omega$ there is $\alpha_n \in U$ such that $\alpha \geq \alpha_n \implies \varphi(\alpha) \in B_{\frac{1}{n}}(x).$ This is a countable sequence, so since $[0, \omega_1)$ is sequentially compact, there is a subsequence converging to a countable ordinal $\beta \in [0, \omega_1)$. Clearly, $\beta$ satisfies that $\phi(\beta) \in B_{\frac{1}{n}}$(x) for every $n \in \omega.$     We can conclude that $\varphi(\beta)= x$ right?   For if $\varphi(\beta) \neq x$, then taking $n$ such that $0 &lt; \frac{1}{n} &lt; d(x, \varphi(\beta)),$ we would have that $\varphi(\beta) \not \in B_{\frac{1}{n}}(x),$ contradicting the hypothesis.  I feel pretty confident about this, but If someone sees an error in the argument, please comment. Thanks. Sum of a power series $n x^n$ I would like to know: How come that  $$\sum_{n=1}^\infty n x^n=\frac{x}{(x-1)^2}$$  Why isn't it infinity? Optional Android notifications for reputation changes I would like to get a notification if my reputation count has changed. I think there is already some internal API for that. (I can see that changes in the menu bar in the top).  I'm sure that some people would not like that so that should be optional. How can I know if $2^{2^{2^{2^{2}}}}+1=?$ is prime? Book about a teenager programmed to be an assassin and trying to get back at the people responsible I read this book a few years back (around 5?). It was part of a multibook series but I have only read one book.  It's about this teenager who I think had been programmed to be an assassin but then somehow retained his conscience and was out to get the people responsible for that.  I briefly remember a girl, and this one part where he realizes he can ride a horse and then there's a chase too. I think the guy's name was Jim or Jimmy, but not quite. I'm also quite sure he was either part computer, or had a chip or something in his brain which had been programmed to give him a host of mental and physical abilities which he retained and used as well as the series progressed. Possible Duplicate:          I received two answers to a question I asked. One solution suggested I do things in a completely different manner than I have been. Another acknowledged that the first solution was correct but went on to explain how to do what I was asking.  Should I accept the first answer because it provides the better way of doing things or should I accept the second one because it answers the precise question that was asked? Why does the CRT formula yield a solution of a congruence system? I'm attempting to do this in a procedure:  DECLARE @a bit = 1; BEGIN     SELECT * INTO #aTemp FROM OPENROWSET( ... );      IF @a = 0     BEGIN         SELECT ... INTO #bTemp FROM #aTemp;     END     ELSE     BEGIN         SELECT ... INTO #bTemp FROM #aTemp;     END END   I get the error:  Msg 2714, Level 16, State 1, Line 10 There is already an object named '#bTemp' in the database.   Why is this happening and is there a work around?  Update  I've attempted to add a DROP statement as suggested , but it still does not work:  DECLARE @a bit = 1; BEGIN     SELECT * INTO #aTemp FROM OPENROWSET( ... );      IF @a = 0     BEGIN         IF OBJECT_ID('[tempdb]..#bTemp') IS NOT NULL         BEGIN             DROP TABLE #bTemp;         END          SELECT ... INTO #bTemp FROM #aTemp;     END     ELSE     BEGIN         IF OBJECT_ID('[tempdb]..#bTemp') IS NOT NULL         BEGIN             DROP TABLE #bTemp;         END          SELECT ... INTO #bTemp FROM #aTemp;     END END i have a huuuuge problem.  Created a snapshot and image from my instance...instance has 1000GB of disk.  Now i need to reduce it but everytime i try to create an image or a snapshot from that, i get the same error "Disk need to be at least 1000GB".  There is a way to reduce disk size directly on instance? Some workaround? How do I find this limit: $\lim_{n\to\infty} \left[ n-{n\over e}\left(1+{1\over n}\right)^n \right]$? Delete Everything(the rest of the text) after a specific string How to detect online/offline event cross-browser? (Ubuntu 13.04 with GNOME Shell, upgraded, GNOME version 3.8) Recently, I upgraded Ubuntu to 13.04. the default desktop is gnome-shell. Except Nautilus, other software border doesn't disappear when I make them to be maximized. I checked the problem for these software:  LibreOffice Firefox Rhythmbox thunderbird GNOME-Terminal  On the other hand there are three bars on maximized mode:  GNOME Shell panel  Title-bar for software which contains - + x (minimise, maximise, close) buttons.  Software menu-bar  Number &quot;2&quot; is extra. Is a package missing? Recent feature changes to Stack Exchange Pointwise Convergence and Convergence in the mean of Riemann-integrable functions Let $(f_n)_{n\in\mathbb{N}}$ be a sequence of Riemann-integrable functions on $[a, b]$.   Assume that $(f_n)_{n\in\mathbb{N}}$ converges pointwise to $f$ on $[a, b]$ and converges in the mean to $g$ on $[a, b]$, where $f$ and $g$ are both continuous. Show that $f = g$.   ($(f_n)_{n\in\mathbb{N}}$ converges in the mean to g on $[a , b]$ means that $\lim_{n\to\infty} d(f_n, g) = 0$, where $d$ is the $L_2$ metric.)  I am studying real analysis now and want to prove this statement. But I don't know how to use condition "$(f_n)_{n\in\mathbb{N}}$ converges in the mean to g on $[a , b]$." How can I prove this? Are universal power supplies for laptops worth it? My laptop's cable broke and sadly it seems like I need to buy a new power supply.  What I wonder is, I've found that universal power supplies are much cheaper than the official HP ones. Are they really worth it?  Another question: the original supply has these specs: 65W, 18.5V, 3.5A. However the universal supplies are more powerful (90W, 100W) and come in integer voltages (17V, 18V, 19V, etc). Are they compatible? Should I set them to 18V or 19V? A book about explorers stranded on a planet with two computers I have been looking for a book that I read in the 80's but it's probably older. It was about a spaceship from Earth in a very long mission to discover life? I don't remember, but they had been far too long in space without any results, so the crew was on the verge of mutiny.  They land on a planet, home of two super-computers called...? Alpha? Beta? One seemed more advanced than the other, the planet was void of any other life, and supposedly it was forseen that the planet would be struck by a comet, and the computers see the ship as a way to save or abandon the planet before the impact.  At some point one member of the crew is captured by the computers, and it's vivisected in an attempt to get data about humans. Then they "reassemble" the crew member before returning it to the ship, hoping that the humans could "reactivate it" since the computers were unable to do so. Which of course enrages the ship's crew.  The ship was unable to take off for reason that I don't remember and they must fight the computers to save themselves.  Does anyone know what this is?  Thanks, as soon as I read the names, they did ring a bell on my memory. The case it's closed then. How do I create a decimal field in Access with Alter Table? Where is the usage of Ubuntu cloud guest image on OpenStack documented?