Python all combinations of one item per list
Get the cartesian product of a series of lists?
In $\mathbb{R}^n$, locally lipschitz on compact set implies lipschitz I need to prove:  Let $A$ be open in $\mathbb{R}^m$, $g:A \longrightarrow \mathbb{R}^n$ a  locally lipschitz function and $C$ a compact subset of $A$. Show that $g$ is lipschitz on $C$.  Can anyone help me? Question on showing a bijection between $\pi_1(X,x_0)$ and $[S^1, X]$ when X is path connected. I am trying to do this question taken from Hatchers algebraic topology and I am struggling to understand the notation and the concepts.  As far as I know $\pi_1(X,x_0)$ is the set of end point preserving homotopy classes of loops in X based at $x_0$ and a loop is just a path    $f:I \rightarrow X$ with $f(0)=f(1)$. The question says we can regard $\pi_1(X, x_0)$ as the set of basepoint preserving homotopy classes of maps $(S^1, s_0) \rightarrow (X, x_0)$.   This confuses me, does it mean the set of basepoint preserving homotopy class on maps $g:S^1 \rightarrow X$ which map loops in $S^1$ based at $s_0$ to loops in X based at $x_0$?  Then how can $\pi_1(X,x_0)$ be regarded as this set?  If someone could explain this it would be really useful Get program execution time in the shell I want to execute something in a linux shell under a few different conditions, and be able to output the execution time of each execution.  I know I could write a perl or python script that would do this, but is there a way I can do it in the shell? (which happens to be bash) How do I make exponential equation with points?  Here are my points:  x = 0, y = 0 x = 1, y = 4.75000 x = 2, y = 9.26250 x = 3, y = 13.54937 x = 4, y = 17.62191   this is same as   x = 0, y = 0 x = 1, y = (0 + 5) * 0.95  x = 2, y = ((5 * 0.95) + 5) * 0.95 x = 3, y = (((5 * 0.95) + 5) * 0.95 + 5)) * 0.95 x = 4, y = ((((5 * 0.95) + 5) * 0.95 + 5)) * 0.95 + 5) ) 0.95   as x value increase by 1, y value is added by 5 and multiplied by 0.95 i tried to make an equation for this but i couldn't  also i tried to use natural exponential but the initial value is 0 so it didn't work  please help me How do I take the limit as $n$ goes to $\infty$ of $\frac{\sqrt{n}}{\log(n)}$? How do take this limit:  $$ \lim_{n\to\infty} \frac{\sqrt{n}}{\log(n)}$$  I have a feeling that it is infinity, but I'm not sure how to prove it. Should I use L'Hopitals Rule? Does deleting iCloud photos affect them on devices? If I delete a photo from my iCloud will it also be removed from my devices that are connected to my account? Debian based system, only one gui program, nothing else I would like to make a debian system where you can only open one GUI program at boot, no other graphical interface, no minimize, or any X apart from that program, is there a way to do it on debian if possible, or any other custom distro? I just want to boot open the program and allow the user to only see and use that program. How can one link / merge / combine / associate two accounts / users? (Anonymous / unregistered / cookie, or Google / Facebook / registered) I accidentally posted a question without being logged in. Is there a way to associate that question with my account?   For more information, visit &quot;&quot; in the .   a.k.a. How can you link a registered account to a cookie-based account? a.k.a. How do I merge an unregistered account with a registered account a.k.a. Merging users a.k.a. How do I associate anonymous questions I’ve asked with my registered account? a.k.a. Is there a way to claim an unregistered user? (in case anyone searches with those terms) How to cross-reference an inequality with \cref? I have inequalities being cross-referenced by \cref as equations.  1-) How can I change that? (and still have inequalities with the same numbering as equations)  2-) How can I change that and have inequalities with their own numbering?  \documentclass[12pt]{article} \usepackage{amsmath} \usepackage{cleveref} \usepackage[letterpaper]{geometry} \begin{document}  \begin{flalign} &amp;f(x) \geq g(x)&amp; \label{i:positivity} \end{flalign}  Admitting that \cref{i:positivity} has a solution, ...    \end{document} Electorate badge rules? I just got the  badge on StackOverflow, which is nice, but I noticed a number of top users aren't yet listed (inluding Jon Skeet and Marc Gravell, who would certainly qualify).  This made me wonder how the badges are retrospectively applied. Is it just that the display is heavily cached and the badge is awarded when the user logs in again or something? I can clearly see that $\dfrac{n!}{n^n}\to 0$ when $n\to\infty$. But how do I know if the sum $$\sum_{n=1}^{\infty}\frac{n!}{n^n}$$ is convergent or not? I know this might be basic, but thank you if anyone can help me. An invalid argument, the conclusion of which is a tautology Why it is not possible to have such argument?  I found some textbook Introduction to Formal Logic and this is from one of the first excercises. This is marked as impossible, but I do not understand why. What is the formula for Real vs Apparent Depth, when not looking perpendicular to the interface?   I know the formula $$\frac{\text{real depth}}{\text{apparent depth}}=n$$   but I'm not looking for this. When I melt 16 oz of chocolate I add 4 oz of oil how long can I keep this and how should it be stored. Someone said something about botulism ?? Using something like this:  try:    # Something... except Exception as excep:    logger = logging.getLogger("component")    logger.warning("something raised an exception: " + excep)    logger.info("something raised an exception: " + excep)   I would rather not have it on the error-level cause in my special case it is not an error. 24% tax on first pay in the UK? Quite a similar thread to others I've seen here - hope I'm not repeating the same questions again!   I just got my first payslip after arriving in the UK and noticed that the tax is far higher than the HMRC rate for my salary bracket.     I did some research but couldn't find any reason why I would be taxed at 24.23% of my gross this month AND then an additional amount for NI.    I have about £640 back pay from April that is only being paid now,but even so, it doesn't explain the rather large discrepancy between the HMRC rate and what I'm seeing here.   Any ideas? How can I avoid soft dull "spots" in my pictures? Recently, I've been doing a lot more photography, particularly with my 100-400mm telephoto and 16-35mm wide. I am skilled enough that I can capture the shot mostly as I want with just the camera gear, requiring minimal post processing. I'm a huge fan of ETTR now, so most of my shots are overexposed to support more shadow DR and improve the noise performance of my el-chepo 450D body.  I've noticed quite a bit lately during post processing in lightroom that my sky's or any other lighter areas of my shots tend have spots on them. They are soft and dull to one degree or another (seems to depend on the zoom factor), so probably something either on the sensor or the lens. I'm having a hard time figuring out exactly what they are, as I try to use my lens pen brush before any shoot, yet I still have them. I am having to make quite a few healing corrections post-process to get rid of them.  Is there an easy way to identify where the spots are on my lenses? Once identified, if a quick brush of the outer lens element with a lens pen (or soft camel hair brush) doesn't do the trick, does that mean the spots are on my sensor? Is it possible there is particulate inside the lens body (all of my gear is less than a year old outside of my 450D body, and its all Canon L-Series gear, so I would home that I don't already have detrimental particulates floating around inside my lenses messing up my shots. :|)  Here are a couple examples. The spots are harder to see on screen, and I first noticed them when I printed a few of my more recent shots. There are quite a few, and the shot the examples below were taken from, where the sky took up about 30% of the top edge of the photo, there were probably 10-12 different spots, some of them darker, many of them lighter. The darker ones are the ones that are very visible in prints, where as the softer ones are not as visible, but still apparent enough to ruin an expensive print. Lorentz Invariant Integration Measure Excel: identifying if all values in a row are not equal I'm using a common charger for both of my laptops.  The charger is specified at 20 Volts and 3.25 Amperes. My other laptop has a specification of 19 V and 3.42 A.  Is it safe to charge my laptop with chargers whose specifications exceed or are not equal to the mentioned specifications?  I have read somewhere that it may cause some damage if the voltage or amperage is not matching the specs.