Does a separable metric space have a countable basis?
Every metrizable space with a countable dense subset has a countable basis
Java: creating a date object from a string and inserting into MySQL Is the .minecraft folder hidden on a Mac? MiKTeX graphics version 1.3b bug on Windows 10 (\set@curr@file undefined) Why won't Smart UV Project automatically unwrap a simple chair? I created a very simple chair mesh and I would like to unwrap it so that I can map a texture. I would like to have Smart UV Project unwrap it automatically, but whether I do it that way or try manually, I am unable to unwrap the model.   Is there something I'm missing?    I tried a few guides, but I'm not sure where I'm going wrong.  My File: If I wave around a bar magnet, the magnetic field in the space around it changes. Is this enough to go through the whole speed of light derivation implying that the motion creates an electromagnetic wave? If so how do I determine the wavelength and direction of the resulting wave? Today I've got 10 upvotes for an answer. Answer was a first answer in the question. I got an Nice Answer badge for this, but no Enlightened badge.  Shouldn't I get both?  is my answer :) After the upgrade of salesforce to Spring 15, I am getting this error "Error: You have exceeded the maximum number (5) of Apex scheduled jobs." when scheduling more than 5 batches. I have this issue in several environment. I used to more than 20 batches scheduled at once.   On the link below, it says that I can schedule up to 100 batches but I am being restricted to 5 only.   I can't have more than 5 jobs here. Proving $\sum_{k=1}^n k k!=(n+1)!-1$ Prove: $\displaystyle\sum_{k=1}^n k k!=(n+1)!-1$ (preferably combinatorially)   It's pretty easy to think of a story for the RHS: arrange $n+1$ people in a row and remove the the option of everyone arranged to height from shortest to highest, but it doesn't hold up for the LHS.   Alternatively, trying to visualize the LHS, I noticed that it's like a right angle tetrahedra:  1  2!+2!  3!+3!+3!  ...  But it doesn't help to see a connection to the RHS.  Note: no integrals or gamma function nor use of other identities without proving them nor generating functions. Can I install Windows OS (Windows 7) on a removable USB hard drive? I wanted to take a sneak peek at Windows 7 so I thought of installing it. I have Windows Vista on my laptop which came pre-installed with it. I didn't want to mess with it.  So I created a partition (20 GB) in my USB external hard disk and tried to install Windows 7 on that partition. But when I booted from a Windows 7 DVD and selected the target partition on USB hard disk, it said it cannot be installed.  Is there any way to install Windows on an external USB hard disk? Why is the Night's Watch so depleted at the start of ASOIAF? At the start of AGOT, the total number of the Night's Watch is said to be less than a thousand. During Aegon's conquest, the Watch numbered ten thousand men. Out of the nineteen castles on the wall, only three are manned today. Castle black itself is once said to have housed 5000.   This rapid deterioration doesn't make sense to me from a world-building perspective. The NW have continued to maintain themselves pretty well for nigh on 8000 years (if the tales can be believed that is, Sam Tarly finds no written evidence of Lord Commanders earlier than #673, which suggests that 8000 years may be an inflated 'legendary' number).   Whereas in the real world, one of the oldest and most venerable institutions, the Catholic Church, has been around for less than 2000 years and has been administered by ~200 popes. The Night's Watch has had a few rocky years, sure, but for it to maintain itself so well for so long and then deteriorate only in the last 300 years seems strange to me.   The NW has two purposes. The ostensible one of defending against the Others, and the (arguably much more real, at least at the start of AGOT) purpose of serving as a dumping ground for the 'losers' of Westeros. By 'losers', I mean the people on the losing side of various wars and political battles, as well as criminals and n-th sons of noble houses with nothing to inherit.  I am currently reading through Fire and Blood, and was struck by one chapter, where an armed revolt of members of the Faith were defeated by Maegor, and 2000 brothers were forced to take the black. Those sorts of numbers don't exist in the recent histories it seems.   One would expect that after Robert's Rebellion, there would be a surfeit of defeated Targaryen loyalists who were forced to take the black, but apart from a smattering of named characters (including Ser Alliser Thorne), there seem to be hardly any Night's watch recruits from recent wars.  Given the way the Night's watch is continually bolstered by the losers of wars and by criminals and other people who elsewise have nothing going for them, why, at the start of AGOT, is the force so depleted? Creation parameters menu greyed out When adding a UV Sphere mesh in Blender 2.8, the creation parameters menu on the bottom left of the attached image for this UV Sphere seems to be greyed out. Any idea why this might be? Thanks. I've just installed ubuntu server 17.10. During installation, it suggested me to connect to the network through wifi, and so i did. After installation was finished and system was rebooted, computer connected to the wifi automatically (which means, it saved the connection creds somewhere). But in /etc/network/interfaces i found nothing. I need my computer connect to wifi network with static ip, so I've put configuration into the /etc/network/interfaces:  # /etc/network/interfaces -- configuration file for ifup(8), ifdown(8) # Generated by debian-installer.  # The loopback interface auto lo iface lo inet loopback   iface wlp2s0b1 inet static         wpa-driver wext         address 192.168.0.12         netmask 255.255.255.0         gateway 192.168.0.1         wpa-ssid *****         wpa-psk **********         dns-nameservers 8.8.8.8 192.168.0.1 auto wlp2s0b1   When system starts, it doesn't connect using my configuration. It does only after  sudo ifdown wlp2s0b1 &amp;&amp; sudo ifup -v wlp2s0b1  and after this command, system getting a SECOND IP! Server is still available by the ip it gets from DHCP, and in the same time, it is available by the static ip! How to install gnome shell extensions offline? I know how to go to the  website and download gnome-shell extensions, but now I need to install some extensions available there on a computer without any internet access at all. It is in a internal corporate network and there's no way I can get outside internet access on it, so I must find another way. I can copy files in a usb disk.   At my home computer, I have found my extensions at ~/.local/share/gnome-shell/extensions/ but just copying this folder to the target corporate computer didn't do the trick.   Running gnome-tweak-tool gives me a "Install Shell Extension" button but I don't know how to download an extension in a format acceptable to install using this button. I have tried to point to the folder above but it didn't work either.  What do I need to do? Create a tar archive split into blocks of a maximum size What is a smart pointer and when should I use one? What is a smart pointer and when should I use one? I want to find the $nth$ derivatives of the function $e^{f(x)}$ with respect to $x$, the first derivative is $$e^{f(x)}f^{\prime}(x).$$  The second derivative is $$\left( {\frac {d^{2}}{d{x}^{2}}}f \left( x \right)  \right) {{\rm e}^ {f \left( x \right) }}+ \left( {\frac {d}{dx}}f \left( x \right)   \right) ^{2}{{\rm e}^{f \left( x \right) }} .$$ The third derivative is $$\left( {\frac {d^{3}}{d{x}^{3}}}f \left( x \right)  \right) {{\rm e}^ {f \left( x \right) }}+3\, \left( {\frac {d^{2}}{d{x}^{2}}}f \left( x  \right)  \right)  \left( {\frac {d}{dx}}f \left( x \right)  \right) { {\rm e}^{f \left( x \right) }}+ \left( {\frac {d}{dx}}f \left( x  \right)  \right) ^{3}{{\rm e}^{f \left( x \right) }} $$  The fourth derivative is $$ \left( {\frac {d^{4}}{d{x}^{4}}}f \left( x \right)  \right) {{\rm e}^ {f \left( x \right) }}+4\, \left( {\frac {d^{3}}{d{x}^{3}}}f \left( x  \right)  \right)  \left( {\frac {d}{dx}}f \left( x \right)  \right) { {\rm e}^{f \left( x \right) }}+3\, \left( {\frac {d^{2}}{d{x}^{2}}}f  \left( x \right)  \right) ^{2}{{\rm e}^{f \left( x \right) }}+6\,  \left( {\frac {d^{2}}{d{x}^{2}}}f \left( x \right)  \right)  \left( { \frac {d}{dx}}f \left( x \right)  \right) ^{2}{{\rm e}^{f \left( x  \right) }}+ \left( {\frac {d}{dx}}f \left( x \right)  \right) ^{4}{ {\rm e}^{f \left( x \right) }} $$  My question is: Is there a general formula or a pattern for the nth derivative of $e^{f(x)}$. You may use the maple command diff(exp(f(x)), x$5) to do some experiments. Thanks a lot ^^ Fancy chapter headings The optical density of a medium is quantified by its refractive index $n$. Does it have any correlation with the mass/number density of the medium? In other words is an optically denser medium must have a greater mass density compared to an optically rarer medium? What's the legal way to stream music online? It's really hard getting a definite answer on this so I'm going to ask it here. Is there a legal way to stream new music on a website without getting artist consent first. There seems to be a lot of popular sites like hotnewhiphop.com doing this that are hosting from both the US and Canada so I'm guessing there is a grey area that allows it. For the record I don't allow downloads of the music and simply stream each song in a player. Pygame: Is there any easy way to find the letter/number of ANY alphanumeric pressed?