I am trying to find titles and author of 1950s era short stories about a family of hillbillies with supernatural powers. One family member was called Cousin Lemuel. This is categorically NOT Ray Bradbury's Elliot Family.    These stories appeared in sci-fi pulp collections, possibly Amazing Stories, in the late 1950s and early 1960s. Any help greatly appreciated.
I'm trying to recall a story I read in the 1960s or 1970s, but which I suspect was older than that.  It was about a quasi-immortal family in the twentieth century who lived in a rural area and kept a low profile. It was a stand-alone story and only the family, and perhaps distant relatives, had unusual powers. I don't think they were aliens, just some offshoot of humanity.   They were of varying ages, ranging from relatively young to thousands of years old. They had lived in Europe before immigrating to the American colonies. Each person had a distinctive set of psi powers, ranging from the grandpa, pa, ma and son. I believe the youngest, just called Baby, was the most powerful and least human looking, and lived in the attic. He slept most of the time.  Nothing remains in my memory of the plot.  As I recall, the story had a Theodore Sturgeon feeling to it, with a humorous, ironic touch, but it probably wasn't his. I haven't been able to identify it from looking at a list of his works.  I probably read it in an anthology, but I might have seen it in an old magazine. I'm just not sure.  If anyone can help me identify it, I'd be grateful. Then I can scratch that mental itch.
Prove that the power set of an $n$-element set contains $2^n$ elements Theorem. Let $X$ denote an arbitrary set such that $|X|=n$. Then $|\mathcal P(X)|=2^n$.      Proof. The proof is by induction on the numbers of elements of $X$.      For the base case, suppose $|X|=0$. Clearly, $X=\emptyset$. But the empty set is the only subset of itself, so $|\mathcal P(X)|=1=2^0$.      Now the induction step. Suppose $|X|=n$; by the induction hypotesis, we know that $|\mathcal P(X)|=2^n$. Let $Y$ be a set with $n+1$ elements, namely $Y=X\cup\{a\}$. There are two kinds of subsets of $Y$: those that include $a$ and those that don't. The first are exactly the subsets of $X$, and there are $2^n$ of them. The latter are sets of the form $Z\cup\{a\}$, where $Z\in\mathcal P(X)$; since there are $2^n$ possible choices for $Z$, there must be exactly $2^n$ subsets of $Y$ of which $a$ is an element. Therefore $|\mathcal P(Y)|=2^n+2^n=2^{n+1}$. $\square$      From the above explanation, I don't understand why the set that contains $\{a\}$ will contain $2^{|n|}$ elements when it should clearly be $2^{|1|}$.  The construction of a new set $S$ is the union of the old set with cardinality $n$ and an new element $\{a\}$, therefore the set that do not contain $\{a\}$ still has cardinality $n$ and the set that contains $\{a\}$ is just $\{a\}$, one element...  Can someone please elucidate? Xml configuration versus Annotation based configuration In a few large projects i have been working on lately it seems to become increasingly important to choose one or the other (XML or Annotation). As projects grow, consistency is very important for maintainability.   My questions are: what are the advantages of XML-based configuration over Annotation-based configuration and what are the advantages of Annotation-based configuration over XML-based configuration? I'm installing a brand new motion activated security light to an existing box on my garage. After removing the old light, I notice it only has white/black wiring while the new light fixture has of course white/black/green (ground) wires to attach. What do I do if no ground wire is available with the old box? I know it might be too easy for you guys here. I'm practicing some problems in the textbook, but this one really drove me crazy. From $\gcd( a, b ) = 1$, I have $ax + by = 1$, where should I go from here? The extra $ac$ is so annoying. Any hint?    Thanks, Chan I am looking for QGIS function to extract (or detect) edge from a raster, which was referred in here,  as answer by @MappaGnosis.  The name could have changed since then, or it may have been integrated into other tool... I cannot find it in my QGIS Processing Toolbox (2.14.10 and 2.18.2).  There are similar tools such as GRASS "i.zc Zero-crossing" and SAGA "Gaussian filter", but I am hoping to find this QGIS geoalgorithm. How do lexical closures work? Continuity of a convex function I'm trying to solve the following problem:  Let $f:K\rightarrow \mathbb{R} $, $f$ convex and $K \subseteq \mathbb{R}^n$ convex. Then $f$ is continuous on $K$.   I have proved the only case $n=1$, but for an arbitrary $n$?? I've been studying about the command line and learned that | (pipeline) is meant to redirect the output from a command to the input of another one. So why does the command ls | file doesn't work?  file input is one of more filenames, like file filename1 filename2  ls output is a list of directories and files on a folder, so I thought ls | file was supposed to show the file type of every file on a folder.  When I use it however, the output is:      Usage: file [-bcEhikLlNnprsvz0] [--apple] [--mime-encoding] [--mime-type]         [-e testname] [-F separator] [-f namefile] [-m magicfiles] file ...     file -C [-m magicfiles]     file [--help]   As there was some error with the usage of the file command Assistive technology not found AWTError $ java -jar aprof-plot.jar Exception in thread "main" java.awt.AWTError: Assistive Technology not found: org.GNOME.Accessibility.AtkWrapper     at java.awt.Toolkit.loadAssistiveTechnologies(Toolkit.java:807)     at java.awt.Toolkit.getDefaultToolkit(Toolkit.java:886)     at java.awt.Toolkit.getEventQueue(Toolkit.java:1734)     at java.awt.EventQueue.invokeLater(EventQueue.java:1264)     at aprofplot.Main.newWindow(Main.java:33)     at aprofplot.Main.main(Main.java:359)   Possible explanations I saw here was to install Java-access-bridge. But I am unable to install libaccess-java-bridge. Diminishing returns / non-linear reputation from “great” answers Over time I realized a very annoying property of the Stack Overflow reputation system: Easy answers to popular question are rewarded with a lot more reputation points than actually great answers. In case anybody actually needs examples for this, here are two examples from :   gained me 420 rep, I invested 2 minutes writing it, and it only was a wild guess.   took me about an hour for the research and the math and gained me 40 rep.  Now I know that you are bound to get more rep for answers that are useful to more people, and I'd say that's fine. But the current situation is quite extreme: 30% of my reputation is from 5 of my 330 answers, and they are definitely far from being my best ones.  A final example that is not from my profile, but more extreme: Do you really think  is worth 40000 reputation?  My proposition to improve that situation would be to make the reputation gain from a single answer non-linear, maybe even have it capped at a certain point. I'm not sure on how that non-linear function should look exactly, and would leave good proposals for that to users with more experience than me. What level is a spell if you cast it without expending a spell slot? How can I copy coverart from flac to opus with ffmpeg I am trying to convert some flac files which all have coverart embedded to opus with ffmpeg. All but the coverart gets copied over just fine, but I find myself unable to move the cover over as well. Tried all sorts of -mapmetadata stuff I could find so far, but no luck, the result is always missing the coverart.  While the original .flac reports to have a video stream with the coverart  Duration: 00:02:53.51, start: 0.000000, bitrate: 910 kb/s    Stream #0:0: Audio: flac, 44100 Hz, stereo, s16    Stream #0:1: Video: mjpeg, yuvj420p(pc, bt470bg/unknown/unknown), 500x500 [SAR 1:1 DAR 1:1], 90k tbr, 90k tbn, 90k tbc   the created opus files does not have any graphics:  size=    2815kB time=00:02:53.51 bitrate= 132.9kbits/s speed= 104x video:0kB audio:2793kB subtitle:0kB other streams:0kB global headers:0kB muxing overhead: 0.811556%   I tried -vcodec copy, -mapmetadata 0, -mapmetadata 0:s:0 so far, with no luck. Doesnt seem to have anything todo with opus, as I have the same problem converting to aac.  So is there a way to get the cover out of the flac file and move it over to the new file in on go using ffmpeg, or do I have to extract it first and then glue it back again later to the new file with extra commands? Why is the gravitational force always attractive? Is there another way to explain this without the curvature of space time?   PS: If the simple answer to this question is that mass makes space-time curve in a concave fashion, I can rephrase the question as why does mass make space-time always curve concavely? How can I get ssh-agent working over ssh and in tmux (on OS X)? I have a private key set up for my github account, the passphrase to which is, I believe, stored in OS X's keychain. I certainly don't have to type it in when I open a terminal window and enter ssh git@github.com.  However, when I'm running bash over an ssh session, or locally inside a tmux session, I have to type in the passphrase every single time I attempt to ssh to github.   suggests that a similar problem exists with screen, but I don't really understand the issue well enough to fix it in tmux. There's also  which includes a fairly complicated solution, but for zsh.  EDIT:  In response to , from a local terminal I get the following output:  [~] $ echo $SSH_AUTH_SOCK /tmp/launch-S4HBD6/Listeners [~]  $ ssh-add -l 2048 [my key fingerprint] /Users/richie/.ssh/id_rsa (RSA) [~] $ typeset -p SSH_AUTH_SOCK declare -x SSH_AUTH_SOCK="/tmp/launch-S4HBD6/Listeners"   Whereas over ssh or in tmux I get:  [~] $ echo $SSH_AUTH_SOCK  [~] $ ssh-add -l Could not open a connection to your authentication agent. [~] $ typeset -p SSH_AUTH_SOCK bash: typeset: SSH_AUTH_SOCK: not found   echo $SSH_AGENT_PID returns nothing whatever shell I run it from. I'm using Ubuntu 14.04 but since some weeks I'm stuck with the old 13.10 lockscreen design for some reason.  I already tried compizconfig-settings-manager but it doesn't offer me any option for changing the lockscreen design and even resetting Compiz and Unity with   dconf reset -f /org/compiz/   didn't help.  Are there any other ways to get the new lockscreen back? How to convert Bedrock texture pack to Java Edition Minecraft I'm trying to use a texture pack designed for the Bedrock Edition of Minecraft, on Java Edition. I looked at the texture names for a Java Edition texture pack and compared those to the names of the Bedrock Edition texture names, and they aren't the same. A lot of the texture names are flipped, such as:   Jungle Log (Java = jungle_log.png) (Bedrock = log_jungle.png)   Most of the texture names are flipped, like the Jungle Log (and all of the other log types) and there are some .json files that are different and/or not there.  Trying to open the Bedrock texture pack would result in some animated blocks not being animated, other blocks play the wrong sound (or no sound) when broken, if OptiFine is in the mix, the skybox could be missing, which I am pretty sure would result in an always black sky, along with no sun and moon textures.  Any help in finding a program or site that can do this would be helpful, because I tried doing it manually, but almost every texture is different.  Any help is appreciated! Why gpedit and the corresponding registry entries are not synchronized? Who or what was Tom Bombadil? What does "if not" mean in the given sentence Error when using TikZ-Feynman package