What's the difference between "stone" and "rock"? When exactly I can use the first word and when the second one?  As far as I understand, if the matter is a part of our planet, you must call it rock and can't call it stone. But how do you define when it is a part of planet and when it is a separate matter, which just stick into the planet?  Also, do you always call "stone" a peace of matter, which is clearly separated from the planet? Or you can call it "rock" in some cases?
I found this pretty good small research, but I am still concerned about "regular usage" in life, say, when I am talking in the office, especially because of this comment:     To me: Stone is something you can pick up with one hand (for   throwing). A rock takes two hands.
Let $\Omega=\mathbb{N}$. For each $E\subset\Omega$ let $N_n(E)$ be the cardinality of the set $E\cap \{1,2,\ldots,n\}$. Define $C=\left\{E: \lim_{n\rightarrow \infty} \frac{N_n(E)}{n} \text{ exists}\right\}$. Show that $C$ isn't a field.  I already know that it isn't closed to finite union of non-disjoint set but I can't see why. I saw a post that somebody said &quot;the set of natural numbers whose first digit is 1 doesn't have this limit&quot;. I'm in trouble to see why this limit wouldn't exists in finite unions. Thanks in advance. Probability of first actor winning a "first to roll seven with two dice" contest? Active Directory: Is it required that the "A" record for a domain point to a Domain Controller? Based on the question , I got curious. Is there a guide or resource that describes how the price of a ticket is determined?  When you search you often see curious effects like cheaper tickets for a flight from A to B with a layover compared to a direct flight. This seems counter-intuitive from an outsider's perspective since you fly twice. Also one way tickets more expensive than 2 ways.  It can be a short set of rules. Something that helps someone to get started with finding good prices. I know these can be very complex and they probably change over time and over airline interests but there is probably a simplified set of rules that can be enunciated. Which Wifi Channel should I use? Very confused.  I'm using inSSiDer, WiFi Overview 360 and Wifi Analyzer apps to try to determine the best wifi channel to use. Assuming all channels are in use and there are about 20 different users in close proximity...  Q1: Signal Strength    If all channels are in equal use, do you select a channel where others that use it have the lowest signal strength?  I'm guessing that a higher signal strength means that it's from a router from your closest neighbour and you want to avoid that.  Is that the case?  Does lower signal strength mean the person using it is further away and therefore less likely to interfere with your signal? If 2 people are on channel 1 and have high signal strength and 2 people are on channel 11 and have low signal strength, do you choose channel 11?  Assume 6 cannot be used.    Q2: Signal Strength Weighted Against Number of People    What is the impact of signal strength compared to number of people using channel?  If 1 person is on channel 1 with very high signal strength and 2 people are on channel 11 with low signal strength, do you choose channel 11 over 1?  Assume 6 cannot be used?    Q3: Channel Overlap    If, for example, I had 11 routers sitting on top of each other, each set to a different channel, I'm guessing channel 1 and 11 would be the least interferred.  Is that right?  People go on about the fact that only channel 1, 6 or 11 should be used (in US) as they don't overlap but surely that statement is wrong.  Yes, if only 3 people were using Wifi, the best channels to use would be 1, 6 and 11 as they don't overlap but in practice, there are about 20 people using the channels in the same area.  What do you do in that scenerio.  Do you go for the shoulder channels if all channels are being used equally with equal strength?    Q4: Auto Channel Select    Do routers set to auto channel select only choose between 1, 6 and 11?  How do they make the choice?  Do they select by choosing channel with lowest other routers and do they factor in signal strengths.  My router auto chooses channel 1 but my closest neighbour is on that channel.  Is that correct.      Q5: Baby Monitors and Wireless Phones    What channels do 2.4 GHz baby monitors and wireless phones use?  No useful info on the internet for them.  Do inSSiDer, etc. pick them up?    Q6: I have access to channel 13.  All other things being equal, am I better to use this over channel 11 as it is further away from the other channels?    Those questions have puzzled me for a number of years and Google is not helping!!  Would really be grateful if someone could give sensible answers to one or all of them.  Thanks, Mike. Is it necessary to explicitly remove event handlers in C# Constants of integration in integration by parts I want to say "someone (or something) intends to help, but instead it makes things worse". Is there any succinct expression or phrase for this?  Thanks. Error creating GeoPackage raster store in GeoServer How do I remove the limit on PC keyboard button presses? Prove that $n^3=n \text{ mod }6$ for every integer $n$. Prove that for every integer $n$ , $n^3=n \text{ mod }6$  I was having no clue how to do this, then I thought of case-by-case analysis and obviously it worked. The problem is that there were six case and together they are long.   Is there any shorter method of proving this. Kindly provide some hints. Let $(x_n)_{n=1}^{\infty}$ be a sequence such that $|x_{n+1} - x_n| &lt; r^n$ for all $n \geq 1$, for some $0 &lt; r &lt; 1$. Prove that $(x_n)_{n=1}^{\infty}$ is a Cauchy sequence.  I understand that a Cauchy sequence means that for all $\varepsilon &gt; 0$ $\exists N$ so that for $n,m \ge N$ we have $|a_m - a_n| \le \varepsilon$. But this one is really giving me a headache.  I tried doing something like: let $ m &gt; n$. Therefore $x_n - x_m$ =  $(x_n - x_{n-1}) + (x_{n-1} - x_{n-2}) + ... + (x_{m+1} - x_m) $ and then somehow using the triangle inequality to compute some sum such that $x_n - x_m$  &lt; sum which would be epsilon?  any help is appreciated, thank you. How should an educational institute woo good faculty? What steps must an educational institution wanting to recruit good faculty take? There is a cycle in the academia:    Good doctorates from top universities invariably join other top universities as faculty members.  Good students aspire to study in top universities under excellent faculty members.   Suppose a new educational institution or department springs up and desires to set up a top-quality group, how does it break into this cycle? I suppose this could take some years, but is money-power the only thing that could be wielded by the institute to achieve its end? Show that, if $a$ and $h$ are positive numbers, $h &lt; a^2$, then $$\sqrt{a^2 + h}-a &lt; \frac{h}{2a} &lt; a - \sqrt{a^2 - h}$$  I've been working on this problem for about 2 hours now, but I've made no progress. I'm not looking for an answer, but I just need some help to get me started since we didn't practice inequalities this complex in highschool. Thanks.   All I can tell is that we're supposed to take the square root of an expression at some point since one inequality ( h &lt; a^2 ) becomes two.   Edit : Thank you guys for the replies, but I'd appreciate only hints in the future (like Robert Israel) so that I can learn. Regardless, I found a different way to do it, so it's cool :) How do I deal with 'sudoers.so must be only be writable by owner'? Whenever I try to install or remove something using terminal it gives the following error message:  bluebird@bluebird:~$ sudo apt-get update sudo: /usr/lib/sudo/sudoers.so must be only be writable by owner sudo: fatal error, unable to load plugins bluebird@bluebird:~$ sudo apt-get remove vlc sudo: /usr/lib/sudo/sudoers.so must be only be writable by owner sudo: fatal error, unable to load plugins bluebird@bluebird:~$ sudo apt-get install apt-file sudo: /usr/lib/sudo/sudoers.so must be only be writable by owner sudo: fatal error, unable to load plugins How do I check whether a module is installed in Python, and install it if needed? In terminal, after I start Python, how will I know what are the modules present in python? Suppose I need to learn the modules NumPy and SciPy.   How will I install it if it is not installed?  How will I know if it is already installed? How do you read C declarations? I have heard of some methods, but none of them have stuck. Personally I try to avoid complex types in C and try to break them into component typedef.  I'm now faced with maintaining some legacy code from a so called 'three star programmer', and I'm having a hard time reading some of the ***code[][].  How do you read complex C declarations? Store won't open after upgrade Punctuation in an indirect quotation Consider the brief passage:     "I love your work, but calling you 'the artist' {1} just doesn't seem to be   cutting it anymore. What shall I call you?"      "OK. Call me George." {2}   So my instincts tell me to put {1} in single quotes as opposed to no punctuation (or perhaps even italics) but to do the opposite for {2}. Is this right? Why?  Let me expand this one further iteration:     "Wow, that's a great name, especially with this crowd. Maybe for your next book    you should call yourself Ringo."{3} What counts as "observation" in Schrödinger's Cat, and why are superpositions possible? So if I understood correctly, Schrödinger's Cat is a thought experiment that puts a cat inside a box, and there's a mechanism that kills the cat with 50% probability based on a quantum process. The argument is that the cat now must be in a superposition of dead and alive.  This makes sense at first, but the state of the cat inside the box will affect the outside world in an observable way, right? For example if the cat dies, it might meow loudly which would be audible. If it didn't meow, it would produce a thud on the ground when it dies. And even if the ground was very solid, the redistribution of mass inside the box will affects its gravity field which means the whole universe theoretically immediately observe's the cat's death.  So extending this argument to all superpositions, the different states would cause different effects on the rest of the universe, usually a slight change in the gravity field is the minimum. This gravity perturbation would propagate throughout the universe, and even all the experimenters go to sleep with thick, thick earplugs, somebody or something in the universe is going to inadvertently observe the event and the superposition immediately collapses. Thus superpositions cannot exist beyond an extremely short amount of time.  What's wrong with my reasoning?