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What are the differences between "to talk" and "to speak"? Both verbs "to talk" and "to speak" refer to the same action.  Is their meaning exactly the same? When is more appropriate to use one, or the other verb? Short story identification: society partitioned off by high wall Reading another question today reminded me of a short story I read in the early 90s (probably written in 60s or 70s though). A society is blocked off by a really high wall; the story follows a girl who tries to get over the wall. I think she manages it with a hot air balloon. When she reaches the other side she meets an older man who had managed to scale the wall in his youth - his solution had been to use a flock of birds to carry him.  UPDATE  I seem to recall that it splits off an elite group of people - getting over the wall is like a rite of passage. Most people don't even bother to get over it (or even be concerned by its existence at all), but a few try. There might be some magic involved (on the other / better side), or they might just be more advanced technologically.  FINAL UPDATE  As pointed out in the answer, and confirmed by me re-reading the story, I was mistaken in a few details. The main protagonist is not a girl, it's a boy called Porgie. He doesn't use a balloon, it's a glider he made, assisted with a broom. Magic is involved, but it's on the inside, with technology on the outside. Can I force an iPhone user to upgrade an application? Compact vs Mirrorless - why pick one over another? What would be a reason for one to pick the compact (whatever it'd be P&amp;S or something more advanced) over mirrorless compact system camera  ?  Right now market is quite confusing — we have huge market of tiny-sensor compacts, we have mirrorless that use sensors in a size of these from P&amp;S cameras (Nikon 1 being notable example), we have compacts with sensors bigger than most popular mirrorless system (Canon G1X vs m4/3), we have lot of APS-C sensor mirrorless which are matched by some of the compacts (Fuji X100 being most notable example, but even Leica has its X2),  and to make it even more confusing — Sony released RX1 with full frame sensor, beating crap out of every mirrorless on a market.  So what are your arguments to pick compact over a mirrorless?  Why are they better, what's the reason behind logic of companies like Fujifilm which at the same time offers P&amp;S and X-mount mirrorless using same sensor size? When I search for Chromium in Ubuntu Software on Ubuntu 16.04, There are 2 options.    Which one should I select?    The same can be observed with , ,  etc. Logical Volume, Physical Volume and Volume Groups Please can someone explain to me the meaning of Logical Volume, Physical Volume and Volume Groups? Of what importance and advantage are they in linux? I often see $I(t)\propto |E(t)|^2$. What is the exact form ? Which constants are missing to make this an equality and why are they so often omitted ? $\textit{Why}$ the cases in 4 $\nmid n^2 - 3?$ (bases cases in modular induction) This question has already been answered . My question is, when we suppose the hypothesis is not true (proof by contradiction), namely that $4 \mid (n^2 - 3)$, we get $n^2 - 3 = 4k$ for some integer $k$ and then we have two cases. But where does the two cases come from? In addition, why does putting them into two cases work to prove the statment? My thought process would be to try to prove this statement by contradiction and somehow figure out a way to produce a contradiction similar to how $\sqrt{2}$ is proved by contradiction. Any help is great! Let me know if I need to clarify more! What packages do people load by default in LaTeX? When cutting/copying some cells to paste them into another sheet/page, sometimes Excel freezes/locks up and fades out. At the top toolbar it says in brackets "not responding".  Eventually, I must click 'X' to close the program. It offers to wait for the program to respond, but never does – it just does nothing until I finally close it, where it offers to recover files etc.   Is there an issue with memory here? What can I do to stop it locking up? I am a Chinese citizen married to a US citizen last year. I am going to apply for a UK tourist visa. The name shows on my passport is my maiden name, while any other documents the UK visa needed, such as bank statement, is with my married name. I can provide my marriage license to prove the link between my maiden name and married mane.   Can I apply for this UK visa with my situation? How to store credit card info on iphone? Mac turns off randomly and has lines on screen Proof that no term (of a language of predicate logic) is a (non-empty) initial segment of another How to stop creating .DS_Store on Mac? Vieta Jumping: Related to IMO problem 6, 1988: If $ab + 1$ divides $a^2 + b^2$ then $ab + 1$ cannot be a perfect square. The famous IMO problem 6 states that if $a,b$ are positive integers, such that $ab + 1$ divides $a^2 + b^2$, then $\frac{ a^2 + b^2}{ab + 1 }$ is a perfect square, namely, $gcd(a,b)^2$.  How about a modification of this problem:    If $a,b$ are (strictly) positive integers, such that $ab + 1$ divides $a^2 + b^2$, then $ab + 1$ cannot be a perfect square.    I am looking for a proof of the claim above, or a counter-example.  One possible approach towards a proof is the following:   Suppose there is such a pair $(a,b)$ as above, then by the famous IMO problem 6 from 1988, $\frac{ a^2 + b^2}{ab + 1 } = g^2$ where $g = gcd(a,b)$. Since $ab + 1$ is a perfect square, $a^2 + b^2 = c^2$ for some integer $c$. So that $(a,b,c)$ is a Pythagorean tripple, therefore there exists positive integers $n,m,l$ with $n$ coprime to $m$, such that $a = l(n^2 - m^2)$ and $b = 2lnm$ - by Euclids formula.  Then by plugging in $a$ and $b$ in terms of $n,m,l$ into the original equation, and solving for $l$, it is possible to obtain the following:  There exists positive coprime integers $n,m$ such that   $\frac{(n^2 + m^2 + 1)(n^2 + m^2 - 1)}{2mn(n+m)(n-m)}$ is a perfect square.  If we put the quotient above into a program, as in this python code snipet:  N = 1000  for n in range(1,N):     for m in range(n+1, N):         A = (n*n + m*m + 1)*(n*n + m*m - 1)         B = 2*m*n*(n+m)*(m-n)         if A % B == 0:             print(A/B)   The quotient always is 2, regardless of whether or not $n$ and $m$ are co prime! So if the very strong implication   $2mn(n+m)(n-m) \mid (n^2 + m^2 + 1)(n^2 + m^2 - 1) \implies \frac{(n^2 + m^2 + 1)(n^2 + m^2 - 1)}{2mn(n+m)(n-m)} = 2$    holds, then the original problem will be solved. Arrangements of a,a,a,b,b,b,c,c,c in which no three consecutive letters are the same Q: How many arrangements of a,a,a,b,b,b,c,c,c are there such that  $\hspace{5mm}$ (i). no three consecutive letters are the same?  $\hspace{5mm}$ (ii). no two consecutive letters are the same?  A:(i). 1314. ${\hspace{5mm}}$ (ii). 174.  I thought of using the General Principle of Inclusion and Exclusion along with letting $p_i$ denote a property that.. , and doing so, I will evaluate $E(0)$, which gives us the number of arrangements without any of the properties.   How do I go about doing that? I am trying to use the method stated above in solving this question, but I am unable to generalize the properties $p_i$. What is meant by a "random variable"? What do they mean when they say "random variable"? Process descendants Why do people omit the definite article? I'm used to always hearing or seeing a  before certain nouns.  Yet on certain occasions the article is totally omitted, and it bothers me.  I'm wondering what the justification for omitting the article is, especially when the definite article would seem to be required, or if it is just bad English either on the part of the individual in question or more likely by tradition.  The most frequent place I hear this is at the doctor or dentist's office. In every one I have ever visited, the receptionist or assistant always says things like "Doctor will see you shortly" instead of "The doctor will see you shortly."  The wikipedia article linked above says this: "A definite article indicates that its noun is a particular one (or ones) identifiable to the listener".  In the case of a clinical setting, I know who the doctor is, especially if this is not my first visit.  The people in the office know the doctor even better than I, so it would seem to be inappropriate to omit the article. Even the indefinite article would be incorrect. It further says, under "Zero article":  "In languages having a definite article, the lack of an article specifically indicates that the noun is indefinite."  Since the noun is not indefinite, why are they omitting the article?  Another place I see the article omitted is with the word "bar".  Bartenders apparently don't say "I tend the bar" they say "I tend bar".  Unless a bartender works in multiple bars, it would seem like an article would be required.  Furthermore, "the bar" can mean any bar a person goes to, so even in a case like , it seems like the word "the" should be in the sentence.  The only thing I can think of in this case is maybe the speaker doesn't want to confuse the listener into thinking they work in the legal field.  Is this just a bad habit, a historical corruption or tradition, or is there really a valid reason (or perhaps more than one) for these omissions?