What's the name of a classic sci-fi short story about a planet where their religion makes people willingly merge with a parasite in a cave and die?   Outsiders can't understand why anyone would do such a thing, and when off-world visitors start joining the religion and committing suicide, two humans (a couple) with psychic abilities are sent to get their impressions.  They discover the reason everyone happily merges with the parasite is that, by merging (and slowly dying), in return they join a joyous mental community of every previous person who has joined, with overwhelming feelings of happiness--ecstasy, really.  All the psychic love is nirvana for the very sensitive female partner. She joins the religion and merges. She asks her partner to join the parasite as well but he refuses.  The male leaves the planet with the realization that their love for each other couldn't compete with the parasite-mediated mass love and happiness on the planet.  After finishing the story it brings up thought-provoking ideas on whether you would join such a community, about the ties of your love to your own family,and does organized religion gain our interest by similar promises of eternal happiness?
In the early '80s, I read a story about a Terran man on another planet, where the natives develop skin lesions and eventually die, but are happy, as they become part of the planet they live on. I remember that the protagonist is not developing the lesions, because he hates the planet. Once he starts loving the planet, he starts having the lesions as well. In this story, the planet is "alive".  I have read about "" and "". They do not match my memory. Thank you.
Disable emojicons introduced with WP 4.2 So WP 4.2 introduced emojis (smileys) that basically adds JS and other junk all over your pages. Something some people may find shocking. How does one completely erase all instances of this? Some cards in magic has something happen for each {something}. For instance:  makes you gain 2 life for each creature you control. Tapping  adds one green mana to your mana pool, and you gain 1 life for each non-land card revealed.  How is this life gained: all at once or "one bit" at a time? Say I tap Selvala and 1 land, and 2 non-lands are revealed: do I gain 2 life, or do I gain 1 life two times? Would  have one or two +1/+1 counters placed on it if I had it in play at that point? How do I effectively defeat the Wall of Flesh? I've been having trouble defeating this monster. Even with lots of buff potions, health potions, high tier armor (Molten), and ranged weapons with plenty of ammo (Minishark), I can't seem to kill this boss.  Worse, when I get it down to about 2000 hp, even if I'm fairly far away, it'll suck me in and continually rise towards the skybox, which doesn't allow me to do anything for some reason.  How do I defeat the Wall of Flesh? What gear should I be using and what kind of potions do I need? Show that $U_n:=\left(1+\dfrac{1}{n}\right)^n$, $n\in\Bbb N$, defines a monotonically increasing sequence.   I must show that $U_{n+1}-U_n\geq0$, i.e. $$\left(1+\dfrac{1}{n+1}\right)^{n+1}-\left(1+\dfrac{1}{n}\right)^n\geq0.$$  I am trying to go ahead of this step. Deferring updates in Windows 10 In Windows 10 version 1607, it was still possible to defer updates by a few months via the Local Group Policy Editor, but now there's a subfolder containing two entries where it's only possible to defer them by 30-60 days with a maximum of 365 days (timer has to be set anew every time).  Am I seeing this correct or am I missing something?  And what's the difference between feature and quality updates? Why is a person's location exclusively tied to their communicator? Is there a way to remove an overlap from multiple polygons to make one final polygon?..programmatically, I am using the GeoTools or/and OpenGIS/JTS.. any ideas to put me on the right path...  example initial:  final: Let $(x_n)_{n\in \mathbb{N}}$ be a sequence of real numbers. A well known result is:     The sequence $(x_n)_{n\in \mathbb{N}}$ converges to $a\in \mathbb{R}$ if and only if every subsequence $(x_{n_k})_{k\in \mathbb{N}}$ converges to $a\in \mathbb{R}$.   Now, I'm working on an exercise which essentialy asks to prove the following:     The sequence $(x_n)_{n\in \mathbb{N}}$ converges to $a\in \mathbb{R}$ if and only if for every subsequence $(x_{n_k})_{k\in \mathbb{N}}$ there is a (sub)subsequence $(x_{n_{k_j}})_{j\in \mathbb{N}}$ which converges to $a$.   Now, one direction is trivial. If in fact $(x_n)_{n\in \mathbb{N}}$ converges to $a$, then by the result I've mentioned, every subsequence of $(x_{n})_{n\in \mathbb{N}}$ converges to $a$. Let then $(x_{n_k})_{k\in \mathbb{N}}$ be an arbitrary subsequence. In that case, we know that it is a subsequence of itself, and hence we've found a (sub)subsequence which converges to $a$.  The other way around seems quite complicated for me. The reason is as follows: I must assume that every subsequence $(x_{n_k})_{k\in \mathbb{N}}$ has a (sub)subsequence which converges to $a$ and the proof that the original one converges to $a$.  My problem is exactly that "a". If it had all (sub)subsequences converging to $a$, then by the result i've mentionted, the subsequence $(x_{n_k})_{k\in \mathbb{N}}$ would converge to $a$. In that case, we would have every subsequence converging to $a$ and the result would follow.  My idea to prove the claim was then:  First remember that a subsequence is the restriction of the original one $x: \mathbb{N}\to \mathbb{R}$ to an infinite subset $\mathbb{N}'\subset \mathbb{N}$. In that case a (sub)subsequence is the restriction of $\tilde{x} = x|\mathbb{N}'$ to an infinite subset $\mathbb{N}''\subset \mathbb{N}$. But since $\tilde{x}$ is the restriction of $x$ to $\mathbb{N}'$ and since $\mathbb{N}''\subset \mathbb{N}'$, the restriction of $\tilde{x}$ to $\mathbb{N}''$ is itself the restriction of $x$ to $\mathbb{N}''$.  In other words, every (sub)subsequence can be viewed as a subsequence of the original one. Considering this, by hypothesis every subsequence has a (sub)subsequence which converges to $a$. But by this argument, this means that we can replace every subsequence with a convergent one. And then we can use the result I stated.  Is my idea correct? Is this really the way to prove the claim? My only doubt is that I need every subsequence converging to $a$ to use the result. In this case I can't see how I can argue that this implies every subsequence converges to $a$.  How can I finish this proof? Best books for mathematical background? What are the best textbooks to read for the mathematical background you need for modern physics, such as, string theory?  Some subjects off the top of my head that probably need covering:   Differential geometry, Manifolds, etc. Lie groups, Lie algebras and their representation theory. Algebraic topology. How do I stop mod_rewrite from appending links to url? Prove $\sum\limits_{i=2}^{n}\frac{1}{(i-1)i}$ = $\frac{(n-1)}{n}$ using induction. I need to prove $\sum\limits_{i=2}^{n}\frac{1}{(i-1)i}$ = $\frac{(n-1)}{n}$ using induction. I am getting stuck midway through the inductive step.   Here is what I have:  $\forall n\geq 2$, where $n\in\mathbb{N}, P(n)$ is the statement "$\sum\limits_{i=2}^{n}\frac{1}{(i-1)i}$ = $\frac{(n-1)}{n}$".  Base case:  $\sum\limits_{i=2}^{2}\frac{1}{(i-1)i}$ = $\frac{1}{2}$ = $\frac{(2-1)}{2}$ so $P(2)$ is true.  Inductive assumption: Assume $P(n)$ is true. Need to show $\sum\limits_{i=2}^{n+1}\frac{1}{(i-1)i}$ = $\frac{((n+1)-1)}{(n+1)}$.  $\sum\limits_{i=2}^{n}\frac{1}{(i-1)i}$ + $\frac{1}{n^{2}}$ = $\frac{(n-1)}{n}$ + $\frac{1}{n^{2}}$  = $\frac{n(n-1) + 1}{n^{2}}$ = $\frac{n^{2}-n+1}{n^{2}}$  I got stuck here and tried working backward from $\frac{((n+1)-1)}{(n+1)}$, which gives me:  $\frac{((n+1)-1)}{(n+1)}$ = $\frac{n}{(n+1)}$   Any suggestions on what to do next or where I may be going wrong? How to check if a point is inside a rectangle? There is a point $(x,y)$, and a rectangle $a(x_1,y_1),b(x_2,y_2),c(x_3,y_3),d(x_4,y_4)$, how can one check if the point inside the rectangle? Enabling CORS in GeoServer (jetty)? Do messages in archive count to your inbox space? Pretty much as the title says, do messages in archive count to your total inbox space? Proof of $\int_{[0,\infty)}pt^{p-1}\mu(\{x:|f(x)|\geq t\})d\mu(t)=\int_{[0,\infty)}\mu(\{x:|f(x)|^p\geq s\})d\mu(s)$ Let $({\Bbb R},{\mathcal A},\mu)$ be the measure space where ${\mu}$ is the Lebesgue measure.  Assume that $\int_{\Bbb R}|f|^pd\mu&lt;\infty$ ($p\geq1$). There is an exercise for proving that       $$\int_{[0,\infty)}pt^{p-1}\mu(\{x:|f(x)|\geq t\})d\mu(t)=\int_{[0,\infty)}\mu(\{x:|f(x)|^p\geq s\})d\mu(s).$$   If one formally let $s=t^p$, then $ds=pt^{p-1}dt$ and one would immediately get the equality above. However, how can I justify it rigorously in the sense of Lebesgue integration?    [Edited] What puzzles me is that I have the "change of variable" theorem for Riemann integration, but all the integrations here are in the Lebesgue sense. Unless one has shown that the integrands are also Riemann integrable, how can I directly use "change of variable"? Geometric series and big theta Consider the following function:  $$S(n)=1+ c + c^2 + ··· + c^n,$$  where c is a positive real number.  (A) This function is the sum of a geometric series. Give a precise closed-form formula for $S(n)$, interms of $c$ and $n$, in the case where $c \neq 1$.  (B) Show that $S(n)$  is:  $\theta(1)$ if $c&lt;1$  $ \theta(n)$ if $c=1$  $\theta(c^n)$ if $c&gt;1$    can someone please explain how i can go about finding the solutions for these problems, i have never encountered these and am stuck, i know that big theta means that the function is bond on both sides but how do i got about finding the answer?  (edit) im still having trouble understanding part B. can someone please explain? (can someone walk me through the second one) so far i have $n \leq c^{n+1} \leq ???$  (edit #2) i tried doing the first one can someone verify if i did it right  $S(n)$ is $\Theta(1)$ if c&lt;1  (1)$S(n)$ is $O(1)$ if c&lt;1  (2)$S(n)$ is $\Omega(1)$ if c&lt;1  (1) $$\frac{C^{n+1}-1}{C-1} \lt (C_1)(1)$$ $$\frac{C^{n+1}-1}{C-1} \lt (C_1)$$ $$C^{n+1} \lt C_1(C-1)$$ $$C^nC-1 \lt C_2C-1$$ $$C^n \lt C_2$$ $$C^n \lt 1$$ since c&lt;1 this means that any number that will be $C^n$ will be less then 1 for all positive n  i did the omega part pretty much the same way and got $$C^n \gt C_2$$ $$C^n \gt 0$$ since c&lt;1, $C^n$ can potentially become very very small so the only thing bounding it is 0 for all positive n Using a Single system() Call to Execute Multiple Commands in C In an information security lab I'm working on, I've been tasked with executing multiple commands with a single call to "system()" (written in C, running on Fedora).  What is the syntax that will allow me to execute more than command through system()?  (The idea being you could execute arbitrary commands through a program running on a remote computer, if the program interacts with the OS through the system() call.)  I.e.:  char command[] = "????? \r\n";  system(command); Do rainbows have ultraviolet bands and infrared bands? We have seen that rainbows looks so colorful as we are only able to see only the visible light. But Do they also have ultraviolet bands and infra-red bands, that we are unable to see? I know someone has already asked the same question but I am concern about the specific ultraviolet and infrared bands only rather than any other wavelength. Explicitly calling a default method in Java I've finished the game, got all the items except one. This is the one to the right of the green shark fin. What and where is it?