Sometimes when going through questions, I can see that someone has previously voted to close it.    However quite often I disagree with the close vote and I would like to vote for the question to stay open instead. However I can't do that.  Maybe adding it as an option to this popup:    But make it only show up when not doing a review task since the review tasks have their own way to vote to keep a question open.
My request is simple: Many times, there will be a question where some people feel like it should be closed. At the same time, I'll feel like it's a perfectly legit question, and it should therefore NOT be closed. Right now, I have to wait till it gets enough close votes (which it always does for some reason, as soon as 1 or 2 people vote to close, e/o else decides to vote as well) and then vote to re-open. How about, as soon as there's one vote to close, there should be an option to counter the close vote, something like "vote not to close" or whatever. This would then bring the "Vote to close" number down by one. Only when the vote to close outnumbers the vote not to close by 5, that's when a question is indeed closed. Any thoughts?
Peppers evolved chemicals like capsaicin to discourage animals from eating them, and that chemical itself can cause internal damage if consumed in large quantities, though this is usually only a concern for the hottest of peppers (which people do eat).   Still, why is it that humans seem to be the only animal that often "like" spicy food? How to avoid nested With[]? QGIS installation error Do I have to buy a second wildcard certificate for a subdomain? We already have a wildcard certificate for *.mycompany.com. Our network has hosts that are only reachable internally. All of them belong to the internal.mycompany.com subdomain. There is a private server with the host name server.internal.mycompany.com on which I deployed our wildcard certificate.  When I visit the web server I get a host name mismatch error. Do I really have to get another wildcard certificate for *.internal.mycompany.com or is there another (free!?) way to use our wildcard certificate for all of our subdomains and its subdomains without getting an error in the browser? Optimizing $(X_{n}+c)^{2}$ to show that $P(\overline{X}_{n}\geq \lambda) \leq E(X_{n}^{2})/(EX_{n}^{2}+ \lambda^{2})$ Define $\overline{X}_{n}:=\max\limits_{1\leq m \leq n} X_{m}$ and let $(X_{n})_{n}$ be a martingale where $X_{0}:=0$ and $EX_{n}^{2}&lt; \infty$  Show that $P(\overline{X}_{n}\geq \lambda) \leq E(X_{n}^{2})/(EX_{n}^{2}+ \lambda^{2})$  As a hint: Consider $(X_{n}+c)^{2}$ and optimize over $c$.  It is clear that $((X_{n}+c)^{2})_{n}$ is a submartingale and when I optimize over $c$, I get:   $X_{n}^{2}+2X_{n}c +c^{2}\Rightarrow 0=2X_{n}+2c=0\Rightarrow -X_{n}=c$  It is also clear I need to use Doob's inequality but I am not sure how to go about this, and how the above optimization helps me. Modern movie where rich people can buy a personal assistant that sit in a small egg This is a modern movie and rich people can buy this egg with a personal assistant. It's an actual person in it (or a person's mind). I believe it can even operate a toaster.  I believe later in the movie, a person (or their mind) can be transferred to such an egg. As a punishment, they increase the speed of time inside that egg to make the person inside the egg bored to death, so to speak. In Windows, you can run android application using BlueStack.   I was wondering, is there any way these apps can be run on Ubuntu 12.04? Windows 10 update broke my MBR / GRUB After I ran Windows 10 update this afternoon my partition table broke... I had dual boot with Windows 10 and Ubuntu 14 with Grub as the boot loader. The error that came up was "Error no such partition, Entering rescue mode... grub rescue>". I googled it,  about the boot-repair ISO, installed it on a USB, ran the repair, got this report, but still no luck:    Now the boot skips Grub entirely and goes to Windows boot manager which fails with "The boot configuration data for your PC is missing or contains errors". So now instead of dual boot I have zero boot. Thanks Microsoft.  Anyway can you guys help me interpret the disk info in the pastebin link? I don't remember my partition configuration but I believe Ubunut had slightlty less disk space than Windows. Questions I have:   Is the Ubuntu partition still there? Could it be the one named "Extended"? (sda4) Where would GRUB be? Gone? Can it be reinstalled? how?   I don't really care about the Windows partition anymore, but it would be nice to rescue Ubuntu. How do I get attention for one of my own questions without a good answer? Syntax error while defining an array as a property of a class Alignment issue in Area 51 main site - site switcher, inbox and achievements The probability of two dice summing to k is simple enough, make a diagram of the throws,  $$ \begin{array}{c}  &amp;|&amp;1&amp;2&amp;3&amp;4&amp;5&amp;6\\\hline 1&amp;|&amp;2&amp;3&amp;4&amp;5&amp;6&amp;7\\ 2&amp;|&amp;3&amp;4&amp;5&amp;6&amp;7&amp;8\\ 3&amp;|&amp;4&amp;5&amp;6&amp;7&amp;8&amp;9\\ 4&amp;|&amp;5&amp;6&amp;7&amp;8&amp;9&amp;\color{green}{10}\\ 5&amp;|&amp;6&amp;7&amp;8&amp;9&amp;\color{green}{10}&amp;11\\ 6&amp;|&amp;7&amp;8&amp;9&amp;\color{green}{10}&amp;11&amp;12\\ \end{array} $$  and the probability of a sum is just the length of the corresponding diagonal divided by $36$. For instance, $\mathrm{P}(\mathrm{sum} = 10) = \frac{3}{36} = \frac{1}{12}$. However, it's not as easy to draw a diagram for three dice or more, so how would a general formula look? Automorphisms of the complex plane How can it be shown that $$Aut(\mathbb{C})=\{f|f(z)=az+b,a\neq 0\},$$ where an automorphism of $\mathbb{C}$ is defined as a bijective entire function with entire inverse?  If $f$ is of the form $f(z)=az+b$, with $a\neq 0$, then obviously $f$ is in $Aut(\mathbb{C})$. How can I prove the converse? How do I change login screen theme or background in Ubuntu 20.04? How can I change the Ubuntu 20.04 login screen theme or background?  In the previous version 19.10, I can change it from the CSS file under Yaru theme but now there is no CSS file. I'm very new to classical propositional logic, and my lecturer is using a system with the following axioms:  A1. X→(Y→X)  A2. (X→(Y→Z))→((X→Y)→(X→Z))  A3. (¬Y→¬X)→(X→Y)  Use uniform substitution and Modes Ponens (MP) as rule of inference. Deduction Theorem also allowed.  I'd like to deduce the following:  (a) X, Y ⊢ ¬(X→(¬Y)) (conjunction, but expressed in terms of NOT and IMPLIES)  (b) X→((X→Y)→Y)  (c) (X→Y)→(((¬Y)→X)→Y)  (d) (((¬Y)→X)→Y)→(X→Y)  Remark: The last two are to show that the axiom (A3) can be replaced with a different axiom:  B3. (¬Y→¬X)→(((¬Y)→X)→Y).  Solution: Bram28 proves (b) and (c) below. I demonstrate (a) and (d).  (d) is alright; first, I claim that X, ((¬Y→X)→Y) ⊢ Y.  Axiom (A1) gives ⊢X→(¬Y→X) so that ((¬Y→X)→Y)⊢X→Y by Hypothetical Syllogism (HS), which Bram28 shows to be valid.  Now that we have ((¬Y→X)→Y)⊢X→Y just apply the deduction theorem to get what we want: ⊢((¬Y→X)→Y)→(X→Y).  (a) is slightly trickier. Axiom (A1) gives ⊢ Y→(X→Y) so that X, Y ⊢ (X→Y).  Next, by part (b), we have as a theorem that ⊢X→((X→¬Y)→¬Y).  Therefore X, Y ⊢(X→¬Y)→¬Y.  But ⊢(¬¬(X→¬Y))→(X→¬Y) by DN Elim, which Bram28 shows to be valid.  By HS, X, Y ⊢(¬¬(X→¬Y))→¬Y.  By Axiom (A3) and MP, X, Y ⊢(Y→¬(X→¬Y)).  Also, rather trivially X, Y ⊢Y.  Finally by MP we conclude X, Y ⊢¬(X→¬Y) as required. What happens if light/particles exceeded the speed of light for a particular medium? A finite summation of double binomial coefficients I find the following identity and have checked on Mathematica, while I have no idea how to prove it:  $$\sum_{j=0}^n(-1)^{n-j}\binom{p+j}{j}\binom{n+\beta}{n-j}=\binom{p-\beta}{n}, \quad \beta&gt;-1, \quad p&gt;\beta-1.$$  It seems that proof by induction does not work and because of the gamma function, the transform technique does not work either. How to export / dump a MySql table into a text file including the field names (aka headers or column names) Target='_blank' to show in new window, NOT new tab, possible? Should my first trip be to the country which issued my Schengen Visa? In case, if I get a multiple-entry Schengen visa in one of the embassies in Ukraine, Kyiv - should my first trip be to the country which issued the visa?  Any there any requirements of this sort? Does this condition vary depending on embassy which issued the visa?  What are the possible consequences on not visiting that country first? Does it somehow depend on country where the embassy is (i.e. non-Schengen and not EU members)?