I didn't see any change in rep when I got upvoted on Board and Card Games meta; how does the system work?
I noticed that the reputation from the main site carried over to meta on Gaming (at least the first upvote), I guess that doesn't work the other way around, right?  Is it then impossible to have a meta reputation higher than the site reputation?
Is there a name for function with the exponential property $f(x+y)=f(x) \cdot f(y)$? I was wondering if there is a name for a function that satisfies the conditions  $f:\mathbb{R} \to \mathbb{R}$ and $f(x+y)=f(x) \cdot f(y)$?  Thanks and regards! Creating a virtual microphone Prove that there exists irrational numbers $x$ and $y$ such that $x + y$ is rational, without using subtraction My homework has this problem:     Prove that there exist irrational numbers $x$ and $y$ such that $x +  y$ is rational.   There is an easy solution that I found on mathbitsnotebook.com:     \begin{align} \left(2+6\sqrt{7}\right) + \left(-6\sqrt{7}\right) = 2.\end{align}   Can we prove the same without using subtraction? One of the answers in a reading exercise in my class today was:   100,000,000,000,000,000,000   ... which was the value of the highest denomination note ever issued. It was a 100,000,000,000,000,000,000 Pengo note, issued by Hungary in 1946. The students in my class wanted to know how they could say that last sentence in words in English. So I told them that I didn't know. They pointed out to me that if they wanted to read this bit of writing to someone they'd want to be able to use the words. Fair point.  Can anyone help?  [In case you're interested, a 100,000,000,000,000,000,000 Pengo note was worth about $0.20!] Specific system of differential equations I have the following system of equations:  \begin{eqnarray}\frac{dx}{dt} = x(1 - x^2 - y^2) \\ \frac{dy}{dt} = y(4 - x^2 - y^2) \end{eqnarray}  I want to prove that if a solutions starts (at time $t = 0$) in the region   $$ G = \{(x, y) \in \mathbb{R}^2 : x &gt; 0, y &gt; 0 \text{ and } 1 &lt; x^2 + y^2  &lt; 4\} $$  that it remains there for all $t \geq 0$. I have already proven that, from $G$, a solution cannot cross the $x$-axis where $0 &lt; x &lt; 2$ or the $y$-axis where $0 &lt; y &lt; 2$ (since those line segments are orbits), but the pieces of the circles with radius 1 and 2 (where $x &gt; 0, y &gt; 0$) are the lines I haven't done yet. In this question we can focus on just the circle with radius 1 since the proof for the other circle is completely analogous to it.  In my book, there is a similar problem where they show that if a solution crosses a certain line, that solution attains its maximum or minimum value for $x$ and $y$, and then they derive a contradiction. However, in this case, for $n \geq 1$ the $n$-th derivative of $x$ equals 0 on the circle with radius 1. (If the second derivative were negative, $x$ would attain its maximum on the circle, a contradiction since $\frac{dx}{dt} &lt; 0$ in $G$, so $x$ is decreasing.)  I don't see why a solution can't cross the circle at all. On the circle, $\frac{dx}{dt} = 0$ and $\frac{dy}{dt} &gt; 0$, so after crossing the circle, the solution would go back up to $G$.  Is the circle itself an orbit?  EDIT I think I have found the answer. Using polar coordinates, I found $$ \frac{dr}{dt} = r - r^3 + 3r \sin^2(\theta) $$ Now, $$ \frac{dr}{dt} &gt; 0 \Leftrightarrow 0 &lt; r - r^3 + 3r \sin^2(\theta) \leq r - r^3 + 3r = 4r - r^3 $$ since $0 \leq \sin^2(\theta) \leq 1$. Note that $0 &lt; r \leq 1$ satisfies $4r - r^3 &gt; 0$, and thus $\frac{dr}{dt} &gt; 0$. Therefore, if a solution goes from $G$ to the edge of the unit circle, $r$ must, on the edge, either be decreasing or constant (i.e., its derivative is less than or equal to 0), contradicting the fact that the derivative is positive.  Can someone tell me if this is correct? Can PostGIS and QGIS provide dependable multi-user editing? After considering a few options, I'm trying to give my 15-20 QGIS 2.2 users the ability to concurrently view/edit one or two basic point PostGIS layers, largest one has just 16,000 records. I've installed PostgreSQL 9.1 / PostGIS 2.0 and basic testing seems to work ok but haven't unleashed it to the masses yet.  We'll typically only have 2-3 editors at a time, but possibly 15 viewers. Edits will all be in QGIS, viewers will be QGIS and ArcGIS (but we don't have SDE).  As I said, these are just basic point files, and  edits will just be adding/deleting points and some table edits. I am not worried about editing the same features at the same time.  Can the combination provide dependable multi-user editing for two basic point files? Why is the determinant of a symplectic matrix 1? Suppose $A \in M_{2n}(\mathbb{R})$. and$$J=\begin{pmatrix} 0 &amp; E_n\\   -E_n&amp;0  \end{pmatrix}$$ where $E_n$ represents identity matrix. if $A$ satisfies $$AJA^T=J.$$ How to figure out $$\det(A)=1~?$$ My approach: I have tried to separate $A$ into four submartix:$$A=\begin{pmatrix}A_1&amp;A_2 \\A_3&amp;A_4 \end{pmatrix}$$ and I must add a assumption that $A_1$ is invertible. by elementary transfromation:$$\begin{pmatrix}A_1&amp;A_2 \\ A_3&amp;A_4\end{pmatrix}\rightarrow \begin{pmatrix}A_1&amp;A_2 \\ 0&amp;A_4-A_3A_1^{-1}A_2\end{pmatrix}$$ we have: $$\det(A)=\det(A_1)\det(A_4-A_3A_1^{-1}A_2).$$ From$$\begin{pmatrix}A_1&amp;A_2 \\ A_3&amp;A_4\end{pmatrix}\begin{pmatrix}0&amp;E_n \\ -E_n&amp;0\end{pmatrix}\begin{pmatrix}A_1&amp;A_2 \\ A_3&amp;A_4\end{pmatrix}^T=\begin{pmatrix}0&amp;E_n \\ -E_n&amp;0\end{pmatrix}.$$ we get two equalities:$$A_1A_2^T=A_2A_1^T$$ and $$A_1A_4^T-A_2A_3^T=E_n.$$ then $$\det(A)=\det(A_1(A_4-A_3A_1^{-1}A_2)^T)=\det(A_1A_4^T-A_1A_2^T(A_1^T)^{-1}A_3^T)=\det(A_1A_4^T-A_2A_1^T(A_1^T)^{-1}A_3^T)=\det(E_n)=1,$$ but I have no idea to deal with this problem when $A_1$ is not invertible. If $f(x)\to 0$ as $x\to\infty$ and $f''$ is bounded, show that $f'(x)\to0$ as $x\to\infty$ Show that $\frac{P(z)}{Q(z)} = \sum_{k=1}^{n}\frac{P(\alpha_k)}{Q'(\alpha_k)(z-\alpha_k)}$ Proving if $d_0$ is the smallest positive integer in $S$ then $d_0 = \gcd(a,b)$ I've recently started maintaining someone else's JavaScript code. I'm fixing bugs, adding features and also trying to tidy up the code and make it more consistent.  The previous developer used two ways of declaring functions and I can't work out if there is a reason behind it or not.  The two ways are:  var functionOne = function() {     // Some code };     function functionTwo() {     // Some code }   What are the reasons for using these two different methods and what are the pros and cons of each? Is there anything that can be done with one method that can't be done with the other? Number of moves necessary to solve Rubik's cube by pure chance Suppose, random moves are made to solve Rubik's cube. A move consists of a $90$-degree-rotation of some side. The starting position is also random.   What is $E(X)$, where $X$ is the number of moves until the cube is solved ? How many moves must be made, that the probability that the cube is solved, exceeds $99$% ? I am looking for a word that would describe being obsessed with the details of a larger entity such that the "looker" neglects to see the whole or (perhaps more importantly) the purpose of the whole.  Basically, "not seeing the big picture".  What can [more] succinctly describe this?  Edit: I just found this post: . I think I want the exact opposite. I have a DEM that I would like to smooth or generalize to remove topographic extremes (chop off peaks and fill-in valleys). Ideally, I would also like to have control over the radius or level of "blurriness". In the end, I will need a set of rasters that range from slightly blurry to really blurry. (Theoretically, the blurriest would be a constant raster of the arithmetic mean of all values).  Are there any tools or methods I can use (based on Esri, GDAL, GRASS)?   Do I need to home bake my own  routine?   Could I use a low-pass filter (e.g. ArcGIS's ), and if so, would I need to run it a bunch of times to get the effect of a large radius? Attempting to create a tag wiki when a user has hit the suggested edit limit should alert the user that no more edits can be suggested at this time I ran into an issue on Gaming.SE where I attempted to create a tag wiki and wiki excerpt for a tag which did not have one already while I already have the maximum of five suggested edits in the queue.  Navigating to the tag page for the  provides a link to  for this tag. This link redirects to the  for this tag, without telling me that I can't submit an edit because I've reached the maximum number of suggested edits. Instead of silently redirecting, the page should alert me that I can't suggest any more edits until my suggestions are reviewed. I can seem to run scripts (.sh) with and without them being set as executable. So where exactly this matters? How can I tell if an ETF is expensive? For stocks, I can easily look at the price/earnings ratio, and, according to The Intelligent Investor, stand clear of those with a ratio higher than 20.  How can I tell if the current price of an ETF is a good price to buy it? Are there such simple metrics? I have a seven hour layover at Brussels airport, and I'd like to know whether there is enough time to leave the airport and go into the Brussels city center for a beer or a meal?  If so, what transportation is available, how does it work, how long does it take, and how much does it cost?  Are there convenient luggage lockers in the airport so that I can avoid taking my carry-on luggage into the city?  This layover is from 8:30 in the morning to 15:30 in the afternoon on a Monday, and the flight is arriving from the United States.  The outgoing flight is within Western Europe. Where are the evolutionary "inbetweeners"? The problem I've always had with evolution is the actual lack of variation between animals. More specifically, the lack of observable gradual change between species.  Take for example the hammerhead shark. It obviously has a strong connection with a normal shark, but where's the "half-hammerhead" shark? Where's the species that only has a SLIGHTLY wider head?  I really doubt that a single mutation on a normal shark resulted in a head shaped like that, it had to happen gradually. Right? As far as I understand, evolution works by random mutation in a child being somehow slightly beneficial to that animal so it get's to live longer and reproduce more, eventually resulting in it's genetic material in dominating the inferior ones before it. But if it was for whatever reason beneficial to have a slightly wider head, why don't all the sharks have slightly wider heads now? On the other hand, if it wasn't beneficial, how come the hammerhead still exists?  Furthermore, I feel like some characteristics of a certain animal can't really have gradual benefits. There's a lizard that shoots blood out of it's eyes. The original ancestor certainly didn't, and I'm sure that if it's child only bled slightly from it's eyes it wouldn't really help if much in life. So for it to actually become beneficial, it seems to me that there had to be a ton of lizards that had a disadvantage of bleeding slightly. In fact, there had to be so many that they evolved even further in the same direction and kept doing that until they bled so much it's an actual benefit (sorry for this turning so gross). So why did the inbetweeners survive long enough to evolve even more, and why did they THEN die out? Denote by $\mathbb{N}$ the set of natural numbers and by $2^{\mathbb N}$ the set of all subsets of $\mathbb N$. Let $E$ be some subset of $2^{\mathbb N}$ such that for  every pair of elements in $E$, one is a subset of the other. Clearly, $E$ could be countable by considering $E=\big\{\{1,\cdots, n\}, n\in\mathbb N\big\}$. My question is the following: could we find an example that $E$ is uncountable? Many thanks for the answer!