How would you convince the child-me this is false: $0.\bar{9} = 1 \implies \bar{9} = - 1$?
Why does an argument similiar to 0.999...=1 show 999...=-1?
Is there a direct proof that $\pi$ is not constructible, that is, that squaring the circle cannot be done by rule and compass?  Of course, $\pi$ is not constructible because it is transcendental and so is not a root of any polynomial with rational coefficients. But is there a simple direct proof that $\pi$ is not a root of polynomial of degree $2^n$ with rational coefficients?  The kind of proof I seek is one by induction on the height of a tower of quadratic extensions, one that ultimately relies on a proof that $\pi$ is not rational. Does any one know of a proof along these lines or any other direct proof?  I just want a direct proof that $\pi$ is not constructible without appealing to transcendence. Special Relativity - Regarding the Simultaneity of Events During the Train Paradox My questions concerns that classic train paradox, wherein there is a train and a tunnel of equal length, and the train is traveling and some fraction of the speed of light towards the tunnel.  According to the Special Theory of Relativity, an observer outside the tunnel will see the train length contracted (Lorentz Contraction), whereas an observer inside will see the tunnel contracted.   Additionally, suppose that there were doors at the ends of the tunnel and that the observer outside the tunnel closed both doors instantaneously when he/she saw that the train was completely inside the tunnel.  The classic resolution of this paradox invokes the non-simultaneity of events, explaining that the observer in the train sees the far door close first, and then, once the train has begun to exit the tunnel, looks back to see the door at the beginning close. Thus, both observers agree that the train does not touch the door when they are closed for an instant.  Now my questions.  Why is it that the observer on the train sees the far door close first? It seems to me that the information coming from the far door would reach the observer on the train only after the information from the other door is reach.   Under this interpretation, the observer on the train would observe the train getting hit by the doors. What if, by some means, this event can be explained in terms of a stationary observer too? Everyone always concludes that the train remains untouched by the doors, but really the only condition that needs to be met is that both observers must agree. Why can't they both agree that the train was hit?  So, to summarize.   Why is the door that is farther away from the train observed to close first? Why can't the other possible conclusion (both see a hit train) be observed? Browning Avocados - What Helps? Years ago  asked "Oxidized Avocado: What's Going on &amp; How to Prevent It?" That question has been merged with this one because it's dealing with the same issue.  Recently, we had this question: . Now I'm just curious, I want an answer.  After Logophobe's answer to the acidity question, and my own research backing up that answer, I feel like I know less than I did before!  Lemon contains more ascorbic acid (Vitamin C) and citric acid than limes, yet limes are more acidic overall. Distilled vinegar is more acidic than lemons and almost as acidic as limes,  is an extremely highly concentrated mixture of ascorbic acid and citric acid specifically developed to prevent browning in fruits.  So what works to keep avocados pretty and green?  Perhaps some experimentation is in order. I think I'll start with acids, since the common wisdom is that acid helps keep avocados green.  EDIT As of 1/8/15, I have added a new answer, as the highly upvoted one really only says what doesn't help. The accepted answer  shows the results of further experimentation, and what does help. How to analyze trend in non-periodic time series Suppose I have following non-periodic time series. Obviously the trend is decreasing and I would like to prove it by some test (with p-value). I am unable to use classic linear regression due to strong temporal (serial) auto-correlation among values.  library(forecast) my.ts &lt;- ts(c(10,11,11.5,10,10.1,9,11,10,8,9,9,                6,5,5,4,3,3,2,1,2,4,4,2,1,1,0.5,1),             start = 1, end = 27,frequency = 1) plot(my.ts, col = "black", type = "p",      pch = 20, cex = 1.2, ylim = c(0,13)) # line of moving averages  lines(ma(my.ts,3),col="red", lty = 2, lwd = 2)     What are my options? How to make an international emergency call? Solving the recurrence $T(n) = \sqrt n T(\sqrt{n}) + \sqrt{n}$ Unable to preserve ownership in a copy but able with a move? Can I run an HTTP GET directly in SQL under MySQL? I'd love to do this:  UPDATE table SET blobCol = HTTPGET(urlCol) WHERE whatever LIMIT n;   Is there code available to do this? I known this should be possible as the  include an example of adding a function that does a DNS lookup.  MySQL / windows / Preferably without having to compile stuff, but I can.  (If you haven't heard of anything like this but you would expect that you would have if it did exist, A "proly not" would be nice.)  EDIT: I known this would open a whole can-o-worms re security, however in my cases, the only access to the DB is via the mysql console app. Its is not a world accessible system. It is not a web back end. It is only a local data logging system I'm writing a tool to report information about .NET applications deployed across environments and regions within my client's systems.  I'd like to read the values of assembly attributes in these assemblies.  This can be achieved using Assembly.ReflectionOnlyLoad, however even this approach keeps the assembly loaded.  The issue here is that I cannot load two assemblies that have the same name from different paths, so naturally I can't compare the same application deployed in different systems.  At this point I'm assuming the solution will involve using temporary AppDomains.  Can someone detail how to load an assembly into another AppDomain, read the attributes from it and then unload the AppDomain?  This needs to work for assemblies on the file system as well as those at URL addresses. I am asked to prove this theorem:  If $f:U \rightarrow C$ is holomorphic in $U$ and invertible, $P\in U$ and if $D(P,r)$ is a sufficently small disc about P, then   $$f^{-1}(w) = \frac{1}{2\pi i} \oint_{\partial D(P,r)}{\frac{sf'(s)}{f(s)-w}}ds$$     The book says to "imitate the proof of the argument principle" but I am not seeing the connection. In Cycles, is there a way to create a procedural texture that follows the longitudinal lines of a sphere? Like a beach ball or globe? The texture should be able to be mapped to any sphere-shaped object, not just perfect spheres.    My current approach is to use a rotated wave texture, but that doesn't come from the poles (It uses latitudes) An integrable and periodic function $f(x)$ satisfies $\int_{0}^{T}f(x)dx=\int_{a}^{a+T}f(x)dx$. I want to prove:     For an integrable function $f(x)$ and periodic with period $T$, for every $a \in \mathbb{R}$, $$\int_{0}^{T}f(x)\;dx=\int_{a}^{a+T}f(x)\;dx.$$   I tried to change the values and define $y=a+x$ so that $dy=dx$ and the limits of the integrals are as we want, but I'm not sure how to use the fact that $f(x)$ is periodic.  Thanks a lot! How to do logistic regression subset selection? I am fitting a binomial family glm in R, and I have a whole troupe of explanatory variables, and I need to find the best (R-squared as a measure is fine). Short of writing a script to loop through random different combinations of the explanatory variables and then recording which performs the best, I really don't know what to do. And the leaps function from package  does not seem to do logistic regression.  Any help or suggestions would be greatly appreciated. Disable browser 'Save Password' functionality One of the joys of working for a government healthcare agency is having to deal with all of the paranoia around dealing with PHI (Protected Health Information). Don't get me wrong, I'm all for doing everything possible to protect people's personal information (health, financial, surfing habits, etc.), but sometimes people get a little too jumpy.  Case in point: One of our state customers recently found out that the browser provides the handy feature to save your password. We all know that it has been there for a while and is completely optional and is up to the end user to decide whether or not it is a smart decision to use or not. However, there is a bit of an uproar at the moment and we are being demanded to find a way to disable that functionality for our site.  Question: Is there a way for a site to tell the browser not to offer to remember passwords? I've been around web development a long time but don't know that I have come across that before.  Any help is appreciated. Why is $\mathbb{Z}[\sqrt{-n}], n\ge 3$ not a UFD? I'm considering the ring $\mathbb{Z}[\sqrt{-n}]$, where $n\ge 3$ and square free. I want to see why it's not a UFD.   I defined a norm for the ring by $|a+b\sqrt{-n}|=a^2+nb^2$. Using this I was able to show that $2$, $\sqrt{-n}$ and $1+\sqrt{-n}$ are all irreducible. Is there someway to conclude that $\mathbb{Z}[\sqrt{-n}]$ is not a UFD based on this? Thanks. SELECT DISTINCT on multiple columns Supposing we have a table with four columns (a,b,c,d) of the same data type.  Is it possible to select all distinct values within the data in the columns and return them as a single column or do I have to create a function to achieve this? Let $M$ be a smooth manifold and let $N$ be a manifold with boundary. If $dF_{p}$ is an isomorphism, then $F\left(p\right)\in\mbox{int}M $. Let $M$ be a smooth manifold and let $N$ be a manifold with boundary, both with the same dimension $n$. If $dF_{p}$ is an isomorphism, then $F\left(p\right)\in\mbox{int}N  $.  I am trying to prove this theorem to prove a result about smooth embeddings.  Here is how I am thinking the problem could be solved. Assume thet $F(p)$ is a boundary point of $N$. Then there exists a chart $(V,\psi)$ at $F(p)$ such that $\psi(V) $ is an open subset of the upper half space $\mathbb{H}^{n}$. I guess we have to use some fact about $M$ having no boundary and the the fact that $dF_p$ is an isomorphism to show that there is a contradiction, but I cannot figure that out. One of the topics that seems to come up regularly on mailing lists and online discussions is the merits (or lack thereof) of doing a Computer Science Degree. An argument that seems to come up time and again for the negative party is that they have been coding for some number of years and they have never used recursion.  So the question is:   What is recursion? When would I use recursion? Why don't people use recursion? How many numbers are in the Fibonacci sequence below a given threshold? Assuming I'm asked to generate Fibonacci numbers up to N, how many numbers will I generate? I'm looking for the count of Fibonacci numbers up to N, not the Nth number.  So, as an example, if I generate Fibonacci numbers up to 25, I will generate:   1, 1, 2, 3, 5, 8, 13, 21 that's 8 numbers   How do I calculate this mathematically for an arbitrary "n"? Missing dollar problem This sounds silly but I saw this and I couldn't figure it out so I thought you could help. The below is what I saw.  You see a top you want to buy for $\$97$, but you don't have any money so you borrow $\$50$ from your mom and $\$50$ from your dad.  You buy the top and have $\$3$ change, you give your mom $\$1$,your dad $\$1$, and keep $\$1$ for yourself.  You now owe your mom $\$49$ and your dad $\$49$.  $\$49 + \$49 = \$98$ and you kept $\$1$.   Where is the missing $\$1$?