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Prove: $\gcd(a,b) = \gcd(a, b + at)$. Is it possible to wipe an entire iCloud Photo Library? I've been using the beta iCloud Photo Library for a week and a bunch of photos got duplicated and I'd like to wipe all the photos out and start over.  I have backups of all the photos and have turned off iPhoto Cloud Library on all iOS devices. When I log into the web app - it still shows dozens of albums and I can delete all the photos, then go to deleted items and then purge them, but the ghost albums are still there messing things up.  I've turned off the library entirely and you can see there is a 30 day waiting period.     If I click on albums, there are pages of them and no delete button anywhere. If I turn on the library on an iOS device, data starts flooding back as if I wanted to recover the photos.  I don't want to recover anything, I want a clean wipe and clean slate.  Currently, there are 7807 photos in the deleted album and no way to mass delete them. I have 31 albums that show up in iCloud and no way to delete them.  Is there some way to accelerate this or must people wait a month for a corrupt library to eventually be purged to start over?  (I have tickets open with AppleCare after  and it's escalated to engineering, but I was informed that it might be a week or two before it gets seen :-( Perhaps someone has a better idea to clear things out or noticed something I've missed.) Canned reasons for up/down vote (w/ example of how it would work) I'm annoyed by down voters that don't explain why they down voted a question or an answer. Although, at the same time, I understand that they . I think there is a middle ground, though, where the voter can remain anonymous, while the poster can get aggregated feedback on ways to improve the post.  Rather than having to imagine what it might be like, the current stackoverflow engine can emulate this rather effectively with the use of comments and the up-voting of those comments (essentially saying "I agree"). So I thought I would give it a try. The only difference is that in this testing post, you will always see the list of "canned responses" where as in the complete version, it will most likely be hidden in a popup (e.g. when you hover over the score of an answer/question). To try it out, simply up or down vote this question (or one of its answers), and press the up arrow next to the comment which best describes why are voting that way. For example, if you hate this idea, give this a down vote, and then press the up arrow near -1: I don't like this idea.  In addition to retaining anonymity, this will also save time for the voter so that they don't need to write out the comment. This wouldn't be required, obviously, and there could be a default option selected don't leave a reason. In addition, there could be a custom option which allows you type exactly why you are down-voting this way. Depending on the final implementation, this could either simply be converted to a comment automatically prefixed with -1:  or +1:; or, to retain anonymity, it would be added to this same list that shows the canned responses and how many users have voted that way.  Here are some ideas for the canned responses:  Question:   +1: Well formatted and thought out question. -1: It doesn't seem like enough time was spent trying to solve this issue on your own. -1: I don't like this idea. (Could be especially useful on meta.stackoverflow.com feature-request.) -1: No prior research/work. (Idea from .) -1: Poor question. Please see . -1: Doesn't contain code. (This would be useful on stackoverflow.com. Idea from )   Answer:   +1: Concise. +1: Insightful. +1: Worked for me. -1: It's wrong. -1: Confusing. -1: Encouraging bad behavior (e.g. answering a question that shouldn't have been asked; see ).   I made this a community-wiki since there will probably be testing of up/down votes. Several of these canned responses have been taken from . This same idea was also . I have proved in earlier exercises of this book that $\sqrt 2$ and $\sqrt 3$ are irrational. Then, the sum of two irrational numbers is an irrational number. Thus, $\sqrt 2 + \sqrt 3$ is irrational. My first question is, is this reasoning correct?  Secondly, the book wants me to use the fact that if $n$ is an integer that is not a perfect square, then $\sqrt n$ is irrational. This means that $\sqrt 6$ is irrational. How are we to use this fact? Can we reason as follows:  $\sqrt 6$ is irrational  $\Rightarrow \sqrt{2 \cdot 3}$ is irrational.  $\Rightarrow \sqrt 2 \cdot \sqrt 3$ is irrational  $\Rightarrow \sqrt 2$ or $\sqrt 3$ or both are irrational.  $\Rightarrow \sqrt 2 + \sqrt 3$ is irrational.  Is this way of reasoning correct? Prove that the normalisation of $A=k[X,Y]/(Y^2-X^2-X^3)$ is $k[t]$ where $t=Y/X$ (Reid, Exercise 4.5) This is a problem about finding the normalisation of a quotient polynomial ring. So I have to find the integral closure of the ring in its field of fractions. The problem statement is as follows:     Let $A=k[X,Y]/(Y^2-X^2-X^3)$. Prove that the normalisation of $A$ is $k[t]$ where $t=Y/X$.   Can I do this by showing that the field of fractions $\text{Frac} A$ of $A$ is equal to $k[t]$, and subsequently showing that the field of fractions is normal? (This could be done by showing that $k[t]$ is a UFD?)  I am lost at calculating/determining $\text{Frac}A$, or similarly proving that $k[t]=\text{Frac}A$. Also, how do I show that it is normal?  I hope you can help! Two particles with initial positions and velocities $r_1,v_1$ and $r_2,v_2$ are interacting by the inverse square law (with G=1), so that  $$ {d^2r_1\over dt^2} = - { m_2(r_1-r_2)\over |r_1-r_2|^3} $$ $$ {d^2r_2\over dt^2} = - { m_1(r_2-r_1)\over |r_1-r_2|^3} $$  (the inverse square law along the line of separation). What is the complete solution of these differential equations? What is the position of the two objects as a function of time?  After reading a lot on Wikipedia, I've come to the definition of center of mass and relative coordinates:   $$R(t) ~=~ \frac{m_1 r_1 + m_2 r_2}{m_1+m_2}$$  $$\ddot{r}(t) r(t)^2 ~=~ (m_1+m_2)G$$  Where $R$ is the center of mass, and $r$ is the displacement between the particles... Is this correct? How do I proceed to solve the differential equation? Expanding a parent  to the height of its children I have a page structure similar to this:  &lt;body&gt;   &lt;div id="parent"&gt;     &lt;div id="childRightCol"&gt;       /*Content*/     &lt;/div&gt;     &lt;div id="childLeftCol"&gt;       /*Content*/     &lt;/div&gt;   &lt;/div&gt; &lt;/body&gt;   I would like for the parent div to expand in height when the inner div's height increases.  Edit: One problem is that if the width of the child content expands past the width of the browser window, my current CSS puts a horizontal scrollbar on the parent div.  I would like the scrollbar to be at the page level. Currently my parent div is set to overflow: auto;  Can you please help me with the CSS for this? In high school we learned to say "than I" and "as I" because you could potentially add an "am" to the end of the sentence.  Examples:  "She is smarter than I."  (Think: "...than I am.") "He is as tall as I."  (Think "...as I am.")  So analogously, shouldn't it be "like I" as well:  "He is sincere, just like I."  (Think: "... like I am.")  But universally, it seems that we use "like me".  Where does this reasoning break down?  Is there history here? A very basic ring theory question, which I am not able to solve. How does one show that    $\mathbb{Z}[i]/(3-i) \cong \mathbb{Z}/10\mathbb{Z}$. Extending the result: $\mathbb{Z}[i]/(a-ib) \cong \mathbb{Z}/(a^{2}+b^{2})\mathbb{Z}$, if $a,b$ are relatively prime.   My attempt was to define a map, $\varphi:\mathbb{Z}[i] \to \mathbb{Z}/10\mathbb{Z}$ and show that the kernel is the ideal generated by $\langle{3-i\rangle}$. But I couldn't think of such a map. Anyhow, any ideas would be helpful. Should Stack Exchange have a spam filter? (Does it already and I’m not aware?) Of course spam posts should be flagged, and if they come up in review, rejected.  Over on Mi Yodeya during the past 24 hours I’ve helped delete and reject four spam posts through the review queue, and I can only imagine that others were posted over the course of the night. To clarify, I’m referring to edits and answers that were about 99.274% words that I don’t think any decent person would use in everyday discussions, even if someone got them really angry.   Thing is, if the only thing we can do as a community is delete his posts/reject his edits, and as moderators to ban his account, can’t he just create a new account? Further, some of these posts . Maybe the mods can ban his IP address? I’m not one, so I have no idea what kind of power they wield in that respect. But he can always just get a new computer.   I don’t have the numbers to see what this is like on other sites, but I know this doesn’t happen often on Mi Yodeya. I wonder, then, whether this is the optimal solution, or whether an automatic spam filter be put into place - say, a new review queue that automatically deletes posts or rejects edits that can then be voted on whether to be reposted if it’s a false alarm. Perhaps it can be automatically triggered by certain keywords (like ****, %$#^, or @$+^).   Now, all of these posts that I voted to delete/reject came up in Suggested Edits and First Posts. Maybe such edits would show up in Low Quality in general, and that just wasn’t the case here because of precedence rules. I don’t know. But perhaps the above would be a better solution, if this is even as big of a problem as I’m making it out to be. Why has my Samsung Galaxy S2 become a data hog? Speed of light in a gravitational field? How do I solve the speed of light in gravitational field?  Should I just add gravitational acceleration in speed of light?  $$c'=c_0+g(r)t~?$$ How are reviews assigned? Let $U\subset\mathbb R^3$ be an open set, and $f:U\to \mathbb R$ be a smooth function. Suppose that the level set $S=f^{-1}(\{0\})$ is non-empty, and that at each $p\in S,$ the gradient $\overrightarrow \nabla f(p)$ is not the zero vector. Then $S$ is a smooth two-dimensional surface in $U$, and $p\mapsto \overrightarrow \eta(p)=\frac{1}{||\overrightarrow \nabla f(p)||}\overrightarrow \nabla f(p)$ defines a smooth unit-length normal vector field along $S$. At each $x\in U,$ write $H(f)_{(x)}$ for the $3\times 3$ Hessian matrix specified by $$(H(f)_{(x)})_{ij}=\frac{\partial^2f}{\partial x_i\partial x_j}(x).$$   Show that, at each $p\in S$, the second fundamental form $II_p: T_p(s)\times T_p(s)\to \mathbb R$ is the symmetric bilinear map    $$II_p(\overrightarrow v,\overrightarrow w)=\frac{-1}{||\overrightarrow \nabla f(p)||}\overrightarrow v\cdot H(f)_{(p)}\overrightarrow w,$$for all $\overrightarrow v ,\overrightarrow w \in T_p(s)$.       (Here, we view the tagent space $T_p(S)$ as the two-dimensional subspace $(span\{ {\overrightarrow \eta(p)}\})^{\bot}$ of $\mathbb R^3$.      Edit: Actually my question is why the second fundamental form under the usual definition can be written in this way.      Definition: The quadratic form $II_p$, defined in $T_p(S)$ by $II_p(v)=-&lt;d  N_p(v),v&gt;$ is called the second fundamental form of $S$ at $p$, where $dN_p:T_p(S)\to T_p(S)$ is the differential of the Gauss map.   Hopefully, I express this problem explicitly. I was just wondering how to prove this statement.   I took a diffrential geometry class last semester, and when I organized my notes this morning, I found this statement, but there was no proof...  Looking forward to an understandable explaination. Thanks in advance.     Edit 2:Furthermore, show that, at each point $p\in S$, the expression   $$\phi_p(z)=det\pmatrix{-H(f)_{(p)}-zI_{3\times 3} &amp; \overrightarrow \nabla f(p)\\\ \pm \overrightarrow \nabla f(p)&amp; 0}$$   (the underlying matrix here is $4\times 4$) defines a second-degree polynomial whose roots $\lambda_1$ and $\lambda_2$ are $||\overrightarrow \nabla f(p)||k_1$ and $||\overrightarrow \nabla f(p)||k_2$, where $k_1$ and $k_2$ are the principal curvatures of $S$ at $p$.      Also, if a non-zero vector $\pmatrix {\overrightarrow v \\c}$ lies in the kernel of the $4\times 4$ matrix $$\pmatrix{-H(f)_{(p)}-\lambda_jI_{3\times 3} &amp; \overrightarrow \nabla f(p)\\\ \pm \overrightarrow \nabla f(p)&amp; 0},$$   then $\vec v$ is a non-zero element of $T_p(S)$ and lies in the "principal direction" corresponding to $K_j$. Should I be concerned that the sill plate is not lined up with the foundation? I am in the process of building a one level home in PA. After the formed concrete walls were poured and the framing began, I noticed that on one side of the house that the sill plate was flush with the edge of the foundation wall in the rear, but, by the time the sill plate got to the front it was 2 1/2" away from the edge of the foundation wall. In summary, the sill plate walks from flush with the foundation wall at the rear to 2 1/2" at the front. This happens over about a 50' run.  Any thoughts or concerns would be appreciated. Any recommendations on what sorts of questions to ask when I meet the site supervisor on Monday? How do I tell if matrices are similar? How do I fork a process that doesn't die when shell exits? I have the following configuration, but I have not able to find any documentation on how to set a maximum backup files on date rolling style.  I know that you can do this with size rolling style by using the maxSizeRollBackups.  &lt;appender name="AppLogFileAppender" type="log4net.Appender.RollingFileAppender"&gt;     &lt;file value="mylog.log" /&gt;     &lt;appendToFile value="true" /&gt;     &lt;lockingModel type="log4net.Appender.FileAppender+MinimalLock" /&gt;     &lt;rollingStyle value="Date" /&gt;     &lt;datePattern value=".yyMMdd.'log'" /&gt;     &lt;layout type="log4net.Layout.PatternLayout"&gt;       &lt;conversionPattern value="%d %-5p %c - %m%n"  /&gt;     &lt;/layout&gt; &lt;/appender&gt; I have a file containing two columns and 10 million rows. The first column contains many repeated values, but there is a distinct value in column 2. I want to remove the repeated rows and want to keep only one using awk. Note: the file is sorted with values in column 1. For example:    1.123 -4.0 2.234 -3.5 2.234 -3.1 2.234 -2.0 4.432 0.0 5.123 +0.2 8.654 +0.5 8.654 +0.8 8.654 +0.9 . . . .   Expected output  1.123 -4.0 2.234 -3.5 4.432 0.0 5.123 +0.2 8.654 +0.5 . . . . How can I reliably get the operating system's name? Say I am logged into a remote system, how can I know what it's running? On most modern Linuxes (Linuces?), you have the lsb_release command:  $ lsb_release -ic     Distributor ID: LinuxMint Codename:       debian   Which as far as I can tell just gives the same info as /etc/lsb-release. What if that file is not present? I seem to recall that the lsb_release command is relatively new so what if I have to get the OS of an older system?  In any case, lsb stands for Linux Standard Base so I am assuming it won't work on non-Linux Unices. As far as I know, there is no way of getting this information from uname so how can I get this on systems that do not use lsb_release?