What is a "Post" defined as? Does it include all of the following, or just a subset:   Questions Answers Comments Community Wiki Questions Community Wiki Answers Chat message other things?   I'm asking in the context of Badge definitions like "Edited 100 posts that were inactive for 6 months".
The descriptions for the editing badges are:     Editor:    Strunk &amp; White:    Copy Editor:    Does "posts" include your own questions/answers, or are these badges just for edits to other people's stuff?  Other questions about how editor badge works:   What if I edit only a question's tags, but not its body? What if I edit both a question's tags and its body? Do edits to Community Wiki posts count? Do edits to answers count? Do edits to tag wiki pages count? Do edits to comments count? (Moderators can edit other users' comments, even outside of the usual five minute window.)
Proving $\frac{1}{\sqrt{x}}\ge \frac{2}{x+1}$ for $x> 0$ Prove: $$\frac{1}{\sqrt{x}}\ge \frac{2}{x+1}, \quad\forall x&gt;0$$  Yeah, pretty much it. I've tried all manner of rearranging and just can't seem to get it. Thanks. InputStream returning NullPointerException (Java) Black body radiation and spectra lines My understanding was that all objects emit light of continuous spectrum when hot ( black body radiation) but then you see discreet wavelengths in spectra lines and I am confused. I know I am making a mistake somewhere but not able to point it Converting mobi files to pdf files I have a Hanlin V3+ e-book, unfortunately it crashes too often when reading mobi files, so I want to convert them first into pdf, and then read pdf on V3+. Is there any tool for converting mobi files to pdf files? Thanks. When you have a link from lets say twitter that is t.co/foo that links back to your website how does that effect SEO and how do the major search engines handle Shortened URLs? Summarize the mathematical problem at the heart of breaking a Curve25519 public key It's pretty easy to generate a Curve25519 private key: generate 32 random bytes of data and then do:  e[0] &amp;= 248 e[31] &amp;= 127 e[31] |= 64   You can then generate a public key by doing  on the private key. For example, here's a random keypair I just generated:  public: e40ed268dff20db8497d0691421d00b086aad1efedcd5bd223d9eb6c0b85665f secret: e3c0e8b20ba7894882ddb37522dbe90867befcf9f31a5ce29c0d7997e0bd856d   The whole safety of public key encryption is that it is hard to take a public key and reverse the operation. Elliptic curve cryptography, as I understand it, relies on the fact that a  is hard to find. In particular, for a given large b and g, it is hard to find an integer k such that  $b^k = g$  How does that equation relate to Curve25519? Specifically, if I had a public key like the one above, how would I express, in math terms, the problem I need to solve to find the private key? How does it relate to the equation I see from time to time - $y^2 = x^3+486662x^2+x$, and the number $2^{255} - 19$?  I am guessing it is not as simple as "the private key is k and the public key is b and/or g" in the equation above. I'm also a little confused because the keys would appear to have roughly the same number of digits, which would seem to imply that there aren't many feasible values for k? Graph Proof by induction. Can you prove via induction that there exists a node in a directed graph of n nodes that can be reached in at most two edges from every other node in the graph. Every node in the graph is required to have an edge with every other node that either points out or in (For every pair of nodes X and Y, either X points to Y or Y points to X). A similar task for changing the desktop background, can be achieved using the following script:   FILE="/backgrounds/background.png" gsettings set org.gnome.desktop.background picture-uri "$FILE"   How would I achieve the same result, but with the user's avatar/profile picture? Where does the word "torsion" in algebra come from? Using ArcGIS 10.0, is it possible to reorder the fields in a file geodatabase, and have the order persisted to the database?  We considered exporting to XML, and writing a parser to change the field order, then re-creating a new database from the XML. This seems like a laborious process.  Another idea is to import the existing field definitionss into Excel, re-order them, export to CSV, then write a Python script to create these fields in a new Geodatabase. Does a script like this exist, before we write it from scratch?  Unfortunately the ArcGIS Diagrammer doesn't seem to support field re-ordering.  Are there any scripts or hacks we could use to simplify this process? Will Google punish me if I import a story from my own blog to content sharing sites such as Medium.com? I've heard that Google punishes sites with duplicate content.   If I write an article on my blog then import it on Medium (basically a copy/paste) will Google regard it as a duplicate?   Medium.com is a blog platform (sort of). How do I recover my Google account (or Gmail) password or username? I have forgotten the password or username for my Google account, or I'm unable to access my account for other reasons.  How can I recover my account?  (This Q&amp;A is meant as a general description for all Google and Gmail username/password questions. See: ) How Do I Choose Between a Hash Table and a Trie (Prefix Tree)? So if I have to choose between a hash table or a prefix tree what are the discriminating factors that would lead me to choose one over the other. From my own naive point of view it seems as though using a trie has some extra overhead since it isn't stored as an array but that in terms of run time (assuming the longest key is the longest english word) it can be essentially O(1) (in relation to the upper bound). Maybe the longest english word is 50 characters?  Hash tables are instant look up once you get the index. Hashing the key to get the index however seems like it could easily take near 50 steps.  Can someone provide me a more experienced perspective on this? Thanks! Wifi hotspot software package other than ap-hotspot? Ordered Pair Formal Definition I understand what an ordered pair is, but I'm having trouble the formal Kuratowski definition which says that $\langle a,b \rangle = \{\{a\},\{a,b\}\}$. What about this definition imposes order on the pair? I Need to Shrink My Database - I just freed a lot of space This question is asked in various forms here but the question boils down to:  I know shrinking a database is risky. In this case, I've removed so much data and I'll never use it again.   How can I shrink my database? What files do I shrink?  What should my considerations be while doing this?  Should I do anything after? What if it is a large database? Can I shrink it in smaller increments? Why must the eigenvalue of the number operator be an integer? My apologies if this question has already been answered. Using the notation of Sakurai, we have an energy eigenket N and an eigenvalue n.  $$N | n \rangle = n | n \rangle$$  For the number operator $N = a^\dagger a $. My question is precisely why does n have to be an integer. I do understand that it must be positive definite due to the norm condition on $ a | n \rangle $:  $$\langle n | a^\dagger a | n \rangle \geq 0$$  I can see that we can show:  $$ a | n \rangle = \sqrt{n-1} | n-1 \rangle $$ and similarly for $a^\dagger | n \rangle$  Sakurai argues that the sequential operation of $a$ operators leads to the form which he does not write, but I will write here for clarity:  $$ a^k | n \rangle = \left(\sqrt{n}\sqrt{n-1}...\sqrt{n-k+1}\right) | n - k + 1 \rangle $$   Since  $$ a|0 \rangle = 0 $$  the sequence must terminate, but can only terminate if n is an integer. How can we make that jump? Is there a formal mathematical proof that the sequence $\left(\sqrt{n}\sqrt{n-1}...\sqrt{n-k+1}\right)$ will terminate if and only if n is an integer? $f,g$ continuous from $X$ to $Y$. if they are agree on a dense set $A$ of $X$ then they agree on $X$ Problem:      Suppose $f$ and $g$ are two continuous functions such that $f: X \to Y  $ and $g : X \to Y $. $Y$ is a a Hausdorff space. Suppose $f(x) = g(x)  $ for all $x \in A \subseteq X $ where $A$ is dense in $X$, then $f(x)  = g(x) $ for all $x \in  X $.   Attempt at a solution:  Put $h(x) = f - g $. Therefore, $h: X \to Y $ is continuous and $Y$ is Hausdorff by hypothesis. Also we know $h(x) = 0 $ for all $x \in A $ such that $A$ is dense in $X$. I want to show that $h(x)$ vanishes everywhere in $X$. We can show $h(x) = 0 $ for all $x \in X \setminus A $. Suppose $h(x) &gt; 0 $ on $X \setminus A$. Pick points $y_1,y_2 \in Y $. Since $Y$ is Hausdorff, can find open set $O_1, O_2 \subseteq Y $ which are disjoint such that $y_1 \in O_1$ and $y_2 \in O_2$. By continuity, $f^{-1}(O_1), f^{-1}(O_2)$ are open in $X$.   I know that if I can show that one of the $f^{-1}(O_i)$ lies in $X \setminus A $, then we would have a contradiction since we have non-empty open set in $X \setminus A$ and this implies $A$ cannot be dense in $X$. But this is the part I am stuck. Any help would greatly be appreciated.  Also, Would be be possible to prove this without using the Hausdorff condition on $Y$? Generating random numbers in C Today I was cut off in the middle of the following sentence:     Between Cook, Strauss, and Pietersen—   My friend said I was wrong. He said that for more than two entities, among/amongst are used, and that between is only for two entities.   I vaguely remember some rule like this, but I asked him to hear the whole sentence, which was:     Between Cook, Strauss, and Pietersen, they’ve notched up 56 centuries in Test cricket.   Should I have used among here? Seems correct to me to use between, but my friend was certain.   Another friend pointed out the following sentence:     I’m still choosing between Harvard, Yale, and MIT.    Certainly among doesn’t seem to fit here, and she, to me, was correct in using between.