decision making process
Is there any way to know when I will receive my UK visa?
Conjectures that have been disproved with extremely large counterexamples? I just came back from my Number Theory course, and during the lecture there was mention of the Collatz Conjecture.  I'm sure that everyone here is familiar with it; it describes an operation on a natural number – $n/2$ if it is even, $3n+1$ if it is odd.  The conjecture states that if this operation is repeated, all numbers will eventually wind up at $1$ (or rather, in an infinite loop of $1-4-2-1-4-2-1$).  I fired up Python and ran a quick test on this for all numbers up to $5.76 \times 10^{18}$ (using the powers of cloud computing and dynamic programming magic).  Which is millions of millions of millions. And all of them eventually ended up at $1$.  Surely I am close to testing every natural number? How many natural numbers could there be?  Surely not much more than millions of millions of millions. (I kid.)  I explained this to my friend, who told me, "Why would numbers suddenly get different at a certain point?  Wouldn't they all be expected to behave the same?"  To which I said, "No, you are wrong!  In fact, I am sure there are many conjectures which have been disproved by counterexamples that are extremely large!"  And he said, "It is my conjecture that there are none! (and if any, they are rare)".  Please help me, smart math people.  Can you provide a counterexample to his conjecture?  Perhaps, more convincingly, several?  I've only managed to find one! (Polya's conjecture). One, out of the many thousands (I presume) of conjectures. It's also one that is hard to explain the finer points to the layman. Are there any more famous or accessible examples? Requesting review of technically inaccurate answers Some answers are plain wrong, or even harmful. Usually these get spotted pretty quickly and either fixed or deleted by the poster, on the basis of comments/votes.  Sometimes though these slip under the radar - the OP ignores the downvotes/comments, or nobody even picks up on it the first time around.  I've always assumed that VLQ flags in the 10K queue for answers that are technically flawed, but otherwise OK were effectively "request for review by somebody knowledgeable in this area". It seems though that .  How should answers like this be handled instead if VLQ is not appropriate? Is there a mechanism for requesting further review? Raising them in chat is sometimes an option, but not always appropriate.   The useful actions that might happen as a result of increased visibility:   Edits by domain experts Downvotes to hide the poor answer Less flawed answers by experts Delete votes by 20K users   Would a "technical issue flag" that pushes to a tab in  /review help? Understanding Tag badges I very recently earned the below badge. But I am sorry, I do not understand it.    It says      Earned at least 100 total score for at least 20 answers in the java tag.   But I have answered 140 questions under Java tag and pretty sure would have earned more than 100 points. Then why did I receive it so late. Currently I have 3.3K points on SO.  Secondly if so, I have answered about 41 questions under Scala tag, then why didn't I receive this badge for Scala? Proving an entire, complex function with below bounded modulus is constant. How would I show that an entire function $f$ with the property $|f(z)| \geq 1$ must be constant?    I'm aware of Liouville's theorem, just not sure how to apply it here. Making crafted items usable in adventure mode In a map I'm making the player has to survive while locked in a maze. To stop them from breaking out, they will be in adventure mode. However, I still want them to be able to craft items and use them with specified blocks. I have tried several methods already but they all have a flaw.  One method is to have a scoreboard objective called item and giving certain item entities a specific score using something like:  /scoreboard players set @e[type=Item] item 1 {Item:{id:"minecraft:sapling"}}   Then it is possible to select these items with:  /entitydata @e[type=Item,score_item=1,score_item_min=1] {Item:{tag:{CanPlaceOn:["dirt"],HideFlags:24}}}   This works but it requires the item to be dropped, which isn't a problem for saplings, but for tools and other craftable items, it becomes a hassle.  To fix this, I'm currently clearing tools without damage and giving the player a slightly damaged tool in return:  /clear @a minecraft:stone_axe 0 1   /give @a minecraft:stone_axe 1 1 {CanDestroy:["log","log2","leaves","leaves2"],HideFlags:24}   This doesn't work for items without damage values (e.g. torches), but I don't mind these having to be dropped as there aren't too many of these. However, there is another problem. In the nether, the player will have access to an enchantment table and an anvil. This means they can repair enchanted tools, which will cause them to be cleared and replaced with unenchanted ones as soon as they go back to the overworld.  I also thought about using a stat.craftItem scoreboard objective and giving them the usable item if they craft it. However, this would result in the player having a duplicate of every item they crafted, as I think it is impossible to select an item without NBT-data in the /clear command.  Is there any way to make this work? And if not, would it be better to have the player drop all crafted items or have duplicates of them all? In Python, is there a concise way of comparing whether the contents of two text files are the same? I don't care what the differences are.  I just want to know whether the contents are different. In Portal, we are promised cake and a party at the end of our tests. However;       we soon discover that the cake is a lie.     Then, at the final scene;       there really is a cake (and my companion cube is waiting for me).   What's the meaning of this?  Was GLADOS not deceiving me? Her comments seem to suggest that;       ...she had the intention of killing me. Was the cake for us (player) and not for the character in the game? Well, I have come to understand persons with the following traits will be usually be Sorted to Slytherin   Resourcefulness  Cunning Ambition Leadership Qualities Self-Preservation Determination  Cleverness Fraternity  Power   On which trait(s) was Snape Sorted into Slytherin?  One more point: Lily Evans was Sorted before Snape, and when she was placed in Gryffindor, obviously Snape wanted to be in Gryffindor too, because Lily is his only friend.   So why is he Sorted into Slytherin? Is there a stronger reason for the Sorting Hat to override his preference and Sort him into Slytherin? Where to put the escape characters? I've tried to change my prompt by editing .bashrc:  export PS1="\e[0;32m[\u@\h \W]\$ \e[m"   This seems to work, but ctrl-r to access reverse history ends up with my typing not appearing in the same place as it will be interpreted (like ). It is fine when using the up or down arrows to select previous commands though.  I've had a look at that question, but can't seem to work out where to apply the escape characters in my prompt. I've tried a few combinations but then I break normal text typing functionality or simple back/forwards through history.  If you could include an explanation of which instances of characters need escaping and why, that would help me (and hopefully others) learn. Gosper's unusual formula connecting $e$ and $\pi$ I've fitted my model and am trying to understand whether it's any good. I've calculated the recommended metrics to assess it ($R^2$/ AUC / accuracy / prediction error / etc) but do not know how to interpret them. In short, how do I tell if my model is any good based on the metric? Is an $R^2$ of 0.6 (for example) sufficient to let me proceed to draw inferences or base scientific/business decisions?     This question is intentionally broad, to cover a wide variety of situations that members frequently encounter; such questions could be closed as duplicates of this one. Edits to broaden the scope beyond the metrics mentioned here are welcome, as are additional answers - particularly those that offer insight about other classes of metrics. What is a natural response to &quot;Good to see you. How you doing?&quot;? Will a natural response include &quot;doing&quot; as in &quot;I'm doing okay&quot; or will &quot;I'm okay&quot; be more natural? The sum of powers of two and two's complement – is there a deeper meaning behind this? Why is $\frac{1}{\frac{1}{0}}$ undefined? Compare 2 files and remove any lines in file2 when they match values found in file1 app engine datastore auto-clears every time project runs Add UI elements to UIScrollView? todonotes: How to make multiple listoftodos? In this MWE, I made two commands to highlight parts of the text as a reviewer comment, while the comments are colored uniquely to indicate the author whose comment is typeset.  If I want to make two listoftodos, each has the comments entries of one author, how can it be done?  \documentclass{article} \usepackage{hyperref,lipsum}  \usepackage[textwidth=2.5cm,colorinlistoftodos]{todonotes} \setlength{\marginparwidth}{2.5cm}  \newcommand\stR[2]{% 1st reviewer comment     \todo[%     author=1st Reviewer,noline,caption={1st Reviewer #1 Comment},color=blue!20%     ]%     {#1 Comment}{\color{blue}{\bfseries#2}}}  \newcommand\ndR[2]{% 2nd reviewer comment     \todo[%     author=2nd Reviewer,noline,caption={2nd Reviewer #1 Comment},color=red!50!white%     ]%     {#1 Comment}{\color{red}{\bfseries#2}}}  \begin{document} \listoftodos[Reviewers Comments] \section{Section} Text \stR{2nd}{2nd comment of the 1st reviewer} another text\vspace{\baselineskip} \lipsum[1]\vspace{\baselineskip} Some text \ndR{1st}{1st comment of the 2nd reviewer} continue text \end{document} Keyboard shortcut to autocomplete the user in comments Unable to run any GRASS 7 algorithms in QGIS 2.18.10 on Windows 7(64)