C++ underflow example?
How do I detect unsigned integer multiply overflow?
What is the Hausdorff dimension of the set of irrationals on $\mathbb R^1$ I am sorry if this is a dump question but I can't find any reference for this. What is the Hausdorff dimension of the set of irrationals on $\mathbb R^1$? I speculate this is $1$ but don't know how to prove it rigorously. Is every metric space a subspace of some connected metric space? If the space itself is connected then we're done, but if not then I think we can extend our metric space to make it connected.  I'm not sure whether this will work or not, but intuitively I think the answer is yes. This morning I upgraded my system to Windows 10 2004, the upgrade went smooth and was through Windows Update. I am using Hyper-V as my virtualization program for virtual machines and to provide extra layer of protection to the system through core isolation. After the upgrade, I noticed that a new Virtual Switch was created with the name &quot;vEthernet (Ethernet)&quot; where &quot;Ethernet&quot; within the parentheses is the name of my primary network adapter. Also noticed this behavior has a specific pattern of creating new vSwitches correspond to the adapters you have, e.g. if you created a new Virtual Switch and restarted the system, a new additional switch will appear with the name &quot;vEthernet (your-new-switch-name)&quot;. Tried to remove Hyper-V and reinstall it but no luck. I am aware of a similar  on SuperUser but has no answers on it. Any clues for the root of the problem? Using principal component analysis (PCA) for feature selection When I'm using  find . -type f -name "*.htm*" -o -name "*.js*" -o -name "*.txt"  it finds all the types of file. But when I add -exec at the end:  find . -type f -name "*.htm*" -o -name "*.js*" -o -name "*.txt" -exec sh -c 'echo "$0"' {} \;  it seems it only prints .txt files. What am I doing wrong?  Note: using MINGW (Git Bash) execute command on a defined range of directories Is it possible to 'partition' a directory listing - say in to blocks of some number, to perform different actions on each 'range'?  For example, lets say I have the following directories inside another folder:  $ ls test abc/ def/ hij/ klm/ nop/ qrs/ tuv/ wxy/ zzz/   And I want to perform some action on the first 3 directories, another on the second 3, and so on.  My thought was that perhaps a loop across numbers would work, based on the output of something like ls | nl (but before anyone mentions it, I know parsing ls is a no-no!)  This obviously doesn't work, but illustrates my point I hope:  for dir in `ls | nl`;  do     do-something-with ${dir{1..3}} # Where $dir has taken on some numerical value linked to the folder)     do-something-with ${dir{4..6}}  # And so on...     do-something-with ${dir{n-3..n}}  done   The folders I intend to actually do this on, can be worked on in any order (i.e. the final splits can be totally arbitrary), but they have no logical naming consistency - by which I mean they can't be organised sensibly alphabetically or numerically based on any key within the directory name themselves. Can a legendary creature use a legendary resistance to pass a concentration check? As I was looking through some legendary creatures, I had a thought. Most legendary creatures get three Legendary Resistances per day, which they can use to automatically succeed on a saving throw.  A Concentration check is technically a Constitution saving throw, so does that mean that a creature can use a Legendary Resistance to automatically pass a Concentration check, or is it not considered a saving throw? Is there a quick way to set an HTML text input (&lt;input type=text /&gt;) to only allow numeric keystrokes (plus '.')? Showing that the roots of a polynomial with descending positive coefficients lie in the unit disc. Probability that the sum of 6 dice rolls is even What is the fastest way to create a 90° joint? I often want to create joints like this:    Since I end up making these more than a little, I'd like a fast way to do it (i.e. on the order of &lt; 10 seconds)  I've found a couple tools which come close to being the ideal solution, but I've had some problems with them as listed below:   When using the spin tool I usually end up having to fiddle with the location for a while in order to to get a natural curve:    Are there any techniques to expedite this process of fiddling? The bridge tool is nice because I can precisely specify where both ends of the joint will be, however I often end up with subtly uneven joints, probably due to my initial mesh being not quite square.    Is there a fast way to correctly line up the initial edge loops in a way that will result in an even joint? Elastic IP address on EC2 instance interface without 1:1 NAT Creating a copy of primary database and attaching the copy database in the same sql instance I just got into a project in which we have only one SQL Server 2012 copy. We have 12 databases attached to the primary instance of SQL Server 2012.  As I don't have SQL Server 2012 or supporting OS, I have to depend on the primary instance of SQL Server 2012.  I am not sure whether it is good to create copy/clone of all 12 databases and attach it to same instance and work on the copy for data manipulation and query testing purpose.  Based on Kin's query  SELECT    SERVERPROPERTY ('MachineName') AS PhysicalMachineName,    SERVERPROPERTY ('ServerName') AS SQLServerName,    SERVERPROPERTY ('Edition') AS ServerEdition,    CAST(SUBSTRING(@@Version,charindex('SQL',@@version, 1),15) AS VARCHAR(255)) +  ' + '         + CAST (SERVERPROPERTY ('productlevel')AS VARCHAR (50)) + ' + (Build'        + CAST (SERVERPROPERTY ('ProductVersion') AS VARCHAR (50)) +')' AS ProductVersion,     RIGHT(@@version, (Len(@@Version)-charindex('Windows',@@version, 1))+1) AS [O.S.],  SERVERPROPERTY ('Collation') AS Collation   Following is the output. I ignored PhysicalMachineName and SQLServerName.  ServerEdition : Business Intelligence Edition (64-bit) ProductVersion : SQL Server 2012 + RTM + (Build11.0.2100.60) O.S.           : Windows NT 6.1 &lt;X64&gt; (Build 7601: Service Pack 1)  Collation      : SQL_Latin1_General_CP1_CI_AS I'm looking for a bijection from the closed interval [0,1] to the real line. I have already thought of $\tan(x-\frac{\pi}{2})$ and $-\cot\pi x$, but these functions aren't defined on 0 and 1.   Does anyone know how to find such a function and/or if it even exists?   Thanks in advance! Definite Integral: $\int_0^1\frac{x^{2} -1}{\log x}\,dx$ How to figure out the following integral? I have not been able to solve it from some time. $$\int_0^1\frac{x^{2} -1}{\log x}\,dx$$ Is it possible to know who voted my question/answer up or down? If not, then is it possible to include this feature? By this feature we can come to know if you are being voted up by question owner or persons giving other answers to same question or just the visitors of that question thread.  Like...  If it is a group of people giving other answers, then your answer is most correct If it is readers of that question, then your answer is more popular How to modify a text file? There are several things that I don't understand. I know that zero is a real number, but I'm confused on the how and why aspects. What defines a real number, compared to a number that's considered non-real? For what reason is zero real, and how is it that a value such as infinity isn't when zero is?  Also, what purpose does zero even have? It's obvious that it's used as a place holder, but what value does it have alone? What makes it any different from other numbers? I realize that it is typically interchanged with nothing, but that would technically mean that zero is nothing—and that's not true. People have told me already so many times that zero does not necessarily mean nothing, and I figured it out a long while ago anyway. So, what I want to know is the actual value that can be associated with zero.  However, my question brings up another topic that has been argued and disputed about and disagreed on for years. Zero divided by zero, or 0/0. There are a lot of varying answers about this, but what's been constant throughout everything is that people claim 0/0 is not a real number. So, if I may ask, why is it that zero is considered a real number, and not 0/0? And why is it considered non-real in the first place? True, there is no defined value, but the expression is anything but meaningless; if it was, then there wouldn't be so many people trying to understand it. I guess what I'm trying to figure out is the reason behind the expression's classification as non-real—especially when the sole number of zero is real, despite not having an evident value.  This covers a few different things, so I was uncertain about what to make the title of these questions. I apologize for that. If anyone can answer, though, I'd be extremely grateful! I'm looking for a class in java that has key-value association, but without using hashes.  Here is what I'm currently doing:   Add values to a Hashtable. Get an iterator for the Hashtable.entrySet(). Iterate through all values and:   Get a Map.Entry for the iterator. Create an object of type Module (a custom class) based on the value. Add the class to a JPanel.  Show the panel.   The problem with this is that I do not have control over the order that I get the values back, so I cannot display the values in the a given order (without hard-coding the order).  I would use an ArrayList or Vector for this, but later in the code I need to grab the Module object for a given Key, which I can't do with an ArrayList or Vector.  Does anyone know of a free/open-source Java class that will do this, or a way to get values out of a Hashtable based on when they were added?  Thanks! How to insert text into a root-owned file using sudo?