Finding a $\text C^\infty$ function which is zero just on a given closed set
Every closed subset $E\subseteq \mathbb{R}^n$ is the zero point set of a smooth function
Failed to mount Windows share: Invalid argument Calculate $\lim_{n\rightarrow +\infty}\binom{2n} n$ This is a canonical question and answer developed by the community to help address common questions. If you've been directed here, or your question has been closed as a duplicate, please look through the resources here and use them to shape more specific questions. To browse all canonical questions and answers, including more unit test resources, navigate to the  tag.  This canonical question is intended to address several classes of common questions by providing a quick summary and links to comprehensive resources:   How do I start writing my first unit test?  How do I unit test this code?  I need help writing this unit test.   Salesforce Stack Exchange looks for detailed, specific questions that the community can help you with, and can't write tests on your behalf. We feel that working with the resources below can help you get started, and we encourage you to make an attempt to write your test and return to SFSE with your specific questions when you encounter challenges you can't resolve. I have a file: Base.h  class Base; class DerivedA : public Base; class DerivedB : public Base;  /*etc...*/   and another file: BaseFactory.h  #include "Base.h"  class BaseFactory { public:   BaseFactory(const string &amp;sClassName){msClassName = sClassName;};    Base * Create()   {     if(msClassName == "DerivedA")     {       return new DerivedA();     }     else if(msClassName == "DerivedB")     {       return new DerivedB();     }     else if(/*etc...*/)     {       /*etc...*/     }   }; private:   string msClassName; };  /*etc.*/   Is there a way to somehow convert this string to an actual type (class), so that BaseFactory wouldn't have to know all the possible Derived classes, and have if() for each one of them? Can I produce a class from this string?   I think this can be done in C# through Reflection. Is there something similar in C++? I'm sure everyone is familiar with the Ship of Theseus paradox, basically "If you replace parts of a ship over time until none of the original ship is left, is the end product still the same ship?"  I just read pop philosophy books, so spare me if this is an idiotic question, but could this be applied to the Brain and consciousness? If you were the take individual atoms/neurons, and somehow replace them with its exact copy one at a time, how would the person experience that?   I don't think there would be an interruption of consciousness, but at the end it's a completely separate (but identical) brain from the one you started with. Exactly as if you had just cloned the whole thing, right? But without interruption.  What interests me is the gradual transition of consciousness here, is it possible to know how that would  work?  I think I remember hearing people argue similarly for both the existence of a transcendent soul and also AI consciousness. And the only other discussion I found of this was on a flat earth forum, so I don't know what to make of that.   I hope I articulated my question clearly. Thank you! What is the difference between topological and metric spaces? What is the difference between a topological and a metric space? Short captions for figures in \listoffigures When I use \listoftables and \listoffigures I get in the list long captions that appear next to the tables/figures.  I would like to use short captions for this list which summarize these captions. Is that common to do? If so, what is one way to do it? How can i restrict /admin login page to a particular IP only? Query works on Oracle 11g but fails on Oracle 8i Residuals correlated positively with response variable strongly in linear regression What limitations does converting question links to links with titles have? On this  there are more than 50 links to Stack Overflow questions. However, the last 6 links aren't converted to titles (http://facebook.stackoverflow.com/questions/6530420/control-the-image-that-facebook-shows-when-i-like-a-url should be converted to ).   However:  all http://facebook.stackoverflow.com/... into http://stackoverflow.com/... fixes this, both in the preview and the final result. Also, the preview won't show any title for http://facebook.stackoverflow.com/... links.  My question is, what limitations does this converting have? How are these question titles retreived? Via API? Through database?  I'm not sure about title, feel free to edit that Disallow closing of questions with a certain number of question / answer upvotes With reference to this currently open question   At the time of writing, it has 3 close votes yet has 7 question upvotes and the single answerer (11 upvotes) will have been awarded the enlightened badge (silver).  Therefore in the opinion of many (i) the question adds value and (ii) the answer adds value.  As a staring point for discussion, I suggest that 5 net question upvotes (and perhaps 5 answer net upvotes) should be enough to keep a question permanently open. Let's haggle over the numbers though. Thoughts? How do I give players already enchanted Tools/Armour/Weapons Can ordered list produce result that looks like 1.1, 1.2, 1.3 (instead of just 1, 2, 3, ...) with css? The only solutions that I know of till now are $(x,y) = (1,1) \space , (19,7)$. We can note that: $$x^2-x+1 = y^3 \implies (2x-1)^2 = 4y^3-3$$ Thus, if odd prime $p \mid y$, then $(2x-1)^2 \equiv -3 \pmod{p}$ and thus, $-3$ is a quadratic residue. This implies that $p \equiv 1 \pmod{6}$ .  How can we further proceed into this problem?  Note: As mentioned in one of the links in the comments, if we instead replace $x$ by $x+1$, we get $x^2+x+1 = y^3$. Thus, the solutions for this is $(x,y) = (0,1) \space, (18,7)$. What is the correct way to pluralize an acronym / initialism? For example, if I wanted to write the equivalent of  There are many automated teller machines in this city.  Would it be  There are many ATMs in this city.  or  There are many ATM's in this city. (could get confused with possessive form or contraction).  or just  There are many ATM in this city. (assuming the final s is included in Machines represented by M).  Maybe something else? Inverse metric in linearised gravity From what I've read, in the framework of linearised gravity, one perturbs the metric around a Minkowski background, $\eta_{\mu\nu}$, such that  $$g_{\mu\nu}(x)=\eta_{\mu\nu}+h_{\mu\nu}(x)\tag{1}$$  where $h_{\mu\nu}(x)$ is a small perturbation, i.e. $$\big\lvert h_{\mu\nu}\big\rvert&lt;&lt;1.\tag{2}$$  The inverse metric is then found by assuming the following ansatz:  $$g^{\mu\nu}(x)=\eta^{\mu\nu}+\tilde{h}^{\mu\nu}\tag{3}$$  where $\tilde{h}^{\mu\nu}$ is also small (i.e. $\big\lvert \tilde{h}_{\mu\nu}\big\rvert&lt;&lt;1$).   Using this, it is easy to find that  $$g^{\mu\nu}(x)=\eta^{\mu\nu}-h^{\mu\nu} \tag{4}$$  to first order.   My question is, what is the justification for this ansatz? Is it simply that one expects the inverse metric to have a similar form to the metric in order to satisfy $$g^{\mu\alpha}g_{\alpha\nu}=\delta^{\mu}_{\;\nu}~?\tag{5}$$ Is it possible to show our custom message in QGIS Status bar using python? The is sometimes pronounced &quot;tha&quot; (/ðə/) or &quot;thi&quot; (/ðiː/). Which is the correct pronunciation of this word? Are both correct and used interchangeably at specific places? If the second question is correct, please provide the rule of pronouncing at different places. Formula for the $n$th term of $1, 2, 2, 3, 3, 3, 4, 4 ,4, 4, 5, ...$ There exists a formula for the $n$th term of this sequence  from the OEIS ("$n$ appears $n$ times") $$1, 2, 2, 3, 3, 3, 4, 4 ,4, 4, 5...$$ which is $$\left \lfloor \frac {1+\sqrt{1+8n}}{2} \right \rfloor.$$  Is there a better formula for the $n$th term? A formula that isn't a 'magic' one that just happens to work but one that comes from a well-founded observation. Preferably one not using the floor function. I also have suspicions about the sustainability of the above formula as I feel with very $n$ it may not function properly.