Need help merging two seperate strings together
How to print without newline or space?
Show that $\int_{0}^{1}\{P(x)\}^{2}\,dx = (n + 1)^{2}\left(\int_{0}^{1}P(x)\,dx\right)^{2}$ Proof the Legendre polynomial $P_n$ has $n$ distinct real zeros equirectangular rendering for Blender Internal? Can such frames/videos be rendered in Blender Internal as well? If not, how indirectly?  EDIT: The below solution is great as long as you can write your own Python script and only render solid objects. When you need things like particles/hair, it won't work as those won't be reflected. I have a subomain which I do not want to be listed in any search engine result. Let say I have:   http://www.example.com http://child.example.com   How can I hide all URLs of child.example.com domain which are currently showing in the search engine results? Functions which are Continuous, but not Bicontinuous What are some examples of functions which are continuous, but whose inverse is not continuous?  nb: I changed the question after a few comments, so some of the below no longer make sense. Sorry. variable-variables in PHP Say $\mathbf{x} \in \mathbb{R}^n$, what is the common notation to extract the first component as an operation?  Something like $\mathcal{P}_j = \mathbf{x}_j$? $\mathbf{x}_j$ is the j-th component.   I need this because I have a function $f(\mathbf{x}) \approx \mathbf{x}$, so I need something like $\mathcal{P}f(\mathbf{x}) \approx \mathbf{x}_j$ since my metric is defined for a single component of $\mathbf{x}_j$. Proper subspaces of $ R^n $ I'm trying to prove that proper subspaces of $ R^n $ are closed and have empty interiors.  To prove that they are closed I'm trying to use the fact that inverse images of closed sets are closed sets by continuous functions. So I'm trying to find a linear map such that a proper subspace of $ R^n $ is its Kernel but I don't know how to express it so that it would work on all dimensions.  Regarding the fact that they have empty interiors, I really don't know what to do.  Thanks in advance. Why is the work done on a charge calculated from infinity? Why is the work done on a charge calculated from infinity to a point? Why not from one particular point to other? Wanted: question mark instead of bibtex key for missing citations (biblatex) Instead of having the citation key showing up in the document for missing references, I want to only have [?], as it is the case when using the default bibtex without biblatex. This behavior is driving me crazy, as it messes up all the formatting (especially in tables). I want to focus on writing and only later on deal with the erroneous citations.  This question is related to    and its MWE can be used. However, as pointed out beforehand, I want the question mark in the text instead of the citation key to not mess up the formatting (for missing citations). Evaluating the nested radical $ \sqrt{1 + 2 \sqrt{1 + 3 \sqrt{1 + \cdots}}} $. How does one prove the following limit? $$   \lim_{n \to \infty}   \sqrt{1 + 2 \sqrt{1 + 3 \sqrt{1 + \cdots \sqrt{1 + (n - 1) \sqrt{1 + n}}}}} = 3. $$ Find n such that $n^5 - n$ is divisible by $120$. (*Here $n$ belongs to the natural number set)  Seems a trivial problem, but the answer mentioned in the text book seemed incomplete to me so I'm here just to ensure whether approach to this problem is correct or not.  So my approach is as follows: We know that $n^5 - n$ can be written as $n^5-n = n(n-1)(n+1)(n^2 + 1)$  Now since it's product of three consecutive natural numbers so it's divisible by $3! = 6$. Now using Fermat's Little theorem we can prove that $n^5= n \mod5$ hence $n^5 - n$ is divisible by $5$ as well. So $n^5 - n$ is divisible by $30$. Now to ensure their is another factor of $4$ in the term we need to ensure that $n^5 - n$ is divisible by $8$. I found that all odd natural numbers and multiples of $8$ makes $n^5 - n$ divisible by $8$, hence $n^5 - n$ is divisible by $120$. But in the text book they have only mentioned odd natural numbers as answer, which seemed incomplete to me.  Thanking everyone in advance:P Allow an edit to notify downvoters: "I think I've fixed the issue now - please check" Tagging best practices I am wondering what I should do when tagging a question that fits multiple tags, in the particular case were the question might belong to general as well as more specific tags.  Let me give you an example to illustrate this:  Let's say I have a question about ASP.NET MVC 3.0 and I use C# as my main language.  The following tags could apply:   c# .net .net-4.0 asp.net asp.net-4.0 asp.net-mvc asp.net-mvc-3   Tagging with C# might make .NET redundant (I don't think C# is used anywhere else outside of the .NET scope), and tagging with  certainly makes  and  redundant. However, my question would get a better visibility with tags such as ,  and , as probably no one browses a tag as specific as .  How shall I tag my questions? Using more general or more specific tags, or a mix of the two? How does a  work? If seen from the outer side, we can see through thinking it is transparent, while if seen from the inside, the glass acts as a mirror. How? I am looking to replicate black &amp; white maps in QGis, using hatching patterns and greyscales to indicate different categories of a continuous variable (example below).  It is possible/straightforward to do so in QGis? At first sight I only see color gradients and symbol fills.   ). I am studying English in Korea.   All my friends and I are studying about 'sentence patterns'  Sentence patterns, said in here, are S+V, S+V+C, S+V+O, S+V+I.O+D.O, S+V+O+O.C.  But my teacher said these 5-sentence patterns are not perfect in grammar. But  because we don't use English by mother language, they will be helpful for understanding English.  Then, I came up with something.   Is sentence patterns used everywhere? (like U.S.A, U.K, Australia, anyother country where people use english by their mother language?)  I really wonder. idempotents acting as local identities Let $R$ be a ring with unity (not necessarily commutative) and $I$ an ideal of $R$.  Suppose that for every element $a \in I$ there exists an element $c\in I$ such that $ac=a$. Note that $c$ is related to $a$. Now we have the following question:  Can we say that  for every element  $a\in I$ there exists an idempotent element $c\in I$ such that $ac=a$?    Of course we have many examples such that the answer is true for them but in general  we don't know. Proof that a sequence of continuous functions $(f_n)$ cannot converge pointwise to $1_\mathbb{Q}$ on $[0,1]$ How is the optimal probability cut-off in a ROC defined by the R package Epi? The plot below was created by R package Epi::ROC for a binary classification problem. There is an optimal cut off or threshold for the classification probability at which sensitivity and 1-specifitiy are balanced in some optimal way (called ps3 in the plot). My question is how this point is defined mathematically in this case and if there are other ways to define it.