how can I designate number length? I mean for 1234 = 4, 303 = 3 or 32131 = 5, What is with general n? I mean I want designate C(n)
I read recently that you can find the number of digits in a number through the formula $\lfloor \log_{10} n \rfloor +1$ What's the logic behind this rather what's the proof?
Throw an error preventing a table update in a MySQL trigger If I have a trigger before the update on a table, how can I throw an error that prevents the update on that table? Bootstrap Paradox in Interstellar I use babelbib and I have a source with two authors. Contrarily to when using the plain bib style, as soon as I switch to babplain, the author names are formatted like this:  [1] Müller, Jan und Eva Schulze: Name of the book, 2015.   While I would like both author names to be formatted the same way, that is one of these:  [1] Müller, Jan und Schulze, Eva: Name of the book, 2015. [1] Jan Müller und Eva Schulze: Name of the book, 2015.   sources:  % test.tex \usepackage[ngerman]{babel} \usepackage[fixlanguage]{babelbib} \selectbiblanguage{ngerman} \bibliographystyle{babplain} \bibliography{test}  % test.bib @manual{foo,     author = "Müller, Jan and Schulze, Eva",     title = "Name of the book",     year = "2015", }   I can fix it by specifying and {Schulze, Eva}, but that way all is treated as the last name, that cannot be the solution, can it? Why does $\sum_1^\infty \frac1{n^3}=\frac52\sum_1^\infty\frac{(-1)^{n-1}}{n^3\binom{2n}{n}}$? Apery's original proof that $$ \zeta(3) \equiv \sum_1^\infty \frac1{n^3} $$ is irrational starts from an alternating series  $$ \zeta(3) = \frac52\sum_1^\infty\frac{(-1)^{n-1}}{n^3\binom{2n}{n}} $$  There must be a way to see that those two series are equal, but I have tried various telescoping and other techniques and I just can't see it. Help me out:       Show (preferably by reasonably elementary means) that$$\sum_1^\infty \frac1{n^3}=\frac52\sum_1^\infty\frac{(-1)^{n-1}}{n^3\binom{2n}{n}}$$ Why I cannot use universal instantiation rule here? I have the following premise:      $$\forall x (Fx \vee \neg Fx) \rightarrow Ga$$   Why I cannot use UI and get: $(Fa \vee \neg Fa) \rightarrow Ga$ And what is the difference between the first premise and the below premise:     $$\forall x ((Fx \vee \neg Fx) \rightarrow Ga)$$   Thanks in advance. If $$(1+ \cos A) (1+ \cos B) (1+\cos C)= y = (1- \cos A) (1-\cos B) (1-\cos C)$$ then prove that $$y = \pm \sin A \sin B \sin C$$ Improving "demonstrate a minimal understanding" close reason Density of random variables Let $X$ and $Y$ be independent random variables with respective densities: $f_X (x) = xe^{-\frac{x^2}{ 2}} 1_{]0,+\infty[} (x)$ and $ f_Y (y) =  \frac{1}{\pi \sqrt{1-y^2}} 1_{]-1,1[} (y)$  Let $U:=XY$ and $V:=X\sqrt{1-Y^2}$  I try to check whether U and V are independent and which law they follow.  What I did:  After some calculations, I found the density of $(U,V)$:  $ f_{(U,V)}(u,v)=\frac{1}{\pi } e^{-\frac{u^2}{ 2}}1_{\mathbb{R}}e^{-\frac{v^2}{ 2}}1_{\mathbb{R}_+^* }$ Which mean that $(U,V)$ follows a $ \mathcal{N}(0,1)$ law (because $u^2+v^2=x^2$) and that  U and V are independent because $f_{(U,V)}$ can be factored as the products of densities of $U$ and $V$  My question:  There is a factor $\frac{1}{\pi}$ and I don't know to which density it will belong: to $U$ density or to $V$ density?  Many thanks! Invisible space when trying to remove file (but exclude all files in a list)? I'm trying to accomplish a simple task using the excellent post : I would like to remove all files from a folder except those listed in a .txt file contained in the folder. The syntax works fine, but for some reason all files are removed - basically the script is saying that there are no correspondences between the filenames in the folder and those in the .txt file - but I can see that there are!   I thought maybe there might be some invisible white space after my file names that I cannot see (in the folder or the .txt file). But I don't think so...Is there another solution that I am not thinking of? I never hear "scissor" or "pant" or "jean". It's always "scissors", "pants", and "jeans", respectively. Are they considered plural? How do comment @replies work? How do the comment replies (aka &quot;pinging users&quot;) work?  Who can I send an @reply to? How do I respond to a specific user when entering my comment? Will they be notified? What do people mean when they talk about &quot;pinging&quot; another user?  Related: I have a file, which was encrypted with AES-128 in ECB mode. I know the format of the original file and know that all files in this format have the same headers. So, I have an encrypted block and the original block.  Can I get the encryption key, using this information? Examples proving why the tensor product does not distribute over direct products. I recently read about the result that the tensor product distributes over direct sums. I was curious if it also distributes over direct products, but google tells me it doesn't.   What are some simple counterexamples to why this property isn't true? I know that there is a natural homomorphism  $$ \left(\prod M_i\right)\otimes N\to \prod (M_i\otimes N) $$ given by $(\prod m_i)\otimes n\mapsto \prod (m_i\otimes n)$ when $M$ and $N$ are modules over some commutative ring $R$. Are there standard examples where this homomorphism is not injective/surjective and hence not an isomorphism? Array List count to users I have these two CREATE TABLE statements:   CREATE TABLE GUEST (   id int(15) not null auto_increment PRIMARY KEY,   GuestName char(25) not null );  CREATE TABLE PAYMENT (   id int(15) not null auto_increment   Foreign Key(id) references GUEST(id),   BillNr int(15) not null );   What is the problem in the second statement? It did not create a new table. First, this is about beta sites that might not even exist later, but imagine they will for the sake of this question. Taking the latest 10 questions on , I see 3 questions related to Mac OS X:    From my point of view, all 3 could also fit on , the 1st one could also be on SO, the 2nd and 3rd could also be on SU. How we will deal with this type of situation? When should we close a question as &quot;Belongs on [...]&quot;? I already see identical questions asked on 2 or 3 different sites (by the same or different users). Is there anything planned to link these questions or something like that? I mean something else than the already existing &quot;Linked&quot; feature. Something to include answers from site X in site Y or something like this. In the movies, the pack of Uruk-Hai capture Merry and Pippin, and are bringing them back to Saruman as quickly as possible.  Why didn't they use Wargs to carry the Hobbits instead of packing them on their backs?    Or, better yet, why didn't the Nazgul fly down and take them on their Fell Beasts? How can I resize a partition with Disk Utility? I have 2 partitions, I reduced the size of one and want to expand the other to fill the now available space.   How do I expand the Lion Partition into the empty grey space beneath Macintosh HD partition? Is there an easy way to attach source in Eclipse? I'm a big fan of the way Visual Studio will give you the comment documentation / parameter names when completing code that you have written and ALSO code that you are referencing (various libraries/assemblies).  Is there an easy way to get inline javadoc/parameter names in Eclipse when doing code complete or hovering over methods? Via plugin? Via some setting? It's extremely annoying to use a lot of libraries (as happens often in Java) and then have to go to the website or local javadoc location to lookup information when you have it in the source jars right there! How do I use superposition to solve a circuit? Yes, this is a pedagogical question. While answering another recent question, I wanted to refer the OP to concise instructions for using superposition to solve circuits. I found that all the easily found resources online were somewhat deficient. Typically they were unclear about what kinds of circuits superposition applies to, or about the actual method to apply the superposition theorem to a circuit problem. So,   What kinds of circuits can be solved by superposition?  How are different kinds of sources treated when solving by superposition?  What are the steps to solve a circuit using the superposition theorem?