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 Dec 21 comment Closure in a product of topological spaces What is the closure of a topological space? I know closures of strict subsets of spaces, and completions of metric spaces, but what are closures of spaces? Dec 21 answered Why do some people use $+\infty$ instead of $\infty$? Dec 20 comment Finding the number of points on the straight line joining $(-4,11)$ and $(16,-1)$ @ShaneORourke: oh don't worry, I know how to find the answer, but clearly something's missing. Dec 20 comment Finding the number of points on the straight line joining $(-4,11)$ and $(16,-1)$ How did you find these solutions? Why aren't there more? This is an incomplete answer. Dec 17 comment Can't argue with success? Looking for “bad math” that “gets away with it” Unfortunately, this is almost literally how Cayley-Hamilton is proved in Stoll's syllabus on linear algebra (see Theorem 2.1): math.leidenuniv.nl/~desmit/edu/la2_2012/LinAlg2-index.pdf Dec 17 comment Question involving entire functions @pankaj: you don't need to be "sorry". just read up on the identity theorem, and ask us about that instead of trying to answer these questions. Dec 17 comment Question involving entire functions There's hardly anything to add without giving the answer away at this stage. Dec 17 comment Question involving entire functions If you are still not getting it, you don't know the identity theorem. Dec 17 comment Question involving entire functions Dear pankaj, you have now asked three questions, all of which show no own work. Try investing a little time in the material before you come to us, and if you had any thoughts, please tell us what you've tried. Dec 17 comment boundedness of an operator $\frac{f(x)}{1+|x|+|y|}\leq f(x)$ Dec 17 comment Show the function $x_1\sin(1/x_2)+x_2\sin(1/x_1)$ is continuous everywhere Okay, so $\lim_{x\to1}F(x,x-1)-(x-1)\sin(1/x)$ should be defined by continuity of F and convergence of the term $(x-1)\sin(1/x)$ (convergence because $x-1\to0$ and $\sin$ is bounded). But this limit is your $x\sin(\frac{1}{x-1})$, which indeed does not converge since $\frac{1}{x-1}$ does not (add a few sentences here), ergo $F$ is not continuous. Dec 17 comment Show the function $x_1\sin(1/x_2)+x_2\sin(1/x_1)$ is continuous everywhere I don't know, your reasoning sounds alright but you'll need to add a sentence somewhere - I'm not quite convinced. Dec 17 comment Show the function $x_1\sin(1/x_2)+x_2\sin(1/x_1)$ is continuous everywhere The fact that your calculations do not work does not prove $F$ cannot be continuously defined. In particular, the fact that the individual limits do not exist does not prove that the sum does not (for example, consider $0=\lim 1/x - 1/x=\lim1/x-\lim1/x$). Dec 17 comment Displaying $2 \cdot 10^5$ as $200000$ Right click on the result, Numeric formatting. Dec 17 comment Prove that $\int_0^{+\infty} \frac{\ln x}{a^2+x^2} dx = \frac{\pi\ln a}{2a}$ Perhaps this is not an answer for Leitingok, but this is exactly how they would do it in the book, and shows the power of complex analysis. +1. Dec 17 comment Given joint pdf of $X$ and $Y$, find pdf $Z=XY$ Yes. $X\leq1$ and $Y\leq1$ so $Z=XY\leq1$. Dec 16 comment $f^{-1}$ and continuity This is actually one of the definitions for continuity, so you really need to explain what definition you are using. Dec 16 comment linear hyperbolic PDE with some BCs at infinity Hello there, try putting your equations in latex, as explained here: meta.math.stackexchange.com/questions/107/… Dec 16 comment Prove that $f'$ exists for all $x$ in $R$ if $f(x+y)=f(x)f(y)$ and $f'(0)$ exists You make quite a stronger statement than what was asked for, but it's technically correct. Dec 16 comment Complex Functions Concept Questions I think the fact that these answers are longer than the normal, mathematical, equation-rich answers, says enough about this method of teaching.