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 Dec 22 comment Calculating a function limit What have you tried? What actually is your question? Dec 22 comment Differential Equation So... what exactly do you expect from us? Just the answer? Or is this homework, and do you want a hint? Dec 22 comment Algebra question resubmited Your previous question was closed. This is a literal copy. Why did you think it wouldn't get closed this time? Dec 22 comment Prove that s is finite and find an n so large that $S_n$ approximate s to three decimal places. @rlgordonma: I didn't want to completely give it away, but yes, that is closer to an answer :). Dec 22 comment How can I systematically find the roots of $x^4 + 1?$ Is there some algorithm? Better. Although I'd simply expect this question to be closed as duplicate. Dec 22 comment How can I systematically find the roots of $x^4 + 1?$ Is there some algorithm? Yes, those answers are much better and more welcoming. This just smacks an answer to the question, which is technically correct, but the techniques it relies on are not explained at all. Dec 22 comment How can I systematically find the roots of $x^4 + 1?$ Is there some algorithm? How is someone who doesn't know how to find roots of $x^4+1$ helped by your answer? Dec 22 comment How can I systematically find the roots of $x^4 + 1?$ Is there some algorithm? If you can understand this answer, you wouldn't have needed it in the first place. Dec 22 comment How can I find $\sum_{k=1}^{1233}f(\frac{k}{1234})$ I like how you can solve for $f(1/2)$. Dec 22 comment How many subsets of $\mathbb{N}$ have the same cardinality as $\mathbb{N}$? @DougSpoonwood: see Asaf's answer for an explanation. Dec 22 comment Simple equation misunderstanding I don't know what you're doing wrong, but I'm getting a different value (in fact, the one you're looking for) for the arctan. How are you calculating it? Dec 22 comment How can I find $\sum_{k=1}^{1233}f(\frac{k}{1234})$ Thanks to Mathematica for simplifying the terms, I wouldn't have voluntarily done this. Dec 22 comment How can I algebraically prove that $2^n - 1$ is not always prime? I think the question can be interpreted as "prove that there are infinitely many $n$ such that $2^n-1$ is not prime". Otherwise, as @Hurkyl mentioned, you have already proved your own statement. 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 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.