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 Dec1 answered Removing noise when the signal is not smooth Dec1 comment simple statement proof @doniyor: in that case, every question on this site should have the [set-theory] tag. [set-theory] is about ZFC and such. Dec1 comment Cat Dog problem using integration +1 for a lot of effort. if i could give +3 i would. Nov30 comment Real world applications of prime numbers? Note that this encryption system will be utterly useless as soon as quantum computers are reasonably usable. Nov30 comment $f: V \mapsto V$ is a projection, show $V = \ker(\pi) \oplus \operatorname{Im}(\pi)$ Your map $v\mapsto(v-f(v),f(v))$ is a good one. Is it a linear space? What is its dimension? Nov30 comment $f: V \mapsto V$ is a projection, show $V = \ker(\pi) \oplus \operatorname{Im}(\pi)$ In that case you haven't proven that $\ker(\pi)+\operatorname{im}(\pi)=\ker(\pi)\oplus\operatorname{im}(\pi)$, only $\ker(\pi)\cap\operatorname{im}(\pi)\subset\ker(\pi)+\operatorname{im}(\pi)$ Nov30 comment $f: V \mapsto V$ is a projection, show $V = \ker(\pi) \oplus \operatorname{Im}(\pi)$ Please put your entire equation in the math environment, not just the extra symbols you need. So write \$\pi\circ\pi=\pi\$ instead of \$\pi\$o\$\pi\$=\$\pi\$. Nov30 comment $f: V \mapsto V$ is a projection, show $V = \ker(\pi) \oplus \operatorname{Im}(\pi)$ What do you mean by $\ker(\pi)+im(\pi)$? Do you mean $\ker(\pi)\oplus im(\pi)$? In that case, equivalence is not clear to me. Nov30 comment $f: V \mapsto V$ is a projection, show $V = \ker(\pi) \oplus \operatorname{Im}(\pi)$ A rather quick method would be using the exact sequence $0\to\ker f\to V\to V/\ker f\to0$. Nov30 comment $f: V \mapsto V$ is a projection, show $V = \ker(\pi) \oplus \operatorname{Im}(\pi)$ "So v = (v - π(v)) + π(v) is in Ker(π) + Im(π)." Please explain. Nov29 comment Convergence on open-minus-countable topology What have you tried? Nov29 comment how to calculate the fundamental group using intitutive ideas? @hina: what is unclear. Nov29 comment how to calculate the fundamental group using intitutive ideas? @QiaochuYuan: I don't think so. isn't the fundamental group of what you're saying isomorphic to Z? I don't think hina's group is... Nov27 comment How can I find this result modulo $10^8$? if $N$ is much smaller than $a$, your square root is approximately equal to just $2a+1$. Nov27 comment Solve $x^2(1-x) = 1$ There is only one real solution, there are two complex solutions. See wolframalpha.com/input/?i=solve+x%5E2%281%E2%88%92x%29%3D1 Nov27 comment How to Integrate along a path Trying to save one more unupvoted answer from doom. Nov27 comment proving homeomorphism This answer is correct, but of course the formula you gave is not very helpful - I mean sure, it is right, but how'd you get it? Surely you can shed some light on that. Nov24 comment Is mathematics the only language that is not subject of interpretation? @tomasz: ugh, no, the language of mathematics is not explained in every single paper or a mathematical subject. but that is of course not the point that I was trying to make :-/ Nov23 comment Limit of sequences @yuta, well, do you have a definition for convergence? What have you tried to prove the statements? Nov23 comment Is mathematics the only language that is not subject of interpretation? If you're looking for largely unambiguous languages, take a look at lojban. Mathematics is ambiguous, but usually clear by context.