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 Apr8 comment Is $(-\infty, 0]$ closed in $\mathbb{R}$? Obviously yes.. Mar31 comment An infinite sum based on the mod-parity of Euler's totient function Anyway, by a theorem of Dence and Pomerance, the number of integers in $n \in [1,x]$ such that $12 \mid \phi(x)$ is equal to $(1+o(1))x$ [oh, they derive also other class residues mod 12] .. Mar31 answered Can we find two numbers from $n+2$ numbers chosen from $\{1,2,3,\cdots\}$? Mar30 answered Let $n,r,a$ be positive integers with g.c.d.$(a,d)=1$ , does there exist integer $m$ relatively prime to $n$ such that $d|m-a$? Mar29 revised Showing a function can not be continuous. added 1 character in body Mar29 revised Showing a function can not be continuous. added 2 characters in body Mar29 answered Showing a function can not be continuous. Mar29 accepted The image of a segment is not dense into a square Mar29 comment The image of a segment is not dense into a square Right, I forgot to add "with non-empty interior"; let us say, the cube in $\mathbf{R}^3$ is not homemorphic to a closed square in $\mathbf{R}^3$.. Mar29 comment The image of a segment is not dense into a square I agree, thanks Clement and Amitai; trying to generalize to higher dimensions, is it possible to prove on the same line of reasoning that a compact subset of $\mathbf{R}^3$ is not homeomorphic to a closed square in the plane $x=0$ of $\mathbf{R}^3$? Mar29 asked The image of a segment is not dense into a square Mar29 accepted Subset of open set and subset of its bourdary is open Mar29 comment Subset of open set and subset of its bourdary is open Now it works, well :) Mar29 comment Subset of open set and subset of its bourdary is open Well, $B$ should be the bourdary of $A$, not the bourdary of $A^\prime$.. Mar29 revised Subset of open set and subset of its bourdary is open deleted 10 characters in body Mar29 comment Subset of open set and subset of its bourdary is open Why $(0,0) \in B$? Mar29 comment An infinite sum based on the mod-parity of Euler's totient function Why do you think it should be a relevant sum in number theory? Mar29 asked Subset of open set and subset of its bourdary is open Mar20 awarded Benefactor Mar19 accepted Continuous image of convex hulls