coffeemath
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 1d comment Is the given function injective? @SeyhmusGungoren From $R^2$ to $R^4$ to not be injective means we need two points $(x,y)$ and $(x',y')$ to map to the same point $(a,b,c,d)$ in $R^4.$ But then the map itself already determines $x,y$ uniquely. So I can't figure what it means for the question of injective from $R^2$ to $R^4.$ Also I don't see a map from $R^2$ to $R^4$ in the first place. Could you spell out what you mean by injective/noninjective in your recent comment? 2d revised A Quadrilateral and A Triangle in a Trapizium added 1225 characters in body Feb 9 comment Continous family of $n$-gons @Blue I toyed with that idea, making the furthest vertex from a proposed center move in a little, etc, winding up at an intermediate stage where all vertices on a circle, then moving things until n-gon is regular. But I thought the details would be involved. (Anyway that way one could avoid angles of 180 degrees during the deformation, if initially there were none.) [+1 on comment, I'll look at that answer soon.] Feb 9 revised A Quadrilateral and A Triangle in a Trapizium added 221 characters in body Feb 9 answered A Quadrilateral and A Triangle in a Trapizium Feb 9 comment How did they calculate the possible endings? Please give game rules etc. in the posted question, not a link. Feb 9 answered Logical form of a set-theoretic statement. Feb 9 answered Continous family of $n$-gons Feb 9 comment Continous family of $n$-gons Is a 5-gon formed by inserting a vertex at the midpoint of a side of a square considered a convex 5-gon? Feb 9 comment Can the real part of an entire function be bounded above by a polynomial? Since you are referring to $u$ in $u+iv,$ maybe the title should refer to the real part of an entire function. Feb 9 comment Is the given function injective? I'm curious as to what motivates your mapping-- where does it "come from". Including that in a future question might improve it. I'll think about R2 to R4 injectivity when I get a chance. Feb 9 comment Finding $\sqrt{17}$ and $\sqrt{257}$ in the regular $17$-gon and $257$-gon? Why the initial $1+$ in formula (1)? Without it, it looks like usual distance formula, and gives $(1+\sqrt{5})/2.$ Feb 8 comment Finding $\sqrt{17}$ and $\sqrt{257}$ in the regular $17$-gon and $257$-gon? So to find $(a+b\sqrt{n})/c$ for some integers $a,b,c$ is enough? Feb 8 comment Line postulate in Geometry In the postulate the points are distinct. "Through two points...etc" would say nothing for points $P,P$ since then there are not two points. Also it's a postulate, so could not be proved, unless in a specific model like $\mathbb{R}^2.$ Feb 8 comment Prove by contradiction Irrational number Looks good,but better to set up as proof by contradiction, i.e. start by assuming $(2a-3)/(2a+3)$ rational, then go on as you did. Feb 8 revised Intersection of dense sets in $\mathbb{N}$ deleted 2 characters in body Feb 8 revised Intersection of dense sets in $\mathbb{N}$ added 260 characters in body Feb 7 answered Intersection of dense sets in $\mathbb{N}$ Feb 7 comment Does a neighborhood of a point include that point? Neighboorhod included the point. Feb 7 revised Prove that $\lim\limits_{x\to\infty} f'(x)=0$ added 2 characters in body