0

Let $A=\{(x,y):x=y\}$ and $B=\{(x,y):x^2+y^2=1\}$ (A,B are convex)

Why the sum of $A$ and $B$ is $C=\{(x,y):x-1\le y\le x+1\}?$

Seriously I can't find a relation between A,B and C.

Also geometrically, we are talking about the unit circle and the identity line, but I don't know why C must be a kind of a rectangle.

user441848
  • 1,658
  • Your $C$ doesn't look right. By "sum", do you mean: $$C = A + B \stackrel{def}{=} \Big{; (x_a + x_b, y_a + y_b ) \in \mathbb{R}^2 : (x_a,y_a) \in A, (x_b,y_b) \in B ;\Big}$$ If that is the case, then $C$ should be ${ (x,y) : |x-y| \le \sqrt{2} }$. – achille hui Oct 03 '17 at 20:42
  • Oh, if that is the sum, then what is my C set? @achillehui – user441848 Oct 03 '17 at 20:46
  • It will be a strip of width $2$ having the line $x = y$ as axis. – achille hui Oct 03 '17 at 20:48

0 Answers0