Proving Boundedness of Set S: |x| + |y| <= 2

[javi438]

Is the set S = {(x,y): |x| + |y| <= 2} bounded? If so how do i prove it?

looking at the graph i believe that S is bounded by 2 and -2, but I'm not sure if I'm correct and i don't know how to prove it.

thanks!

 

[morphism]

I'm assuming when you say bounded, you mean with respect to "Euclidean distance."

If so, here's a hint: |x|^2 + |y|^2 = (|x|+|y|)^2 - 2|x||y|.