Is the set $A = \{(x,y,z) \in \mathbb{R}^3 \mid x+z = 0\}$ bounded? According to my source it should be, but can't $x$ and $z$ take on every value therefore the set is not bounded?
Edit: For the solution of the source I was looking at to work out, only the intersection of $A$ and $B = \{(x,y,z) \in \mathbb{R}^3 \mid x^2+y^2 = 1\}$ had to be bounded, which is the case, since the intersection must satisfy both equations and therefore all $|x|,|y|,|z|$ are smaller or equal to 1.
Clearly $S=\{(0,n,0): n\in \mathbb{N}\}$ is subset of $A$ and $S$ is not bounded. Hence given set $A$ is Not bounded.