I'm trying to write the solution to the following equation in set builder notation $$\max\{|x_1|,|x_2| \}=1$$ So far, I've come up with:
$$\big\{ (x_1,x_2) \in \mathbb{R}^2: \big(|x_1|=1, -1\le x_2 \le 1\big) \vee \big(|x_2|=1, -1\le x_1 \le 1\big)\big\}$$ Is this correct? I'd like to be able to write it properly, like the way it would ideally be written but this seem a little shaky to me.