Help me with my assignment which has a notation like this: ${P}_{1}=(x,y,z)\text{}\in \text{}{\mathbb{R}}^{3}:\text{}|x|\text{}\le 1,\text{}|y|\text{}\le 1,\text{}|z|\text{}\le 1$. At first I thought $|x|\text{}=\text{}\sqrt{{{x}_{1}}^{2}+{{x}_{2}}^{2}+{{x}_{3}}^{2}}$, which is the magnitude of 3D vector x. I read in many sources saying there's no absolute value for a vector, there's only $||x||\text{}=\text{}\sqrt{{{x}_{1}}^{2}+{{x}_{2}}^{2}+{{x}_{3}}^{2}}$. So I want to ask if what |x| actually is and how its formula looks like?