EDB — 10X

[10X] Prerequisites:[(11.14)]↺↻.We equip \(ℝ^ n\) with the norm \(\| x \| _∞\): show that in dimension 2 the disk \(\{ x∈ℝ^ n , \| x\| _∞≤ 1\} \) is a square, and in dimension 3 it is a cube, etc etc.

Now we equip \(ℝ^ n\) with the norm \(\| x \| _ 1\): show that in dimension 2 the disk \(\{ x∈ℝ^ n , \| x\| _ 1≤ 1\} \) is a rhombus i.e. precisely a square rotated 45 degrees; and in dimension 3 the disk is an octahedron.