Q: Verify d(x,y) = |x-y| is a metric on ℝ. Is d(x,y) = (x-y)²? |x-y| ≥ 0 ✓; = 0 ⟺ x=y ✓; symmetric ✓. Triangle: |x-z| ≤ |x-y|+|y-z| ✓ METRIC! (x-y)²: triangle fails! x=0,y=1,z=2: 4 ≤ 1+1? NO ✗. (Square breaks triangle inequality!)