The squared norm of w is exact rational arithmetic. Turning that squared norm into a numeric width uses a square root, so the width is rendered as a named radical symbol rather than a decimal.

highlighted = computed this step

The exact squared norm

The squared norm is w·w=1/2. This value is exact rational arithmetic from w=(1/2,1/2), b=-1.

ww=1/2w\cdot w=1/2
Named margin widthThe table verifies exact margins and names the square-root width.SVM margin tablepointyw·x+by(w·x+b)support(2,2)+111yes(0,0)-1-11yes(3,3)+122no(-1,-1)-1-22now·w=1/2margin width=2/√(1/2)√ is named; no decimal margin is pinned

Why the width is named

The margin width is 2/√(1/2). The square-root step is the named boundary, so no decimal width is pinned.

width=2/1/2\text{width}=2/\sqrt{1/2}
Named margin widthThe table verifies exact margins and names the square-root width.SVM margin tablepointyw·x+by(w·x+b)support(2,2)+111yes(0,0)-1-11yes(3,3)+122no(-1,-1)-1-22now·w=1/2margin width=2/√(1/2)√ is named; no decimal margin is pinned

Summary

The geometry values are exact; the numeric width crosses the square-root boundary. The renderer keeps it as a symbol.

  is named here\sqrt{\ } \text{ is named here}
Named margin widthThe table verifies exact margins and names the square-root width.SVM margin tablepointyw·x+by(w·x+b)support(2,2)+111yes(0,0)-1-11yes(3,3)+122no(-1,-1)-1-22now·w=1/2margin width=2/√(1/2)√ is named; no decimal margin is pinned