=+. 1 Use the ideas of Problem 6.8 to give a new proof of Borel's normal number theorem, Theorem 1.2. The point is to return to first principles and use only negligibility and the other ideas of Section 1, not the apparatus of Sections 2 through 6; in particular, P( 4) is to be taken as defined only if A is a finite, disjoint union of intervals.