Page 248

		10-13 Use a technique similar to the one for Exercise 10-11 to show that, for all d1 and d2 with d1 + d2 < 1, . Also, verify that this result implies that, for all d < 1, .

		10-14 Show that, for all d1 > 0 and all d2 < 1, .

		Hint: Without loss of generality, assume that d1 = 2/m and d2 = (m - 2)/m for an integer . Let no n0 = 0, n2i+1 = mi+1 + n2i, and n2i+2 = n2i+1 + (i + 1) · m. Let and, for each j, . Then, use C, the class of functions , each of which satisfies:

		1. For all ,f(x) = 0.

		2. For all j and all , f(x) = f(j).

		10-15 Suppose d1, d2, and d3 are such that d2 < dl and d3 < 1. Show

		Hint: Without loss of generality, assume that d2 = l/m, d1 = (l + 2)/m, and d3 = (m - 2)/m for integers and . Let n0 = 0, n2i+1 = mi+1 + n2i, and n2i+2 = n2i+1 + (i + 1) · m. Let and, for each j, let . Then, use C, the class of functions each of which satisfies:

		1. For each , f(x) = 0

		2. For all j and all , f(x = f(j)..

		10-16 Use a technique similar to the one in the hint for Exercise 10-15 to show that, for all dl and d2 with d1 > d2, .

		10-17 Use a technique similar to the one in the hint for Exercise 10-15 to show that, for all d1, d2, and d3 with d2 > d1 and d1 + d3 < 1, .

		10-18 Give a proof of Proposition 10.36.

		Hint: Without loss of generality, assume that d2 = (k + 3)/m and d1 = k/m for integers k and m with . Let n0 = -1 and ni = mi. Let Sj denote the set . Let . Consider the class C of functions , each of which satisfies:

		1.

		2. For each j, .