Solution for Section 3.5 Question 5

5. Suppose that n is an odd integer. We need to show that n / 2 = n / 2+ 1.

Proof Since n is an odd integer, n = 2k + 1   for some integer k. 

Left-hand side:	n / 2 = (2k + 1) / 2 = k + 1/2 = k + 1 (by the definition of ceiling, see illustration below).
Right-hand side:	n / 2 + 1 = (2k + 1) / 2 + 1 = k + 1/2+ 1 = k + 1  (by the definition of floor, see illustration below).

Thus n / 2 = n / 2+ 1.

Back to Section 3.5