Solution for Section 3.5 Question 4

4. Suppose that n is an even integer. We need to show that n / 2 = n / 2.

Proof Since n is an even integer, n = 2k   for some integer k. 

Left-hand side:	n / 2 = 2k / 2 = k = k  (since the ceiling of an integer is equal to that integer).
Right-hand side:	n / 2 = 2k / 2 = k= k  (since the floor of an integer is equal to that integer).

Thus n / 2 = n / 2.

Back to Section 3.5